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第243行： − For problems with all these properties, the running time of [[Grover's algorithm]] on a quantum computer will scale as the square root of the number of inputs (or elements in the database), as opposed to the linear scaling of classical algorithms. A general class of problems to which [[Grover's algorithm]] can be applied is [[Boolean satisfiability problem]]. In this instance, the ''database'' through which the algorithm is iterating is that of all possible answers. An example (and possible) application of this is a [[Password cracking|password cracker]] that attempts to guess the password or secret key for an [[encryption|encrypted]] file or system. [[Symmetric-key algorithm|Symmetric ciphers]] such as [[Triple DES]] and [[Advanced Encryption Standard|AES]] are particularly vulnerable to this kind of attack.{{citation needed|date=November 2019}} This application of quantum computing is a major interest of government agencies.<ref>{{cite news |url=https://www.washingtonpost.com/world/national-security/nsa-seeks-to-build-quantum-computer-that-could-crack-most-types-of-encryption/2014/01/02/8fff297e-7195-11e3-8def-a33011492df2_story.html |title=NSA seeks to build quantum computer that could crack most types of encryption |first1=Steven |last1=Rich |first2=Barton |last2=Gellman |date=2014-02-01 |newspaper=Washington Post}}</ref>+ − 对于具有所有这些性质的问题，[[Grover算法]]在量子计算机上的运行时间将按输入（或数据库中元素）数量的平方根进行缩放，而不是经典算法的线性缩放。一类可以应用[[Grover算法]]的一般问题是<ref>{{cite journal |last1=Ambainis |first1=Ambainis |title=Quantum search algorithms |journal=ACM SIGACT News |date=June 2004 |volume=35 |issue=2 |pages=22–35 |doi=10.1145/992287.992296 |arxiv=quant-ph/0504012 |bibcode=2005quant.ph..4012A |s2cid=11326499 }}</ref>[[布尔可满足性问题]]。在本例中，算法迭代使用的“数据库”是所有可能答案的数据库。这方面的一个例子（也是可能的）应用是一个[[密码破解|密码破解器]]试图猜测[[加密|加密]]文件或系统的密码或密钥。[[对称密钥算法|对称密码]]例如[[Triple DES]]和[[Advanced Encryption Standard | AES]]特别容易受到此类攻击。{{引文需要{日期=2019年11月}}量子计算的这一应用是政府机构主要感兴趣的。 − − − Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to simulate in an efficient manner classically, many believe quantum simulation will be one of the most important applications of quantum computing. Quantum simulation could also be used to simulate the behavior of atoms and particles at unusual conditions such as the reactions inside a collider. 第256行：
第252行： − Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to simulate in an efficient manner classically, many believe [[Quantum simulator|quantum simulation]] will be one of the most important applications of quantum computing. − − Quantum annealing or Adiabatic quantum computation relies on the adiabatic theorem to undertake calculations. A system is placed in the ground state for a simple Hamiltonian, which is slowly evolved to a more complicated Hamiltonian whose ground state represents the solution to the problem in question. The adiabatic theorem states that if the evolution is slow enough the system will stay in its ground state at all times through the process. 第267行：
第260行： − [[Quantum annealing]] or [[Adiabatic quantum computation]] relies on the adiabatic theorem to undertake calculations. A system is placed in the ground state for a simple Hamiltonian, which is slowly evolved to a more complicated Hamiltonian whose ground state represents the solution to the problem in question. The adiabatic theorem states that if the evolution is slow enough the system will stay in its ground state at all times through the process. − − The Quantum algorithm for linear systems of equations, or "HHL Algorithm", named after its discoverers Harrow, Hassidim, and Lloyd, is expected to provide speedup over classical counterparts. 第277行：
第267行： − The [[Quantum algorithm for linear systems of equations]], or "HHL Algorithm", named after its discoverers Harrow, Hassidim, and Lloyd, is expected to provide speedup over classical counterparts.<ref name="Quantum algorithm for solving linear systems of equations by Harrow et al.">{{Cite journal |arxiv = 0811.3171|last1 = Harrow|first1 = Aram|last2 = Hassidim|first2 = Avinatan|last3 = Lloyd|first3 = Seth|title = Quantum algorithm for solving linear systems of equations|journal = Physical Review Letters|volume = 103|issue = 15|pages = 150502|year = 2009|doi = 10.1103/PhysRevLett.103.150502|pmid = 19905613|bibcode = 2009PhRvL.103o0502H|s2cid = 5187993}}</ref>+ − 以其发现者哈罗、哈西迪姆和劳埃德命名的[[用于线性方程组的量子算法]]或“HHL算法”，有望提供比经典算法更快的速度。 − − John Preskill has introduced the term quantum supremacy to refer to the hypothetical speedup advantage that a quantum computer would have over a classical computer in a certain field. Google announced in 2017 that it expected to achieve quantum supremacy by the end of the year though that did not happen. IBM said in 2018 that the best classical computers will be beaten on some practical task within about five years and views the quantum supremacy test only as a potential future benchmark. Although skeptics like Gil Kalai doubt that quantum supremacy will ever be achieved, in October 2019, a Sycamore processor created in conjunction with Google AI Quantum was reported to have achieved quantum supremacy, with calculations more than 3,000,000 times as fast as those of Summit, generally considered the world's fastest computer. Bill Unruh doubted the practicality of quantum computers in a paper published back in 1994. Paul Davies argued that a 400-qubit computer would even come into conflict with the cosmological information bound implied by the holographic principle. 第289行：
第276行： − [[John Preskill]] has introduced the term ''[[quantum supremacy]]'' to refer to the hypothetical speedup advantage that a quantum computer would have over a classical computer in a certain field. [[Google]] announced in 2017 that it expected to achieve quantum supremacy by the end of the year though that did not happen. [[IBM]] said in 2018 that the best classical computers will be beaten on some practical task within about five years and views the quantum supremacy test only as a potential future benchmark. Although skeptics like [[Gil Kalai]] doubt that quantum supremacy will ever be achieved, in October 2019, a [[Sycamore processor]] created in conjunction with Google AI Quantum was reported to have achieved quantum supremacy, with calculations more than 3,000,000 times as fast as those of [[Summit (supercomputer)|Summit]], generally considered the world's fastest computer. [[Bill Unruh]] doubted the practicality of quantum computers in a paper published back in 1994. [[Paul Davies]] argued that a 400-qubit computer would even come into conflict with the cosmological information bound implied by the [[holographic principle]]. − − There are a number of technical challenges in building a large-scale quantum computer. Physicist David DiVincenzo has listed the following requirements for a practical quantum computer: 第299行：
第283行： − There are a number of technical challenges in building a large-scale quantum computer. Physicist [[David P. DiVincenzo|David DiVincenzo]] has listed the following [[DiVincenzo's criteria|requirements]] for a practical quantum computer:+ − 建造大型量子计算机面临许多技术挑战。<ref>{{cite journal |last=Dyakonov |first=Mikhail |url=https://spectrum.ieee.org/computing/hardware/the-case-against-quantum-computing |title=The Case Against Quantum Computing |journal=[[IEEE Spectrum]] |date=2018-11-15}}</ref>物理学家[[David P.DiVincenzo | David DiVincenzo]]为一台实用的量子计算机列出了以下[[DiVincenzo的标准|要求]] ：<ref>{{cite journal| arxiv=quant-ph/0002077|title=The Physical Implementation of Quantum Computation|last=DiVincenzo |first=David P.|date=2000-04-13|doi=10.1002/1521-3978(200009)48:9/11<771::AID-PROP771>3.0.CO;2-E|volume=48|issue=9–11|journal=Fortschritte der Physik|pages=771–783|bibcode=2000ForPh..48..771D}}</ref> − * Scalable physically to increase the number of qubits − * Qubits that can be initialized to arbitrary values − * Quantum gates that are faster than [[decoherence]] time − * Universal gate set − Sourcing parts for quantum computers is also very difficult. Many quantum computers, like those constructed by Google and IBM, need Helium-3, a nuclear research byproduct, and special superconducting cables that are only made by the Japanese company Coax Co. 第318行：
第296行： − − − The control of multi qubit systems requires the generation and coordination of a large number of electrical signals with tight and deterministic timing resolution. This had led to the development of quantum controllers which enable interfacing the qubit. Scaling these systems to support a growing number of qubits is an additional challenge in the scaling of quantum computers. − Sourcing parts for quantum computers is also very difficult. Many quantum computers, like those constructed by [[Google]] and [[IBM]], need [[Helium-3]], a [[Nuclear physics|nuclear]] research byproduct, and special [[superconducting]] cables that are only made by the Japanese company Coax Co.<ref>{{cite news |last1=Giles |first1=Martin |title=We'd have more quantum computers if it weren't so hard to find the damn cables |url=https://www.technologyreview.com/s/612760/quantum-computers-component-shortage/ |publisher=MIT Technology Review |date=17 January 2019}}</ref> − + − − The control of multi qubit systems requires the generation and coordination of a large number of electrical signals with tight and deterministic timing resolution. This had led to the development of [[quantum controllers]] which enable interfacing the qubit. Scaling these systems to support a growing number of qubits is an additional challenge in the scaling of quantum computers.{{Citation needed|date=August 2020}} 第335行：
第307行： − One of the greatest challenges involved with constructing quantum computers is controlling or removing quantum decoherence. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates, and the lattice vibrations and background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time T<sub>2</sub> (for NMR and MRI technology, also called the dephasing time), typically range between nanoseconds and seconds at low temperature. Currently, some quantum computers require their qubits to be cooled to 20 millikelvins in order to prevent significant decoherence. A 2020 study argues that ionizing radiation such as cosmic rays can nevertheless cause certain systems to decohere within millisections. 第341行：
第312行： − − As a result, time-consuming tasks may render some quantum algorithms inoperable, as maintaining the state of qubits for a long enough duration will eventually corrupt the superpositions. − − One of the greatest challenges involved with constructing quantum computers is controlling or removing [[quantum decoherence]]. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates, and the lattice vibrations and background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time ''T''<sub>2</sub> (for [[Nuclear magnetic resonance|NMR]] and [[MRI]] technology, also called the ''dephasing time''), typically range between nanoseconds and seconds at low temperature.<ref name="DiVincenzo 1995">{{cite journal |last=DiVincenzo |first=David P. |title=Quantum Computation |journal=Science |year=1995 |volume=270 |issue=5234 |pages=255–261 |doi= 10.1126/science.270.5234.255 |bibcode = 1995Sci...270..255D |citeseerx=10.1.1.242.2165 |s2cid=220110562 }} {{subscription required}}</ref> Currently, some quantum computers require their qubits to be cooled to 20 millikelvins in order to prevent significant decoherence.<ref>{{cite journal|last1=Jones|first1=Nicola|title=Computing: The quantum company|journal=Nature|date=19 June 2013|volume=498|issue=7454|pages=286–288|doi=10.1038/498286a|pmid=23783610|bibcode=2013Natur.498..286J|doi-access=free}}</ref> A 2020 study argues that [[ionizing radiation]] such as [[cosmic rays]] can nevertheless cause certain systems to decohere within millisections.<ref>{{cite journal |last1=Vepsäläinen |first1=Antti P. |last2=Karamlou |first2=Amir H. |last3=Orrell |first3=John L. |last4=Dogra |first4=Akshunna S. |last5=Loer |first5=Ben |last6=Vasconcelos |first6=Francisca |last7=Kim |first7=David K. |last8=Melville |first8=Alexander J. |last9=Niedzielski |first9=Bethany M. |last10=Yoder |first10=Jonilyn L. |last11=Gustavsson |first11=Simon |last12=Formaggio |first12=Joseph A. |last13=VanDevender |first13=Brent A. |last14=Oliver |first14=William D. |display-authors=5 |title=Impact of ionizing radiation on superconducting qubit coherence |journal=Nature |date=August 2020 |volume=584 |issue=7822 |pages=551–556 |doi=10.1038/s41586-020-2619-8 |pmid=32848227 |url=https://www.nature.com/articles/s41586-020-2619-8 |language=en |issn=1476-4687|arxiv=2001.09190 |s2cid=210920566 }}</ref> − These issues are more difficult for optical approaches as the timescales are orders of magnitude shorter and an often-cited approach to overcoming them is optical pulse shaping. Error rates are typically proportional to the ratio of operating time to decoherence time, hence any operation must be completed much more quickly than the decoherence time. 第358行：
第324行： − As described in the Quantum threshold theorem, if the error rate is small enough, it is thought to be possible to use quantum error correction to suppress errors and decoherence. This allows the total calculation time to be longer than the decoherence time if the error correction scheme can correct errors faster than decoherence introduces them. An often cited figure for the required error rate in each gate for fault-tolerant computation is 10<sup>−3</sup>, assuming the noise is depolarizing. − These issues are more difficult for optical approaches as the timescales are orders of magnitude shorter and an often-cited approach to overcoming them is optical [[pulse shaping]]. Error rates are typically proportional to the ratio of operating time to decoherence time, hence any operation must be completed much more quickly than the decoherence time. − Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between L and L<sup>2</sup>, where L is the number of qubits in the number to be factored; error correction algorithms would inflate this figure by an additional factor of L. For a 1000-bit number, this implies a need for about 10<sup>4</sup> bits without error correction. With error correction, the figure would rise to about 10<sup>7</sup> bits. Computation time is about L<sup>2</sup> or about 10<sup>7</sup> steps and at 1 MHz, about 10 seconds. − − As described in the [[Quantum threshold theorem]], if the error rate is small enough, it is thought to be possible to use quantum error correction to suppress errors and decoherence. This allows the total calculation time to be longer than the decoherence time if the error correction scheme can correct errors faster than decoherence introduces them. An often cited figure for the required error rate in each gate for fault-tolerant computation is 10<sup>−3</sup>, assuming the noise is depolarizing. − − A very different approach to the stability-decoherence problem is to create a topological quantum computer with anyons, quasi-particles used as threads and relying on braid theory to form stable logic gates. − − Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between ''L'' and ''L''<sup>2</sup>, where ''L'' is the number of qubits in the number to be factored; error correction algorithms would inflate this figure by an additional factor of ''L''. For a 1000-bit number, this implies a need for about 10<sup>4</sup> bits without error correction. With error correction, the figure would rise to about 10<sup>7</sup> bits. Computation time is about ''L''<sup>2</sup> or about 10<sup>7</sup> steps and at 1 MHz, about 10 seconds. − − Physicist Mikhail Dyakonov has expressed skepticism of quantum computing as follows: − − A very different approach to the stability-decoherence problem is to create a [[topological quantum computer]] with [[anyon]]s, [[quasi-particle]]s used as threads and relying on [[braid theory]] to form stable logic gates. − "So the number of continuous parameters describing the state of such a useful quantum computer at any given moment must be... about 10<sup>300</sup>... Could we ever learn to control the more than 10<sup>300</sup> continuously variable parameters defining the quantum state of such a system? My answer is simple. No, never." 第404行：
第356行： − There are a number of quantum computing models, distinguished by the basic elements in which the computation is decomposed. The four main models of practical importance are: 第417行：
第368行： − − The quantum Turing machine is theoretically important but the physical implementation of this model is not feasible. All four models of computation have been shown to be equivalent; each can simulate the other with no more than polynomial overhead. 第444行：
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第401行： − * [[quantum circuit|Quantum gate array]] (computation decomposed into a sequence of few-qubit [[quantum gate]]s) − * [[One-way quantum computer]] (computation decomposed into a sequence of one-qubit measurements applied to a highly entangled initial state or [[cluster state]])+ − * [[Adiabatic quantum computation|Adiabatic quantum computer]], based on [[quantum annealing]] (computation decomposed into a slow continuous transformation of an initial [[Hamiltonian (quantum mechanics)|Hamiltonian]] into a final Hamiltonian, whose ground states contain the solution) − * [[Topological quantum computer]] 第505行：
第451行： − Conversely, any problem solvable by a quantum computer is also solvable by a classical computer; or more formally, any quantum computer can be simulated by a Turing machine<!-- add mention about Quantum Virtual Machines which can simulate quantum computer on classical one -->. In other words, quantum computers provide no additional power over classical computers in terms of computability. This means that quantum computers cannot solve undecidable problems like the halting problem and the existence of quantum computers does not disprove the Church–Turing thesis. 第512行：
第457行： − − As of yet, quantum computers do not satisfy the strong Church thesis. While hypothetical machines have been realized, a universal quantum computer has yet to be physically constructed. The strong version of Church's thesis requires a physical computer, and therefore there is no quantum computer that yet satisfies the strong Church thesis. 第519行：
第462行： − For physically implementing a quantum computer, many different candidates are being pursued, among them (distinguished by the physical system used to realize the qubits): 第525行：
第467行： − <!-- Power and limits of quantum computers --> − *[[Trapped ion quantum computer]] (qubit implemented by the internal state of trapped ions) − While quantum computers cannot solve any problems that classical computers cannot already solve, it is suspected that they can solve many problems faster than classical computers. For instance, it is known that quantum computers can efficiently factor integers, while this is not believed to be the case for classical computers. However, the capacity of quantum computers to accelerate classical algorithms has rigid upper bounds, and the overwhelming majority of classical calculations cannot be accelerated by the use of quantum computers. − − *Neutral atoms in [[Optical lattice]]s (qubit implemented by internal states of neutral atoms trapped in an optical lattice)<ref>{{Cite journal|last1=Khazali|first1=Mohammadsadegh|last2=Mølmer|first2=Klaus|date=2020-06-11|title=Fast Multiqubit Gates by Adiabatic Evolution in Interacting Excited-State Manifolds of Rydberg Atoms and Superconducting Circuits|journal=Physical Review X|volume=10|issue=2|pages=021054|doi=10.1103/PhysRevX.10.021054|bibcode=2020PhRvX..10b1054K|doi-access=free}}</ref><ref>{{Cite journal|last1=Henriet|first1=Loic|last2=Beguin|first2=Lucas|last3=Signoles|first3=Adrien|last4=Lahaye|first4=Thierry|last5=Browaeys|first5=Antoine|last6=Reymond|first6=Georges-Olivier|last7=Jurczak|first7=Christophe|date=2020-06-22|title=Quantum computing with neutral atoms|journal=Quantum|volume=4|page=327|doi=10.22331/q-2020-09-21-327|arxiv=2006.12326|s2cid=219966169}}</ref> − − *[[Quantum dot]] computer, spin-based (e.g. the [[Loss-DiVincenzo quantum computer]]<ref>{{cite journal |last1=Imamog¯lu |first1=A. |last2=Awschalom |first2=D. D. |last3=Burkard |first3=G. |last4=DiVincenzo |first4=D. P. |last5=Loss |first5=D. |last6=Sherwin |first6=M. |last7=Small |first7=A. |title=Quantum Information Processing Using Quantum Dot Spins and Cavity QED |journal=Physical Review Letters |date=15 November 1999 |volume=83 |issue=20 |pages=4204–4207 |doi=10.1103/PhysRevLett.83.4204 |bibcode=1999PhRvL..83.4204I |arxiv=quant-ph/9904096 |s2cid=18324734 }}</ref>) (qubit given by the spin states of trapped electrons) − <!-- Basic definition of BQP --> − *Quantum dot computer, spatial-based (qubit given by electron position in double quantum dot)<ref>{{cite journal |last1=Fedichkin |first1=L. |last2=Yanchenko |first2=M. |last3=Valiev |first3=K. A. |title=Novel coherent quantum bit using spatial quantization levels in semiconductor quantum dot |journal=Quantum Computers and Computing |date=June 2000 |volume=1 |page=58 |bibcode=2000quant.ph..6097F |arxiv=quant-ph/0006097 }}</ref> − The class of problems that can be efficiently solved by a quantum computer with bounded error is called BQP, for "bounded error, quantum, polynomial time". More formally, BQP is the class of problems that can be solved by a polynomial-time quantum Turing machine with error probability of at most 1/3. As a class of probabilistic problems, BQP is the quantum counterpart to BPP ("bounded error, probabilistic, polynomial time"), the class of problems that can be solved by polynomial-time probabilistic Turing machines with bounded error. It is known that BPP<math>\subseteq</math>BQP and is widely suspected that BQP<math>\nsubseteq</math>BPP, which intuitively would mean that quantum computers are more powerful than classical computers in terms of time complexity. − − * Quantum computing using engineered quantum wells, which could in principle enable the construction of quantum computers that operate at room temperature<ref>{{cite journal |last1=Ivády |first1=Viktor |last2=Davidsson |first2=Joel |last3=Delegan |first3=Nazar |last4=Falk |first4=Abram L. |last5=Klimov |first5=Paul V. |last6=Whiteley |first6=Samuel J. |last7=Hruszkewycz |first7=Stephan O. |last8=Holt |first8=Martin V. |last9=Heremans |first9=F. Joseph |last10=Son |first10=Nguyen Tien |last11=Awschalom |first11=David D. |last12=Abrikosov |first12=Igor A. |last13=Gali |first13=Adam |title=Stabilization of point-defect spin qubits by quantum wells |journal=Nature Communications |date=6 December 2019 |volume=10 |issue=1 |page=5607 |doi=10.1038/s41467-019-13495-6 |pmid=31811137 |pmc=6898666 |arxiv=1905.11801 |bibcode=2019NatCo..10.5607I }}</ref><ref>{{cite news |title=Scientists Discover New Way to Get Quantum Computing to Work at Room Temperature |url=https://interestingengineering.com/scientists-discover-new-way-to-get-quantum-computing-to-work-at-room-temperature |work=interestingengineering.com |date=24 April 2020 }}</ref> − *Coupled [[Quantum wire|Quantum Wire]] (qubit implemented by a pair of Quantum Wires coupled by a [[Quantum point contact|Quantum Point Contact]])<ref>{{cite journal |last1=Bertoni |first1=A. |last2=Bordone |first2=P. |last3=Brunetti |first3=R. |last4=Jacoboni |first4=C. |last5=Reggiani |first5=S. |title=Quantum Logic Gates based on Coherent Electron Transport in Quantum Wires |journal=Physical Review Letters |date=19 June 2000 |volume=84 |issue=25 |pages=5912–5915 |doi=10.1103/PhysRevLett.84.5912 |pmid=10991086 |bibcode=2000PhRvL..84.5912B |hdl=11380/303796|hdl-access=free }}</ref><ref>{{cite journal |last1=Ionicioiu |first1=Radu |last2=Amaratunga |first2=Gehan |last3=Udrea |first3=Florin |title=Quantum Computation with Ballistic Electrons |journal=International Journal of Modern Physics B |date=20 January 2001 |volume=15 |issue=2 |pages=125–133 |doi=10.1142/S0217979201003521 |arxiv=quant-ph/0011051 |bibcode=2001IJMPB..15..125I |citeseerx=10.1.1.251.9617 |s2cid=119389613 }}</ref><ref>{{cite journal |last1=Ramamoorthy |first1=A |last2=Bird |first2=J P |last3=Reno |first3=J L |title=Using split-gate structures to explore the implementation of a coupled-electron-waveguide qubit scheme |journal=Journal of Physics: Condensed Matter |date=11 July 2007 |volume=19 |issue=27 |pages=276205 |doi=10.1088/0953-8984/19/27/276205 |bibcode=2007JPCM...19A6205R }}</ref> − <!-- Relation of BQP to basic complexity classes --> − *[[Nuclear magnetic resonance quantum computer]] (NMRQC) implemented with the [[nuclear magnetic resonance]] of molecules in solution, where qubits are provided by [[nuclear spin]]s within the dissolved molecule and probed with radio waves − The suspected relationship of BQP to several classical complexity classes. − *Solid-state NMR [[Kane quantum computer]]s (qubit realized by the nuclear spin state of [[phosphorus]] [[Electron donor|donors]] in [[silicon]]) − The exact relationship of BQP to P, NP, and PSPACE is not known. However, it is known that P<math>\subseteq</math>BQP<math>\subseteq</math>PSPACE; that is, all problems that can be efficiently solved by a deterministic classical computer can also be efficiently solved by a quantum computer, and all problems that can be efficiently solved by a quantum computer can also be solved by a deterministic classical computer with polynomial space resources. It is further suspected that BQP is a strict superset of P, meaning there are problems that are efficiently solvable by quantum computers that are not efficiently solvable by deterministic classical computers. For instance, integer factorization and the discrete logarithm problem are known to be in BQP and are suspected to be outside of P. On the relationship of BQP to NP, little is known beyond the fact that some NP problems that are believed not to be in P are also in BQP (integer factorization and the discrete logarithm problem are both in NP, for example). It is suspected that NP<math>\nsubseteq</math>BQP; that is, it is believed that there are efficiently checkable problems that are not efficiently solvable by a quantum computer. As a direct consequence of this belief, it is also suspected that BQP is disjoint from the class of NP-complete problems (if an NP-complete problem were in BQP, then it would follow from NP-hardness that all problems in NP are in BQP). − + − − *Electrons-on-[[helium]] quantum computers (qubit is the electron spin) − *[[Cavity quantum electrodynamics]] (CQED) (qubit provided by the internal state of trapped atoms coupled to high-finesse cavities) − <!-- Summary of relationship to essential complexity classes --> − *[[Single-molecule magnet|Molecular magnet]]<ref>{{cite journal |last1=Leuenberger |first1=Michael N. |last2=Loss |first2=Daniel |title=Quantum computing in molecular magnets |journal=Nature |date=April 2001 |volume=410 |issue=6830 |pages=789–793 |doi=10.1038/35071024 |pmid=11298441 |arxiv=cond-mat/0011415 |bibcode=2001Natur.410..789L |s2cid=4373008 }}</ref> (qubit given by spin states) − The relationship of BQP to the basic classical complexity classes can be summarized as follows: − *[[Fullerene]]-based [[Electron paramagnetic resonance|ESR]] quantum computer (qubit based on the electronic spin of [[Endohedral fullerene|atoms or molecules encased in fullerenes]])<ref>{{cite journal |last1=Harneit |first1=Wolfgang |title=Fullerene-based electron-spin quantum computer |journal= Physical Review A|date=27 February 2002 |volume=65 |issue=3 |page=032322 |doi=10.1103/PhysRevA.65.032322 |bibcode=2002PhRvA..65c2322H }}https://www.researchgate.net/publication/257976907_Fullerene-based_electron-spin_quantum_computer</ref> 第608行：
第525行： − *[[Optical quantum computing|Nonlinear optical quantum computer]] (qubits realized by processing states of different [[Normal mode|modes]] of light through both linear and [[Nonlinear optics|nonlinear]] elements)<ref name="qc1988">K. Igeta and Y. Yamamoto. "Quantum mechanical computers with single atom and photon fields." International Quantum Electronics Conference (1988) https://www.osapublishing.org/abstract.cfm?uri=IQEC-1988-TuI4</ref><ref name="chuang1995">I.L. Chuang and Y. Yamamoto. "Simple quantum computer." Physical Review A 52, 5, 3489 (1995) https://doi.org/10.1103/PhysRevA.52.3489</ref> − It is also known that BQP is contained in the complexity class #P (or more precisely in the associated class of decision problems P<sup>#P</sup>), Theories of quantum gravity, such as M-theory and loop quantum gravity, may allow even faster computers to be built. However, defining computation in these theories is an open problem due to the problem of time; that is, within these physical theories there is currently no obvious way to describe what it means for an observer to submit input to a computer at one point in time and then receive output at a later point in time. − *[[Linear optical quantum computing|Linear optical quantum computer]] (qubits realized by processing states of different [[Normal mode|modes]] of light through linear elements e.g. mirrors, [[beam splitter]]s and [[phase shift module|phase shifters]])<ref name="KLM2001">{{cite journal |last1=Knill |first1=G. J. |last2=Laflamme |last3=Milburn |title=A scheme for efficient quantum computation with linear optics |journal=Nature |year=2001 |volume=409 |doi=10.1038/35051009 |bibcode = 2001Natur.409...46K |first2=R. |first3=G. J. |issue=6816 |pmid=11343107 |pages=46–52 |s2cid=4362012 |url=https://www.semanticscholar.org/paper/054b680165a7325569ca6e63028ca9cee7f3ac9a }}</ref> 第622行：
第536行： − − <!-- New links in alphabetical order please --> 第709行：
第621行： − *[[Bose–Einstein condensate|Bose-Einstein condensate]]-based quantum computer<ref>{{cite journal |last1=Anderlini |first1=Marco |last2=Lee |first2=Patricia J. |last3=Brown |first3=Benjamin L. |last4=Sebby-Strabley |first4=Jennifer |last5=Phillips |first5=William D. |last6=Porto |first6=J. V. |title=Controlled exchange interaction between pairs of neutral atoms in an optical lattice |journal=Nature |date=July 2007 |volume=448 |issue=7152 |pages=452–456 |doi=10.1038/nature06011 |pmid=17653187 |lay-url=https://www.nist.gov/news-events/news/2007/07/thousands-atoms-swap-spins-partners-quantum-square-dance |arxiv=0708.2073 |bibcode=2007Natur.448..452A |s2cid=4410355 }}</ref>+ − *Transistor-based quantum computer – string quantum computers with entrainment of positive holes using an electrostatic trap − *Rare-earth-metal-ion-doped inorganic crystal based quantum computers<ref name="Ohlsson2002">{{cite journal 第780行：
第690行： − *Metallic-like carbon nanospheres based quantum computers<ref name="Nafradi2016">{{cite journal |last1=Náfrádi |first1=Bálint |last2=Choucair |first2=Mohammad |last3=Dinse |first3=Klaus-Peter |last4=Forró |first4=László |title=Room temperature manipulation of long lifetime spins in metallic-like carbon nanospheres |journal=Nature Communications |date=18 July 2016 |volume=7 |issue=1 |page=12232 |doi=10.1038/ncomms12232 |pmid=27426851 |pmc=4960311 |arxiv=1611.07690 |bibcode=2016NatCo...712232N }}</ref> − A large number of candidates demonstrates that quantum computing, despite rapid progress, is still in its infancy.{{citation needed|date=May 2020}} − + − + − Any [[computational problem]] solvable by a classical computer is also solvable by a quantum computer.<ref>Nielsen, p. 29</ref> Intuitively, this is because it is believed that all physical phenomena, including the operation of classical computers, can be described using [[quantum mechanics]], which underlies the operation of quantum computers. − − Category:Models of computation − − − − Category:Quantum cryptography − − − Conversely, any problem solvable by a quantum computer is also solvable by a classical computer; or more formally, any quantum computer can be simulated by a [[Turing machine]]<!-- add mention about [[Quantum Virtual Machines]] which can simulate quantum computer on classical one -->. In other words, quantum computers provide no additional power over classical computers in terms of [[computability]]. This means that quantum computers cannot solve [[undecidable problem]]s like the [[halting problem]] and the existence of quantum computers does not disprove the [[Church–Turing thesis]].<ref>Nielsen, p. 126</ref> − Category:Information theory − − − − Category:Computational complexity theory − − − As of yet, quantum computers do not satisfy the [[Church–Turing thesis|strong Church thesis]]. While hypothetical machines have been realized, a universal quantum computer has yet to be physically constructed. The strong version of Church's thesis requires a physical computer, and therefore there is no quantum computer that yet satisfies the strong Church thesis. − − Category:Classes of computers − − 类别: 电脑类别 − − − − Category:Theoretical computer science
无编辑摘要
< ! -- 历史 -- >
< ! -- 历史 -- >
'''量子计算'''始于20世纪80年代早期，当时物理学家'''保罗 · 贝尼奥夫Paul Benioff'''提出了'''图灵机Turing machine'''的量子力学模型。'''<ref name="The computer as a physical system">{{cite journal|last1=Benioff|first1=Paul|year=1980|title=The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines|journal=Journal of Statistical Physics|volume=22|issue=5|pages=563–591|bibcode=1980JSP....22..563B|doi=10.1007/bf01011339|s2cid=122949592}}</ref><font color="#ff8000">理查德 · 费曼Richard Feynman和尤里 · 曼宁Yuri Manin'''后来提出，量子计算机有潜力去模拟传统计算机所无法模拟的东西。<ref>{{cite journal |last1=Feynman |first1=Richard |title=Simulating Physics with Computers |journal=International Journal of Theoretical Physics |date=June 1982 |volume=21 |issue=6/7 |pages=467–488 |doi=10.1007/BF02650179 |url=https://people.eecs.berkeley.edu/~christos/classics/Feynman.pdf |accessdate=28 February 2019 |bibcode=1982IJTP...21..467F |s2cid=124545445 |archive-url=https://web.archive.org/web/20190108115138/https://people.eecs.berkeley.edu/~christos/classics/Feynman.pdf |archive-date=8 January 2019 |url-status=dead }}</ref><ref name="manin1980vychislimoe">{{cite book| author=Manin, Yu. I.| title=Vychislimoe i nevychislimoe| trans-title=Computable and Noncomputable| year=1980| publisher=Sov.Radio| url=http://publ.lib.ru/ARCHIVES/M/MANIN_Yuriy_Ivanovich/Manin_Yu.I._Vychislimoe_i_nevychislimoe.(1980).%5bdjv-fax%5d.zip| pages=13–15| language=Russian| accessdate=2013-03-04| url-status=dead| archiveurl=https://web.archive.org/web/20130510173823/http://publ.lib.ru/ARCHIVES/M/MANIN_Yuriy_Ivanovich/Manin_Yu.I._Vychislimoe_i_nevychislimoe.(1980).%5Bdjv%5D.zip| archivedate=2013-05-10}}</ref>1994年，Peter Shor 开发了一种量子算法，用于分解整数，这种算法有可能解密 rsa 加密的通信。<ref>{{cite document|last1=Mermin|first1=David|date=March 28, 2006|title=Breaking RSA Encryption with a Quantum Computer: Shor's Factoring Algorithm|url=http://people.ccmr.cornell.edu/~mermin/qcomp/chap3.pdf|work=Physics 481-681 Lecture Notes |publisher=Cornell University|archive-url=https://web.archive.org/web/20121115112940/http://people.ccmr.cornell.edu/~mermin/qcomp/chap3.pdf|archive-date=2012-11-15}}</ref>尽管自20世纪90年代后期以来，实验取得了进展，但大多数研究人员认为，“容错量子计算机仍然是一个相当遥远的梦想。”<ref name="preskill2018">{{cite journal|author=John Preskill|date=2018|title=Quantum Computing in the NISQ era and beyond|journal=Quantum|volume=2|pages=79|arxiv=1801.00862|doi=10.22331/q-2018-08-06-79|s2cid=44098998}}</ref>近年来，量子计算研究的投资在公共和私营部门都有所增加。<ref>{{cite journal |last1=Gibney |first1=Elizabeth |title=Quantum gold rush: the private funding pouring into quantum start-ups |journal=Nature |date=2 October 2019 |volume=574 |issue=7776 |pages=22–24 |doi=10.1038/d41586-019-02935-4 |pmid=31578480 |bibcode=2019Natur.574...22G |doi-access=free }}</ref><ref>{{Cite news|last=Rodrigo|first=Chris Mills|url=https://thehill.com/policy/technology/482402-trump-budget-proposal-boosts-funding-for-artificial-intelligence-quantum|title=Trump budget proposal boosts funding for artificial intelligence, quantum computing|date=12 February 2020|work=The Hill|access-date=|url-status=live}}</ref>2019年10月23日，谷歌AI与'''美国宇航局U.S. National Aeronautics and Space Administration (NASA)'''合作，声称已经完成了在任何传统计算机上都不可能完成的'''量子计算'''。<ref>{{Cite web|url=https://www.ibm.com/blogs/research/2019/10/on-quantum-supremacy/|title=On "Quantum Supremacy"|date=2019-10-22|website=IBM Research Blog|language=en-US|access-date=2020-01-21}}</ref>
'''量子计算'''始于20世纪80年代早期，当时物理学家'''保罗 · 贝尼奥夫Paul Benioff'''提出了'''图灵机Turing machine'''的量子力学模型。'''<ref name="The computer as a physical system">{{cite journal|last1=Benioff|first1=Paul|year=1980|title=The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines|journal=Journal of Statistical Physics|volume=22|issue=5|pages=563–591|bibcode=1980JSP....22..563B|doi=10.1007/bf01011339|s2cid=122949592}}</ref>理查德 · 费曼Richard Feynman和尤里 · 曼宁Yuri Manin'''后来提出，量子计算机有潜力去模拟传统计算机所无法模拟的东西。<ref>{{cite journal |last1=Feynman |first1=Richard |title=Simulating Physics with Computers |journal=International Journal of Theoretical Physics |date=June 1982 |volume=21 |issue=6/7 |pages=467–488 |doi=10.1007/BF02650179 |url=https://people.eecs.berkeley.edu/~christos/classics/Feynman.pdf |accessdate=28 February 2019 |bibcode=1982IJTP...21..467F |s2cid=124545445 |archive-url=https://web.archive.org/web/20190108115138/https://people.eecs.berkeley.edu/~christos/classics/Feynman.pdf |archive-date=8 January 2019 |url-status=dead }}</ref><ref name="manin1980vychislimoe">{{cite book| author=Manin, Yu. I.| title=Vychislimoe i nevychislimoe| trans-title=Computable and Noncomputable| year=1980| publisher=Sov.Radio| url=http://publ.lib.ru/ARCHIVES/M/MANIN_Yuriy_Ivanovich/Manin_Yu.I._Vychislimoe_i_nevychislimoe.(1980).%5bdjv-fax%5d.zip| pages=13–15| language=Russian| accessdate=2013-03-04| url-status=dead| archiveurl=https://web.archive.org/web/20130510173823/http://publ.lib.ru/ARCHIVES/M/MANIN_Yuriy_Ivanovich/Manin_Yu.I._Vychislimoe_i_nevychislimoe.(1980).%5Bdjv%5D.zip| archivedate=2013-05-10}}</ref>1994年，Peter Shor 开发了一种量子算法，用于分解整数，这种算法有可能解密 rsa 加密的通信。<ref>{{cite document|last1=Mermin|first1=David|date=March 28, 2006|title=Breaking RSA Encryption with a Quantum Computer: Shor's Factoring Algorithm|url=http://people.ccmr.cornell.edu/~mermin/qcomp/chap3.pdf|work=Physics 481-681 Lecture Notes |publisher=Cornell University|archive-url=https://web.archive.org/web/20121115112940/http://people.ccmr.cornell.edu/~mermin/qcomp/chap3.pdf|archive-date=2012-11-15}}</ref>尽管自20世纪90年代后期以来，实验取得了进展，但大多数研究人员认为，“容错量子计算机仍然是一个相当遥远的梦想。”<ref name="preskill2018">{{cite journal|author=John Preskill|date=2018|title=Quantum Computing in the NISQ era and beyond|journal=Quantum|volume=2|pages=79|arxiv=1801.00862|doi=10.22331/q-2018-08-06-79|s2cid=44098998}}</ref>近年来，量子计算研究的投资在公共和私营部门都有所增加。<ref>{{cite journal |last1=Gibney |first1=Elizabeth |title=Quantum gold rush: the private funding pouring into quantum start-ups |journal=Nature |date=2 October 2019 |volume=574 |issue=7776 |pages=22–24 |doi=10.1038/d41586-019-02935-4 |pmid=31578480 |bibcode=2019Natur.574...22G |doi-access=free }}</ref><ref>{{Cite news|last=Rodrigo|first=Chris Mills|url=https://thehill.com/policy/technology/482402-trump-budget-proposal-boosts-funding-for-artificial-intelligence-quantum|title=Trump budget proposal boosts funding for artificial intelligence, quantum computing|date=12 February 2020|work=The Hill|access-date=|url-status=live}}</ref>2019年10月23日，谷歌AI与'''美国宇航局U.S. National Aeronautics and Space Administration (NASA)'''合作，声称已经完成了在任何传统计算机上都不可能完成的'''量子计算'''。<ref>{{Cite web|url=https://www.ibm.com/blogs/research/2019/10/on-quantum-supremacy/|title=On "Quantum Supremacy"|date=2019-10-22|website=IBM Research Blog|language=en-US|access-date=2020-01-21}}</ref>
'''量子计算'''有几种模型，包括'''<font color="#ff8000">量子电路模型、量子图灵机、绝热量子计算机、单向量子计算机和各种量子细胞自动机'''。使用最广泛的模型是'''量子电路Quantum circuits '''。量子电路是基于量子比特或'''“量子位”"qubit"'''的，它在某种程度上类似于经典计算中的'''“比特”"bit"'''。'''量子比特'''可以处于1或0的量子态，也可以处于1和0的叠加态。然而，当'''量子比特'''被测量时，测量结果总是0或1; 这两种结果发生的概率取决于量子比特在被测量之前所处的量子状态。计算是通过'''量子逻辑门Quantum logic gates'''操纵量子比特来完成的，这在某种程度上类似于经典逻辑门。
'''量子计算'''有几种模型，包括'''量子电路模型、量子图灵机、绝热量子计算机、单向量子计算机和各种量子细胞自动机'''。使用最广泛的模型是'''量子电路Quantum circuits '''。量子电路是基于量子比特或'''“量子位”"qubit"'''的，它在某种程度上类似于经典计算中的'''“比特”"bit"'''。'''量子比特'''可以处于1或0的量子态，也可以处于1和0的叠加态。然而，当'''量子比特'''被测量时，测量结果总是0或1; 这两种结果发生的概率取决于量子比特在被测量之前所处的量子状态。计算是通过'''量子逻辑门Quantum logic gates'''操纵量子比特来完成的，这在某种程度上类似于经典逻辑门。
< ! -- 物理实现 -- >
< ! -- 物理实现 -- >
目前实现量子计算机主要有两种方法: 模拟和数字。模拟方法进一步分为'''<font color="#ff8000">量子模拟、量子退火模拟和绝热量子计算'''。数字量子计算机使用'''量子逻辑门'''进行计算。两种方法都使用量子比特。<ref name=2018Report/>{{rp|2–13}} There are currently a number of significant obstacles in the way of constructing useful quantum computers. In particular, it is difficult to maintain the quantum states of qubits as they are prone to [[quantum decoherence]], and quantum computers require significant [[error correction]] as they are far more prone to errors than classical computers.<ref>{{cite book |doi=10.1007/1-4020-8068-9_8 |chapter=Challenges in Reliable Quantum Computing |title=Nano, Quantum and Molecular Computing |year=2004 |last1=Franklin |first1=Diana |last2=Chong |first2=Frederic T. |pages=247–266 |isbn=1-4020-8067-0 }}</ref><ref>{{cite news |last1=Pakkin |first1=Scott |last2=Coles |first2=Patrick |title=The Problem with Quantum Computers |url=https://blogs.scientificamerican.com/observations/the-problem-with-quantum-computers/ |publisher=Scientific American |date=10 June 2019}}</ref>
目前实现量子计算机主要有两种方法: 模拟和数字。模拟方法进一步分为'''量子模拟、量子退火模拟和绝热量子计算'''。数字量子计算机使用'''量子逻辑门'''进行计算。两种方法都使用量子比特。<ref name=2018Report/>{{rp|2–13}} There are currently a number of significant obstacles in the way of constructing useful quantum computers. In particular, it is difficult to maintain the quantum states of qubits as they are prone to [[quantum decoherence]], and quantum computers require significant [[error correction]] as they are far more prone to errors than classical computers.<ref>{{cite book |doi=10.1007/1-4020-8068-9_8 |chapter=Challenges in Reliable Quantum Computing |title=Nano, Quantum and Molecular Computing |year=2004 |last1=Franklin |first1=Diana |last2=Chong |first2=Frederic T. |pages=247–266 |isbn=1-4020-8067-0 }}</ref><ref>{{cite news |last1=Pakkin |first1=Scott |last2=Coles |first2=Patrick |title=The Problem with Quantum Computers |url=https://blogs.scientificamerican.com/observations/the-problem-with-quantum-computers/ |publisher=Scientific American |date=10 June 2019}}</ref>
在数学上，逻辑门作用于'''<font color="#ff8000">量子态向量'''可以建模成矩阵乘法。因此 <math display="inline">X|0\rangle = |1\rangle</math> 和 <math display="inline">X|1\rangle = |0\rangle</math>。
在数学上，逻辑门作用于'''量子态向量'''可以建模成矩阵乘法。因此 <math display="inline">X|0\rangle = |1\rangle</math> 和 <math display="inline">X|1\rangle = |0\rangle</math>。
'''整数因式分解Integer factorization'''是'''公钥密码系统Public key cryptographic systems'''安全性的基础，如果一个大整数是几个素数的乘积（例如，两个300位素数的乘积）<ref>{{cite journal |last=Lenstra |first=Arjen K. |url=http://sage.math.washington.edu/edu/124/misc/arjen_lenstra_factoring.pdf |title=Integer Factoring |journal=Designs, Codes and Cryptography |volume=19 |pages=101–128 |year=2000 |doi=10.1023/A:1008397921377 |issue=2/3 |s2cid=9816153 |url-status=dead |archiveurl=https://web.archive.org/web/20150410234239/http://sage.math.washington.edu/edu/124/misc/arjen_lenstra_factoring.pdf |archivedate=2015-04-10 }}</ref>，那么在普通计算机上计算是不可行的。相比之下，量子计算机可以有效地解决这个问题，使用'''肖尔Shor算法'''来寻找它的因子。这种能力将使量子计算机能够破解目前使用的许多密码系统，也就是说，可以用<font color="#ff8000">多项式时间（整数位数）算法'''来解决这个问题。特别是目前流行的公钥密码算法大多是基于大整数因式分解或离散对数问题的困难性，而这两个问题都可以用'''肖尔Shor算法'''来解决。尤其是'''RSA、Diffie-Hellman和椭圆曲线Diffie-Hellman算法'''可能会被破解，它们一般用于保护安全网页、加密电子邮件和许多其他类型的数据。破解这些算法将对电子隐私和安全产生重大影响。
'''整数因式分解Integer factorization'''是'''公钥密码系统Public key cryptographic systems'''安全性的基础，如果一个大整数是几个素数的乘积（例如，两个300位素数的乘积）<ref>{{cite journal |last=Lenstra |first=Arjen K. |url=http://sage.math.washington.edu/edu/124/misc/arjen_lenstra_factoring.pdf |title=Integer Factoring |journal=Designs, Codes and Cryptography |volume=19 |pages=101–128 |year=2000 |doi=10.1023/A:1008397921377 |issue=2/3 |s2cid=9816153 |url-status=dead |archiveurl=https://web.archive.org/web/20150410234239/http://sage.math.washington.edu/edu/124/misc/arjen_lenstra_factoring.pdf |archivedate=2015-04-10 }}</ref>，那么在普通计算机上计算是不可行的。相比之下，量子计算机可以有效地解决这个问题，使用'''肖尔Shor算法'''来寻找它的因子。这种能力将使量子计算机能够破解目前使用的许多密码系统，也就是说，可以用多项式时间（整数位数）算法'''来解决这个问题。特别是目前流行的公钥密码算法大多是基于大整数因式分解或离散对数问题的困难性，而这两个问题都可以用'''肖尔Shor算法'''来解决。尤其是'''RSA、Diffie-Hellman和椭圆曲线Diffie-Hellman算法'''可能会被破解，它们一般用于保护安全网页、加密电子邮件和许多其他类型的数据。破解这些算法将对电子隐私和安全产生重大影响。
Besides factorization and discrete logarithms, quantum algorithms offering a more than polynomial speedup over the best known classical algorithm have been found for several problems, including the simulation of quantum physical processes from chemistry and solid state physics, the approximation of [[Jones polynomial]]s, and solving [[Pell's equation]]. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, although this is considered unlikely.<ref>{{Cite book |first1=Jon |last1=Schiller |url=https://books.google.com/books?id=l217ma2sWkoC&pg=PA11
Besides factorization and discrete logarithms, quantum algorithms offering a more than polynomial speedup over the best known classical algorithm have been found for several problems, including the simulation of quantum physical processes from chemistry and solid state physics, the approximation of [[Jones polynomial]]s, and solving [[Pell's equation]]. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, although this is considered unlikely.<ref>{{Cite book |first1=Jon |last1=Schiller |url=https://books.google.com/books?id=l217ma2sWkoC&pg=PA11
除了因式分解和离散对数外，在很多问题上发现，量子算法相比最著名的经典算法具有超过多项式的加速，<ref>[http://math.nist.gov/quantum/zoo/ Quantum Algorithm Zoo] {{Webarchive|url=https://web.archive.org/web/20180429014516/https://math.nist.gov/quantum/zoo/ |date=2018-04-29 }} – Stephen Jordan's Homepage</ref>其中包括化学和固态物理方面的量子物理过程仿真，'''琼斯多项式Jones polynomials'''的近似，以及'''佩尔方程Pell's equation'''的求解。目前还没有从数学上证明同样快速的经典算法无法被发现，尽管这被认为是不太可能的。然而，量子计算机为某些问题提供了多项式加速。最著名的例子是量子数据库搜索，它可以通过'''<font color="#ff8000">格罗夫Grover算法 '''来解决，比经典算法所需的数据库查询次数少二次方。在这种情况下，这种优势不仅是可证明的，而且是最优的，已经证明Grover的算法为任何数量的oracle查找提供了找到所需元素的最大可能概率。随后又发现了其他一些为查询问题进行可证明的量子加速的例子，例如在两对一函数中寻找碰撞和评估NAND树。
除了因式分解和离散对数外，在很多问题上发现，量子算法相比最著名的经典算法具有超过多项式的加速，<ref>[http://math.nist.gov/quantum/zoo/ Quantum Algorithm Zoo] {{Webarchive|url=https://web.archive.org/web/20180429014516/https://math.nist.gov/quantum/zoo/ |date=2018-04-29 }} – Stephen Jordan's Homepage</ref>其中包括化学和固态物理方面的量子物理过程仿真，'''琼斯多项式Jones polynomials'''的近似，以及'''佩尔方程Pell's equation'''的求解。目前还没有从数学上证明同样快速的经典算法无法被发现，尽管这被认为是不太可能的。然而，量子计算机为某些问题提供了多项式加速。最著名的例子是量子数据库搜索，它可以通过'''格罗夫Grover算法 '''来解决，比经典算法所需的数据库查询次数少二次方。在这种情况下，这种优势不仅是可证明的，而且是最优的，已经证明Grover的算法为任何数量的oracle查找提供了找到所需元素的最大可能概率。随后又发现了其他一些为查询问题进行可证明的量子加速的例子，例如在两对一函数中寻找碰撞和评估NAND树。
对于具有所有这些性质的问题，[[Grover算法]]在量子计算机上的运行时间将按输入（或数据库中元素）数量的平方根进行缩放，而不是经典算法的线性缩放。一类可以应用[[Grover算法]]的一般问题是<ref>{{cite journal |last1=Ambainis |first1=Ambainis |title=Quantum search algorithms |journal=ACM SIGACT News |date=June 2004 |volume=35 |issue=2 |pages=22–35 |doi=10.1145/992287.992296 |arxiv=quant-ph/0504012 |bibcode=2005quant.ph..4012A |s2cid=11326499 }}</ref>[[布尔可满足性问题]]。在本例中，算法迭代使用的“数据库”是所有可能答案的数据库。这方面的一个例子（也是可能的）应用是一个[[密码破解|密码破解器]]试图猜测[[加密|加密]]文件或系统的密码或密钥。[[对称密钥算法|对称密码]]例如[[Triple DES]]和[[Advanced Encryption Standard | AES]]特别容易受到此类攻击。{{引文需要{日期=2019年11月}}量子计算的这一应用是政府机构主要感兴趣的。<ref>{{cite news |url=https://www.washingtonpost.com/world/national-security/nsa-seeks-to-build-quantum-computer-that-could-crack-most-types-of-encryption/2014/01/02/8fff297e-7195-11e3-8def-a33011492df2_story.html |title=NSA seeks to build quantum computer that could crack most types of encryption |first1=Steven |last1=Rich |first2=Barton |last2=Gellman |date=2014-02-01 |newspaper=Washington Post}}</ref>
由于化学和纳米技术依赖于对量子系统的理解，而这样的系统是不可能以有效的经典方式进行模拟的，许多人相信'''量子模拟'''将是量子计算最重要的应用之一。'''量子模拟'''也可以用来模拟原子和粒子在非正常条件下的行为，比如对撞机内部的反应。
由于化学和纳米技术依赖于对量子系统的理解，而这样的系统是不可能以有效的经典方式进行模拟的，许多人相信'''量子模拟'''将是量子计算最重要的应用之一。'''量子模拟'''也可以用来模拟原子和粒子在非正常条件下的行为，比如对撞机内部的反应。
{{Main|Quantum simulator}}
{{Main|Quantum simulator}}
由于化学和纳米技术依赖于对量子系统的理解，而这种系统不可能以经典的方式进行有效的模拟，许多人相信[[量子模拟器|量子模拟]]将是量子计算最重要的应用之一。量子模拟也可以用来模拟原子和粒子在异常条件下的行为，例如[[对撞机]]内部的反应。<ref>{{Cite journal |url=http://archive.wired.com/science/discoveries/news/2007/02/72734 |title=The Father of Quantum Computing |journal=Wired |first=Quinn |last=Norton |date=2007-02-15 }}</ref> Quantum simulation could also be used to simulate the behavior of atoms and particles at unusual conditions such as the reactions inside a [[collider]].<ref>{{cite web |url=http://www.ias.edu/ias-letter/ambainis-quantum-computing |title=What Can We Do with a Quantum Computer? |first=Andris |last=Ambainis |date=Spring 2014 |publisher=Institute for Advanced Study}}</ref>
由于化学和纳米技术依赖于对量子系统的理解，而这种系统不可能以经典的方式进行有效的模拟，许多人相信[[量子模拟器|量子模拟]]将是量子计算最重要的应用之一。量子模拟也可以用来模拟原子和粒子在异常条件下的行为，例如[[对撞机]]内部的反应。<ref>{{Cite journal |url=http://archive.wired.com/science/discoveries/news/2007/02/72734 |title=The Father of Quantum Computing |journal=Wired |first=Quinn |last=Norton |date=2007-02-15 }}</ref> Quantum simulation could also be used to simulate the behavior of atoms and particles at unusual conditions such as the reactions inside a [[collider]].<ref>{{cite web |url=http://www.ias.edu/ias-letter/ambainis-quantum-computing |title=What Can We Do with a Quantum Computer? |first=Andris |last=Ambainis |date=Spring 2014 |publisher=Institute for Advanced Study}}</ref>
'''量子退火或绝热量子计算'''依赖于绝热定理进行计算。在一个简单的'''哈密顿体系'''中，系统处于'''基态'''，这个'''哈密顿体系'''慢慢演化成一个更复杂的哈密顿体系，它的基态代表问题的解。绝热定理指出，如果演化足够慢，系统在整个演化过程中将始终处于'''基态'''。
'''量子退火或绝热量子计算'''依赖于绝热定理进行计算。在一个简单的'''哈密顿体系'''中，系统处于'''基态'''，这个'''哈密顿体系'''慢慢演化成一个更复杂的哈密顿体系，它的基态代表问题的解。绝热定理指出，如果演化足够慢，系统在整个演化过程中将始终处于'''基态'''。
=== Quantum annealing and adiabatic optimization量子退火与绝热优化 ===
=== Quantum annealing and adiabatic optimization量子退火与绝热优化 ===
[[量子退火]]或[[绝热量子计算]]依赖绝热定理进行计算。在一个简单的哈密顿体系中，系统处于基态，这个哈密顿体系慢慢演化成一个更复杂的哈密顿体系，其基态代表问题的解决方案。绝热定理指出，如果演化足够慢，系统将在整个过程中始终保持在基态。
[[量子退火]]或[[绝热量子计算]]依赖绝热定理进行计算。在一个简单的哈密顿体系中，系统处于基态，这个哈密顿体系慢慢演化成一个更复杂的哈密顿体系，其基态代表问题的解决方案。绝热定理指出，如果演化足够慢，系统将在整个过程中始终保持在基态。
以其发现者 '''哈罗Harrow，哈西迪姆Hassidim和劳埃德Lloyd'''命名的线性方程组的量子算法，或称'''“ HHL 算法”'''，有望提供比经典算法更快的速度。
以其发现者 '''哈罗Harrow，哈西迪姆Hassidim和劳埃德Lloyd'''命名的线性方程组的量子算法，或称'''“ HHL 算法”'''，有望提供比经典算法更快的速度。
=== Solving linear equations 求解线性方程===
=== Solving linear equations 求解线性方程===
以其发现者哈罗、哈西迪姆和劳埃德命名的[[用于线性方程组的量子算法]]或“HHL算法”，有望提供比经典算法更快的速度。<ref name="Quantum algorithm for solving linear systems of equations by Harrow et al.">{{Cite journal |arxiv = 0811.3171|last1 = Harrow|first1 = Aram|last2 = Hassidim|first2 = Avinatan|last3 = Lloyd|first3 = Seth|title = Quantum algorithm for solving linear systems of equations|journal = Physical Review Letters|volume = 103|issue = 15|pages = 150502|year = 2009|doi = 10.1103/PhysRevLett.103.150502|pmid = 19905613|bibcode = 2009PhRvL.103o0502H|s2cid = 5187993}}</ref>
约翰 · 普雷斯基尔提出了'''量子优势Quantum supremacy'''这一术语，指的是量子计算机在特定领域相对于经典计算机的设想加速优势。谷歌在2017年宣布，它希望在今年年底前实现'''量子优势'''，尽管这一目标没有实现。IBM 在2018年表示，最好的经典计算机将在大约5年内在某些实际任务上被击败，并将'''量子优势'''测试视为未来的潜在基准。尽管像吉尔 · 卡莱这样的怀疑者对量子优势的实现持怀疑态度，但在2019年10月，据报道，与谷歌人工智能量子公司合作开发的 Sycamore 处理器已经取得了量子优势，其计算速度是最高级计算机的300万倍以上，后者通常被认为是世界上最快的计算机。比尔 · 安鲁在1994年发表的一篇论文中对量子计算机的实用性表示怀疑。保罗·戴维斯认为一台400量子位的计算机甚至会与全息原理暗示的宇宙学信息限制发生冲突。
约翰 · 普雷斯基尔提出了'''量子优势Quantum supremacy'''这一术语，指的是量子计算机在特定领域相对于经典计算机的设想加速优势。谷歌在2017年宣布，它希望在今年年底前实现'''量子优势'''，尽管这一目标没有实现。IBM 在2018年表示，最好的经典计算机将在大约5年内在某些实际任务上被击败，并将'''量子优势'''测试视为未来的潜在基准。尽管像吉尔 · 卡莱这样的怀疑者对量子优势的实现持怀疑态度，但在2019年10月，据报道，与谷歌人工智能量子公司合作开发的 Sycamore 处理器已经取得了量子优势，其计算速度是最高级计算机的300万倍以上，后者通常被认为是世界上最快的计算机。比尔 · 安鲁在1994年发表的一篇论文中对量子计算机的实用性表示怀疑。保罗·戴维斯认为一台400量子位的计算机甚至会与全息原理暗示的宇宙学信息限制发生冲突。
{{Main|Quantum supremacy}}
{{Main|Quantum supremacy}}
[[John Preskill]]引入了“[[量子至上]]”一词来指量子计算机在某一领域相对于经典计算机所具有的假设加速优势。<ref>{{Cite journal|title=Characterizing Quantum Supremacy in Near-Term Devices|journal=Nature Physics|volume=14|issue=6|pages=595–600|first1=Sergio|last1=Boixo|first2=Sergei V.|last2=Isakov|first3=Vadim N.|last3=Smelyanskiy|first4=Ryan|last4=Babbush|first5=Nan|last5=Ding|first6=Zhang|last6=Jiang|first7=Michael J.|last7=Bremner|first8=John M.|last8=Martinis|first9=Hartmut|last9=Neven|year=2018|arxiv=1608.00263|doi=10.1038/s41567-018-0124-x|bibcode=2018NatPh..14..595B|s2cid=4167494}}</ref>[[Google]]在2017年宣布，它预计将在今年年底实现量子霸权，但这并没有实现。[[IBM]]在2018年表示，最好的经典计算机将在大约五年内完成一些实际任务，并将量子优势测试视为未来潜在的基准。<ref>{{cite web|url=https://www.scientificamerican.com/article/quantum-computers-compete-for-supremacy/|title=Quantum Computers Compete for "Supremacy"|first=Neil|last=Savage}}</ref>尽管像[[Gil Kalai]]这样的怀疑论者怀疑量子霸权是否会实现，<ref>{{cite web|url=https://rjlipton.wordpress.com/2016/04/22/quantum-supremacy-and-complexity/|title=Quantum Supremacy and Complexity|date=23 April 2016}}</ref><ref>{{cite web|last1=Kalai|first1=Gil|title=The Quantum Computer Puzzle|url=http://www.ams.org/journals/notices/201605/rnoti-p508.pdf|publisher=AMS}}</ref>据报道，2019年10月，与谷歌AI Quantum联合创建的[[Sycamore processor]]实现了量子优势<ref>{{cite journal|last1=Arute|first1=Frank|last2=Arya|first2=Kunal|last3=Babbush|first3=Ryan|last4=Bacon|first4=Dave|last5=Bardin|first5=Joseph C.|last6=Barends|first6=Rami|last7=Biswas|first7=Rupak|last8=Boixo|first8=Sergio|last9=Brandao|first9=Fernando G. S. L.|last10=Buell|first10=David A.|last11=Burkett|first11=Brian|date=23 October 2019|title=Quantum supremacy using a programmable superconducting processor|journal=Nature|volume=574|issue=7779|first15=Roberto|first57=Murphy Yuezhen|last64=Rubin|first63=Pedram|last63=Roushan|first62=Eleanor G.|last62=Rieffel|first61=Chris|last61=Quintana|first60=John C.|last60=Platt|first59=Andre|last59=Petukhov|first58=Eric|last58=Ostby|last57=Niu|last65=Sank|first56=Charles|last56=Neill|first55=Matthew|last55=Neeley|first54=Ofer|last54=Naaman|first53=Josh|last53=Mutus|first52=Masoud|last52=Mohseni|first51=Kristel|last51=Michielsen|first50=Xiao|last50=Mi|first64=Nicholas C.|first65=Daniel|last49=Megrant|last74=Yeh|last12=Chen|first12=Yu|last13=Chen|first13=Zijun|last14=Chiaro|first14=Ben|first77=John M.|last77=Martinis|first76=Hartmut|last76=Neven|first75=Adam|last75=Zalcman|first74=Ping|first73=Z. Jamie|last66=Satzinger|last73=Yao|first72=Theodore|last72=White|first71=Benjamin|last71=Villalonga|first70=Amit|last70=Vainsencher|first69=Matthew D.|last69=Trevithick|first68=Kevin J.|last68=Sung|first67=Vadim|last67=Smelyanskiy|first66=Kevin J.|first49=Anthony|first48=Matthew|last16=Courtney|last24=Guerin|first30=Trent|last30=Huang|first29=Markus|last29=Hoffman|first28=Alan|last28=Ho|first27=Michael J.|last27=Hartmann|first26=Matthew P.|last26=Harrigan|first25=Steve|last25=Habegger|first24=Keith|first23=Rob|first31=Travis S.|last23=Graff|first22=Marissa|last22=Giustina|first21=Craig|last21=Gidney|first20=Austin|last20=Fowler|first19=Brooks|last19=Foxen|first18=Edward|last18=Farhi|first17=Andrew|last17=Dunsworsth|first16=William|last31=Humble|last32=Isakov|last48=McEwen|first40=Alexander|first47=Jarrod R.|last47=McClean|first46=Salvatore|last46=Mandrà|first45=Dmitry|last45=Lyakh|first44=Erik|last44=Lucero|first43=Mike|last43=Lindmark|first42=David|last42=Landhuis|first41=Fedor|last15=Collins|last40=Korotov|first32=Sergei V.|first39=Sergey|last39=Knysh|first38=Paul V.|last38=Klimov|first37=Julian|last37=Kelly|first36=Kostyantyn|last36=Kechedzhi|first35=Dvir|last35=Kafri|first34=Zhang|last34=Jiang|first33=Evan|last33=Jeffery|last41=Kostritsa|doi=10.1038/s41586-019-1666-5|pmid=31645734|pages=505–510|bibcode=2019Natur.574..505A|arxiv=1910.11333|s2cid=204836822}}</ref>，它的计算速度是世界上最快的计算机[[Summit（supercomputer）| Summit]]的300多万倍。<ref>{{Cite web|url=https://www.technologyreview.com/f/614416/google-researchers-have-reportedly-achieved-quantum-supremacy/|title=Google researchers have reportedly achieved "quantum supremacy"|website=MIT Technology Review}}</ref>比尔 · 安鲁在1994年发表的一篇论文中对量子计算机的实用性表示怀疑。<ref>{{Cite journal|last1=Unruh|first1=Bill|title=Maintaining coherence in Quantum Computers|journal=Physical Review A|volume=51|issue=2|pages=992–997|arxiv=hep-th/9406058|bibcode=1995PhRvA..51..992U|year=1995|doi=10.1103/PhysRevA.51.992|pmid=9911677|s2cid=13980886}}</ref>[[Paul Davies]]认为，一台400 量子比特的计算机甚至会与[[全息原理]所隐含的宇宙信息界发生冲突。<ref>{{cite web|last1=Davies|first1=Paul|title=The implications of a holographic universe for quantum information science and the nature of physical law|url=http://power.itp.ac.cn/~mli/pdavies.pdf|publisher=Macquarie University}}</ref>
[[John Preskill]]引入了“[[量子至上]]”一词来指量子计算机在某一领域相对于经典计算机所具有的假设加速优势。<ref>{{Cite journal|title=Characterizing Quantum Supremacy in Near-Term Devices|journal=Nature Physics|volume=14|issue=6|pages=595–600|first1=Sergio|last1=Boixo|first2=Sergei V.|last2=Isakov|first3=Vadim N.|last3=Smelyanskiy|first4=Ryan|last4=Babbush|first5=Nan|last5=Ding|first6=Zhang|last6=Jiang|first7=Michael J.|last7=Bremner|first8=John M.|last8=Martinis|first9=Hartmut|last9=Neven|year=2018|arxiv=1608.00263|doi=10.1038/s41567-018-0124-x|bibcode=2018NatPh..14..595B|s2cid=4167494}}</ref>[[Google]]在2017年宣布，它预计将在今年年底实现量子霸权，但这并没有实现。[[IBM]]在2018年表示，最好的经典计算机将在大约五年内完成一些实际任务，并将量子优势测试视为未来潜在的基准。<ref>{{cite web|url=https://www.scientificamerican.com/article/quantum-computers-compete-for-supremacy/|title=Quantum Computers Compete for "Supremacy"|first=Neil|last=Savage}}</ref>尽管像[[Gil Kalai]]这样的怀疑论者怀疑量子霸权是否会实现，<ref>{{cite web|url=https://rjlipton.wordpress.com/2016/04/22/quantum-supremacy-and-complexity/|title=Quantum Supremacy and Complexity|date=23 April 2016}}</ref><ref>{{cite web|last1=Kalai|first1=Gil|title=The Quantum Computer Puzzle|url=http://www.ams.org/journals/notices/201605/rnoti-p508.pdf|publisher=AMS}}</ref>据报道，2019年10月，与谷歌AI Quantum联合创建的[[Sycamore processor]]实现了量子优势<ref>{{cite journal|last1=Arute|first1=Frank|last2=Arya|first2=Kunal|last3=Babbush|first3=Ryan|last4=Bacon|first4=Dave|last5=Bardin|first5=Joseph C.|last6=Barends|first6=Rami|last7=Biswas|first7=Rupak|last8=Boixo|first8=Sergio|last9=Brandao|first9=Fernando G. S. L.|last10=Buell|first10=David A.|last11=Burkett|first11=Brian|date=23 October 2019|title=Quantum supremacy using a programmable superconducting processor|journal=Nature|volume=574|issue=7779|first15=Roberto|first57=Murphy Yuezhen|last64=Rubin|first63=Pedram|last63=Roushan|first62=Eleanor G.|last62=Rieffel|first61=Chris|last61=Quintana|first60=John C.|last60=Platt|first59=Andre|last59=Petukhov|first58=Eric|last58=Ostby|last57=Niu|last65=Sank|first56=Charles|last56=Neill|first55=Matthew|last55=Neeley|first54=Ofer|last54=Naaman|first53=Josh|last53=Mutus|first52=Masoud|last52=Mohseni|first51=Kristel|last51=Michielsen|first50=Xiao|last50=Mi|first64=Nicholas C.|first65=Daniel|last49=Megrant|last74=Yeh|last12=Chen|first12=Yu|last13=Chen|first13=Zijun|last14=Chiaro|first14=Ben|first77=John M.|last77=Martinis|first76=Hartmut|last76=Neven|first75=Adam|last75=Zalcman|first74=Ping|first73=Z. Jamie|last66=Satzinger|last73=Yao|first72=Theodore|last72=White|first71=Benjamin|last71=Villalonga|first70=Amit|last70=Vainsencher|first69=Matthew D.|last69=Trevithick|first68=Kevin J.|last68=Sung|first67=Vadim|last67=Smelyanskiy|first66=Kevin J.|first49=Anthony|first48=Matthew|last16=Courtney|last24=Guerin|first30=Trent|last30=Huang|first29=Markus|last29=Hoffman|first28=Alan|last28=Ho|first27=Michael J.|last27=Hartmann|first26=Matthew P.|last26=Harrigan|first25=Steve|last25=Habegger|first24=Keith|first23=Rob|first31=Travis S.|last23=Graff|first22=Marissa|last22=Giustina|first21=Craig|last21=Gidney|first20=Austin|last20=Fowler|first19=Brooks|last19=Foxen|first18=Edward|last18=Farhi|first17=Andrew|last17=Dunsworsth|first16=William|last31=Humble|last32=Isakov|last48=McEwen|first40=Alexander|first47=Jarrod R.|last47=McClean|first46=Salvatore|last46=Mandrà|first45=Dmitry|last45=Lyakh|first44=Erik|last44=Lucero|first43=Mike|last43=Lindmark|first42=David|last42=Landhuis|first41=Fedor|last15=Collins|last40=Korotov|first32=Sergei V.|first39=Sergey|last39=Knysh|first38=Paul V.|last38=Klimov|first37=Julian|last37=Kelly|first36=Kostyantyn|last36=Kechedzhi|first35=Dvir|last35=Kafri|first34=Zhang|last34=Jiang|first33=Evan|last33=Jeffery|last41=Kostritsa|doi=10.1038/s41586-019-1666-5|pmid=31645734|pages=505–510|bibcode=2019Natur.574..505A|arxiv=1910.11333|s2cid=204836822}}</ref>，它的计算速度是世界上最快的计算机[[Summit（supercomputer）| Summit]]的300多万倍。<ref>{{Cite web|url=https://www.technologyreview.com/f/614416/google-researchers-have-reportedly-achieved-quantum-supremacy/|title=Google researchers have reportedly achieved "quantum supremacy"|website=MIT Technology Review}}</ref>比尔 · 安鲁在1994年发表的一篇论文中对量子计算机的实用性表示怀疑。<ref>{{Cite journal|last1=Unruh|first1=Bill|title=Maintaining coherence in Quantum Computers|journal=Physical Review A|volume=51|issue=2|pages=992–997|arxiv=hep-th/9406058|bibcode=1995PhRvA..51..992U|year=1995|doi=10.1103/PhysRevA.51.992|pmid=9911677|s2cid=13980886}}</ref>[[Paul Davies]]认为，一台400 量子比特的计算机甚至会与[[全息原理]所隐含的宇宙信息界发生冲突。<ref>{{cite web|last1=Davies|first1=Paul|title=The implications of a holographic universe for quantum information science and the nature of physical law|url=http://power.itp.ac.cn/~mli/pdavies.pdf|publisher=Macquarie University}}</ref>
建造大型量子计算机存在许多技术挑战。物理学家 David DiVincenzo 列出了实用量子计算机的以下要求:
建造大型量子计算机存在许多技术挑战。物理学家 David DiVincenzo 列出了实用量子计算机的以下要求:
== Obstacles 阻碍==
== Obstacles 阻碍==
建造大型量子计算机面临许多技术挑战。<ref>{{cite journal |last=Dyakonov |first=Mikhail |url=https://spectrum.ieee.org/computing/hardware/the-case-against-quantum-computing |title=The Case Against Quantum Computing |journal=[[IEEE Spectrum]] |date=2018-11-15}}</ref>物理学家[[David P.DiVincenzo | David DiVincenzo]]为一台实用的量子计算机列出了以下[[DiVincenzo的标准|要求]] ：<ref>{{cite journal| arxiv=quant-ph/0002077|title=The Physical Implementation of Quantum Computation|last=DiVincenzo |first=David P.|date=2000-04-13|doi=10.1002/1521-3978(200009)48:9/11<771::AID-PROP771>3.0.CO;2-E|volume=48|issue=9–11|journal=Fortschritte der Physik|pages=771–783|bibcode=2000ForPh..48..771D}}</ref>
*物理上可扩展以增加量子比特的数量
*物理上可扩展以增加量子比特的数量
*可以初始化为随机值的量子位
*可以初始化为随机值的量子位
*比[[退相干]]时间快的量子门
*比[[退相干]]时间快的量子门
*通用门组
*通用门组
寻找量子计算机的零部件也非常困难。许多量子计算机，比如谷歌和 IBM 制造的计算机，需要核研究的副产品氦 -3，以及只有日本 Coax 公司制造的特殊超导电缆。
寻找量子计算机的零部件也非常困难。许多量子计算机，比如谷歌和 IBM 制造的计算机，需要核研究的副产品氦 -3，以及只有日本 Coax 公司制造的特殊超导电缆。
* Qubits that can be read easily
* Qubits that can be read easily
*易于读取的量子位
*易于读取的量子位
多量子比特系统的控制需要产生和协调大量的电信号并保证严格和确定的时序分辨率。这导致了量子控制器的发展，它能够接通量子比特。扩展这些系统以支持越来越多的量子比特是量子计算机扩展的额外挑战。
多量子比特系统的控制需要产生和协调大量的电信号并保证严格和确定的时序分辨率。这导致了量子控制器的发展，它能够接通量子比特。扩展这些系统以支持越来越多的量子比特是量子计算机扩展的额外挑战。
量子计算机的零件采购也非常困难。许多量子计算机，比如由[[Google]]和[[IBM]]建造的量子计算机，需要[[Hemien-3]]，[[Nuclear physics | Nuclear]]研究副产品，以及只由日本Coax Co.公司制造的[[超导]]电缆。
量子计算机的零件采购也非常困难。许多量子计算机，比如由[[Google]]和[[IBM]]建造的量子计算机，需要[[Hemien-3]]，[[Nuclear physics | Nuclear]]研究副产品，以及只由日本Coax Co.公司制造的[[超导]]电缆。<ref>{{cite news |last1=Giles |first1=Martin |title=We'd have more quantum computers if it weren't so hard to find the damn cables |url=https://www.technologyreview.com/s/612760/quantum-computers-component-shortage/ |publisher=MIT Technology Review |date=17 January 2019}}</ref>
多量子比特系统的控制需要产生和协调大量的电信号并保证严格和确定的时序分辨率。这导致了[[量子控制器]]的发展，它能够接通量子比特。扩展这些系统以支持越来越多的量子比特是量子计算机扩展的额外挑战。{{需要引文|日期=2020年8月}}
多量子比特系统的控制需要产生和协调大量的电信号并保证严格和确定的时序分辨率。这导致了[[量子控制器]]的发展，它能够接通量子比特。扩展这些系统以支持越来越多的量子比特是量子计算机扩展的额外挑战。{{需要引文|日期=2020年8月}}
=== Quantum decoherence 量子退相干===
=== Quantum decoherence 量子退相干===
构建量子计算机的最大挑战之一是控制或消除'''量子退相干Quantum decoherence'''。这通常意味着将系统与其环境隔离，因为与外部世界的交互会导致系统退相干。然而，也存在其他的退相干源。例如'''量子门，晶格振动'''和用于实现量子比特的物理系统的背景热核自旋。退相干是不可逆的，因为它实际上是'''非酉Non-unitary'''的，如果不能避免的话，通常也应该高度控制。候选系统的退相干时间，特别是横向弛豫时间T<sub>2</sub>（对于核磁共振和磁共振成像技术，也称为“去相位时间”），在低温下通常处于纳秒和秒之间。目前，一些量子计算机要求将量子比特冷却到20毫开尔文，以防止严重的退相干。2020年的一项研究认为，尽管如此，诸如宇宙射线这样的电离辐射仍能导致某些系统在毫秒范围内退凝。
构建量子计算机的最大挑战之一是控制或消除'''量子退相干Quantum decoherence'''。这通常意味着将系统与其环境隔离，因为与外部世界的交互会导致系统退相干。然而，也存在其他的退相干源。例如'''量子门，晶格振动'''和用于实现量子比特的物理系统的背景热核自旋。退相干是不可逆的，因为它实际上是'''非酉Non-unitary'''的，如果不能避免的话，通常也应该高度控制。候选系统的退相干时间，特别是横向弛豫时间T<sub>2</sub>（对于核磁共振和磁共振成像技术，也称为“去相位时间”），在低温下通常处于纳秒和秒之间。目前，一些量子计算机要求将量子比特冷却到20毫开尔文，以防止严重的退相干。2020年的一项研究认为，尽管如此，诸如宇宙射线这样的电离辐射仍能导致某些系统在毫秒范围内退凝。
因此，耗时的任务可能会使一些量子算法无法操作，因为维持量子位的状态足够长的时间最终会破坏这些叠加。
因此，耗时的任务可能会使一些量子算法无法操作，因为维持量子位的状态足够长的时间最终会破坏这些叠加。
构建量子计算机的最大挑战之一是控制或消除[[量子退相干]]。这通常意味着将系统与其环境隔离，因为与外部世界的交互会导致系统退相干。然而，也存在其他的退相干源。例如量子门，晶格振动和用于实现量子比特的物理系统的背景热核自旋。退相干是不可逆的，因为它实际上是非酉的，如果不能避免的话，通常也应该高度控制。候选系统的退相干时间，特别是横向弛豫时间“T”<sub>2</sub>（对于[[核磁共振| NMR]]和[[MRI]]技术，也称为“去相位时间”），在低温下通常在纳秒到秒之间。.<ref name="DiVincenzo 1995">{{cite journal |last=DiVincenzo |first=David P. |title=Quantum Computation |journal=Science |year=1995 |volume=270 |issue=5234 |pages=255–261 |doi= 10.1126/science.270.5234.255 |bibcode = 1995Sci...270..255D |citeseerx=10.1.1.242.2165 |s2cid=220110562 }} {{subscription required}}</ref>目前，一些量子计算机要求将量子比特冷却到20毫开尔文，以防止严重的退相干。<ref>{{cite journal|last1=Jones|first1=Nicola|title=Computing: The quantum company|journal=Nature|date=19 June 2013|volume=498|issue=7454|pages=286–288|doi=10.1038/498286a|pmid=23783610|bibcode=2013Natur.498..286J|doi-access=free}}</ref>2020年的一项研究认为，尽管如此，诸如[宇宙射线]]这样的[[电离辐射]]仍能导致某些系统在毫秒范围内退凝。<ref>{{cite journal |last1=Vepsäläinen |first1=Antti P. |last2=Karamlou |first2=Amir H. |last3=Orrell |first3=John L. |last4=Dogra |first4=Akshunna S. |last5=Loer |first5=Ben |last6=Vasconcelos |first6=Francisca |last7=Kim |first7=David K. |last8=Melville |first8=Alexander J. |last9=Niedzielski |first9=Bethany M. |last10=Yoder |first10=Jonilyn L. |last11=Gustavsson |first11=Simon |last12=Formaggio |first12=Joseph A. |last13=VanDevender |first13=Brent A. |last14=Oliver |first14=William D. |display-authors=5 |title=Impact of ionizing radiation on superconducting qubit coherence |journal=Nature |date=August 2020 |volume=584 |issue=7822 |pages=551–556 |doi=10.1038/s41586-020-2619-8 |pmid=32848227 |url=https://www.nature.com/articles/s41586-020-2619-8 |language=en |issn=1476-4687|arxiv=2001.09190 |s2cid=210920566 }}</ref>
构建量子计算机的最大挑战之一是控制或消除[[量子退相干]]。这通常意味着将系统与其环境隔离，因为与外部世界的交互会导致系统退相干。然而，也存在其他的退相干源。例如量子门，晶格振动和用于实现量子比特的物理系统的背景热核自旋。退相干是不可逆的，因为它实际上是非酉的，如果不能避免的话，通常也应该高度控制。候选系统的退相干时间，特别是横向弛豫时间“T”<sub>2</sub>（对于[[核磁共振| NMR]]和[[MRI]]技术，也称为“去相位时间”），在低温下通常在纳秒到秒之间。.<ref name="DiVincenzo 1995">{{cite journal |last=DiVincenzo |first=David P. |title=Quantum Computation |journal=Science |year=1995 |volume=270 |issue=5234 |pages=255–261 |doi= 10.1126/science.270.5234.255 |bibcode = 1995Sci...270..255D |citeseerx=10.1.1.242.2165 |s2cid=220110562 }} {{subscription required}}</ref>目前，一些量子计算机要求将量子比特冷却到20毫开尔文，以防止严重的退相干。<ref>{{cite journal|last1=Jones|first1=Nicola|title=Computing: The quantum company|journal=Nature|date=19 June 2013|volume=498|issue=7454|pages=286–288|doi=10.1038/498286a|pmid=23783610|bibcode=2013Natur.498..286J|doi-access=free}}</ref>2020年的一项研究认为，尽管如此，诸如[宇宙射线]]这样的[[电离辐射]]仍能导致某些系统在毫秒范围内退凝。<ref>{{cite journal |last1=Vepsäläinen |first1=Antti P. |last2=Karamlou |first2=Amir H. |last3=Orrell |first3=John L. |last4=Dogra |first4=Akshunna S. |last5=Loer |first5=Ben |last6=Vasconcelos |first6=Francisca |last7=Kim |first7=David K. |last8=Melville |first8=Alexander J. |last9=Niedzielski |first9=Bethany M. |last10=Yoder |first10=Jonilyn L. |last11=Gustavsson |first11=Simon |last12=Formaggio |first12=Joseph A. |last13=VanDevender |first13=Brent A. |last14=Oliver |first14=William D. |display-authors=5 |title=Impact of ionizing radiation on superconducting qubit coherence |journal=Nature |date=August 2020 |volume=584 |issue=7822 |pages=551–556 |doi=10.1038/s41586-020-2619-8 |pmid=32848227 |url=https://www.nature.com/articles/s41586-020-2619-8 |language=en |issn=1476-4687|arxiv=2001.09190 |s2cid=210920566 }}</ref>
这些问题对于光学方法来说更加困难，因为光学方法的时间数量级更小，而克服这些问题的常用方法是光脉冲整形。错误率通常和操作时间与去相干时间的比率成正比，因此任何操作都必须比退相干时间快得多。
这些问题对于光学方法来说更加困难，因为光学方法的时间数量级更小，而克服这些问题的常用方法是光脉冲整形。错误率通常和操作时间与去相干时间的比率成正比，因此任何操作都必须比退相干时间快得多。
因此，耗时的任务可能会使一些量子算法无法操作，因为维持量子位的状态足够长的时间最终会破坏这些叠加。<ref>{{cite arxiv|last1=Amy|first1=Matthew|last2=Matteo|first2=Olivia|last3=Gheorghiu|first3=Vlad|last4=Mosca|first4=Michele|last5=Parent|first5=Alex|last6=Schanck|first6=John|title=Estimating the cost of generic quantum pre-image attacks on SHA-2 and SHA-3|date=November 30, 2016|eprint=1603.09383|class=quant-ph}}</ref>
因此，耗时的任务可能会使一些量子算法无法操作，因为维持量子位的状态足够长的时间最终会破坏这些叠加。<ref>{{cite arxiv|last1=Amy|first1=Matthew|last2=Matteo|first2=Olivia|last3=Gheorghiu|first3=Vlad|last4=Mosca|first4=Michele|last5=Parent|first5=Alex|last6=Schanck|first6=John|title=Estimating the cost of generic quantum pre-image attacks on SHA-2 and SHA-3|date=November 30, 2016|eprint=1603.09383|class=quant-ph}}</ref>
正如量子阈值定理所描述的那样，如果误差率足够小，则可以利用量子误差修正来抑制误差和退相干。如果纠错方案能够比消相干引入的误差更快地纠正误差，则会使得总计算时间比消相干时间更长。假设噪声是去极化的，则容错计算中每个门所需的错误率经常引用的数字是10<sup>−3</sup>。
正如量子阈值定理所描述的那样，如果误差率足够小，则可以利用量子误差修正来抑制误差和退相干。如果纠错方案能够比消相干引入的误差更快地纠正误差，则会使得总计算时间比消相干时间更长。假设噪声是去极化的，则容错计算中每个门所需的错误率经常引用的数字是10<sup>−3</sup>。
这些问题对于光学方法来说更为困难，因为光学方法的时间数量级更小，而克服这些问题的常用方法是[[光脉冲整形]]。错误率通常和操作时间与退相干时间的比率成正比，因此任何操作都必须比退相干时间快得多。
这些问题对于光学方法来说更为困难，因为光学方法的时间数量级更小，而克服这些问题的常用方法是[[光脉冲整形]]。错误率通常和操作时间与退相干时间的比率成正比，因此任何操作都必须比退相干时间快得多。
满足这种可伸缩性条件对于各种系统都是可能的。然而，纠错的使用带来了大量增加所需量子比特的代价。使用Shor算法对整数进行因子运算所需的数量级仍然是多项式的，并且被认为在L和L<sup>2</sup>之间，其中L是要被分解的数量中的量子位数；纠错算法将使这个数字膨胀一个额外的系数L。对于1000位的数字，这意味着需要大约10<sup>4</sup>位没有纠错。通过纠错，这个数字将上升到大约10<sup>7</sup>位。计算时间约为L<sup>2</sup> 或约 10<sup>7</sup>步，在主频为1兆赫时，大约10秒。
满足这种可伸缩性条件对于各种系统都是可能的。然而，纠错的使用带来了大量增加所需量子比特的代价。使用Shor算法对整数进行因子运算所需的数量级仍然是多项式的，并且被认为在L和L<sup>2</sup>之间，其中L是要被分解的数量中的量子位数；纠错算法将使这个数字膨胀一个额外的系数L。对于1000位的数字，这意味着需要大约10<sup>4</sup>位没有纠错。通过纠错，这个数字将上升到大约10<sup>7</sup>位。计算时间约为L<sup>2</sup> 或约 10<sup>7</sup>步，在主频为1兆赫时，大约10秒。
如[[量子阈值定理]]所述，如果错误率足够小，则可以利用量子纠错来抑制误差和退相干。如果纠错方案能够比退相干引入的错误更快地纠正错误，则会使得总计算时间比退相干时间长。假设噪声是去极化的，则容错计算中每个门所需的错误率经常引用的数字是10<sup>-3</sup>。
如[[量子阈值定理]]所述，如果错误率足够小，则可以利用量子纠错来抑制误差和退相干。如果纠错方案能够比退相干引入的错误更快地纠正错误，则会使得总计算时间比退相干时间长。假设噪声是去极化的，则容错计算中每个门所需的错误率经常引用的数字是10<sup>-3</sup>。
稳定性退相干问题的另一种不同的方法是用'''任意子、准粒子Anyons, Quasi-particles'''作为线程，依靠'''辫子理论Braid theory'''形成稳定的逻辑门，创建一个拓扑量子计算机。
稳定性退相干问题的另一种不同的方法是用'''任意子、准粒子Anyons, Quasi-particles'''作为线程，依靠'''辫子理论Braid theory'''形成稳定的逻辑门，创建一个拓扑量子计算机。
满足这种可伸缩性条件对于各种系统都是可能的。然而，纠错的使用带来了大量增加所需量子比特的代价。使用Shor算法对整数进行因子运算所需的数量级仍然是多项式的，并且被认为在L和L<sup>2</sup>之间，其中L是要被分解的数量中的量子位数；纠错算法将使这个数字膨胀一个额外的系数L。对于1000位的数字，这意味着需要大约10<sup>4</sup>位没有纠错。<ref>{{cite journal |title=Is Fault-Tolerant Quantum Computation Really Possible? |last=Dyakonov |first=M. I. |date=2006-10-14 |pages=4–18 |journal=Future Trends in Microelectronics. Up the Nano Creek |editor1=S. Luryi |editor2=J. Xu |editor3=A. Zaslavsky | arxiv=quant-ph/0610117|bibcode=2006quant.ph.10117D }}</ref>通过纠错，这个数字将上升到大约10<sup>7</sup>位。计算时间约为L<sup>2</sup> 或约 10<sup>7</sup>步，在主频为1兆赫时，大约10秒。
满足这种可伸缩性条件对于各种系统都是可能的。然而，纠错的使用带来了大量增加所需量子比特的代价。使用Shor算法对整数进行因子运算所需的数量级仍然是多项式的，并且被认为在L和L<sup>2</sup>之间，其中L是要被分解的数量中的量子位数；纠错算法将使这个数字膨胀一个额外的系数L。对于1000位的数字，这意味着需要大约10<sup>4</sup>位没有纠错。<ref>{{cite journal |title=Is Fault-Tolerant Quantum Computation Really Possible? |last=Dyakonov |first=M. I. |date=2006-10-14 |pages=4–18 |journal=Future Trends in Microelectronics. Up the Nano Creek |editor1=S. Luryi |editor2=J. Xu |editor3=A. Zaslavsky | arxiv=quant-ph/0610117|bibcode=2006quant.ph.10117D }}</ref>通过纠错，这个数字将上升到大约10<sup>7</sup>位。计算时间约为L<sup>2</sup> 或约 10<sup>7</sup>步，在主频为1兆赫时，大约10秒。
物理学家米哈伊尔 · 迪亚科诺夫对量子计算表示怀疑，他说:
物理学家米哈伊尔 · 迪亚科诺夫对量子计算表示怀疑，他说:
解决稳定退相干问题的一个非同寻常的方法是用[[任意子]]s，[[准粒子]]s作为线程，依靠[[辫子理论]]来形成稳定的逻辑门<ref>{{cite journal
解决稳定退相干问题的一个非同寻常的方法是用[[任意子]]s，[[准粒子]]s作为线程，依靠[[辫子理论]]来形成稳定的逻辑门<ref>{{cite journal
“因此，描述这样一个有用的量子计算机在任何给定时刻的状态的连续参数的数量必须是... ... 大约10<sup>300</sup> ... ... 我们能否学会控制定义这样一个系统的量子态的超过10<sup>300</sup> 个连续可变参数？我的答案很简单。不，永远不会。”
“因此，描述这样一个有用的量子计算机在任何给定时刻的状态的连续参数的数量必须是... ... 大约10<sup>300</sup> ... ... 我们能否学会控制定义这样一个系统的量子态的超过10<sup>300</sup> 个连续可变参数？我的答案很简单。不，永远不会。”
| last4 = Wang | first4 = Zhenghan
| last4 = Wang | first4 = Zhenghan
有许多量子计算模型，以计算被分解的基本元素来区分。具有实际重要性的四个主要模式是:
有许多量子计算模型，以计算被分解的基本元素来区分。具有实际重要性的四个主要模式是:
| mr = 1943131
| mr = 1943131
量子图灵机在理论上是重要的，但是这个模型的物理实现是不可行的。所有四种计算模型被证明是等价的; 每种模型只需要不超过多项式的开销就可以模拟另一种模型。
量子图灵机在理论上是重要的，但是这个模型的物理实现是不可行的。所有四种计算模型被证明是等价的; 每种模型只需要不超过多项式的开销就可以模拟另一种模型。
：“因此，描述这样一个有用的量子计算机在任何给定时刻的状态的连续参数的数量必须是...大约10<sup>300</sup>... 我们能不能学会控制定义这样一个系统量子态的超过10<sup>300</sup>个连续可变的参数？我的回答很简单“不，永远不会”。
：“因此，描述这样一个有用的量子计算机在任何给定时刻的状态的连续参数的数量必须是...大约10<sup>300</sup>... 我们能不能学会控制定义这样一个系统量子态的超过10<sup>300</sup>个连续可变的参数？我的回答很简单“不，永远不会”。
== Developments 发展==
==发展==
=== Quantum computing models 量子计算模型===
===量子计算模型===
There are a number of quantum computing models, distinguished by the basic elements in which the computation is decomposed. The four main models of practical importance are:
There are a number of quantum computing models, distinguished by the basic elements in which the computation is decomposed. The four main models of practical importance are:
有许多量子计算模型，其区别在于计算被分解时的基本元素。具有实践重要性的四种主要模式是：
有许多量子计算模型，其区别在于计算被分解时的基本元素。具有实践重要性的四种主要模式是：
*[[量子电路|量子门阵列]]（计算分解为几个量子比特的序列[[量子门]]s）
*[[量子电路|量子门阵列]]（计算分解为几个量子比特的序列[[量子门]]s）
*[[单向量子计算机]]（将计算分解为一个量子比特测量序列，应用于高度纠缠的初始状态或[[团簇状态]]）
*[[单向量子计算机]]（将计算分解为一个量子比特测量序列，应用于高度纠缠的初始状态或[[团簇状态]]）
*[[绝热量子计算|绝热量子计算机]]，基于[[量子退火]]（计算分解为初始[[哈密顿量（量子力学）|哈密顿量]]到最终哈密顿量的缓慢连续变换，其基态包含解）
*[[绝热量子计算|绝热量子计算机]]，基于[[量子退火]]（计算分解为初始[[哈密顿量（量子力学）|哈密顿量]]到最终哈密顿量的缓慢连续变换，其基态包含解）
<ref name="Das 2008 1061–1081">{{cite journal |first1=A. |last1=Das |first2=B. K. |last2=Chakrabarti |title=Quantum Annealing and Analog Quantum Computation | journal=[[Reviews of Modern Physics|Rev. Mod. Phys.]] |volume=80 |issue=3 |pages=1061–1081 |year=2008 |doi=10.1103/RevModPhys.80.1061 |bibcode=2008RvMP...80.1061D|citeseerx=10.1.1.563.9990 |arxiv=0801.2193 |s2cid=14255125 }}</ref>
<ref name="Das 2008 1061–1081">{{cite journal |first1=A. |last1=Das |first2=B. K. |last2=Chakrabarti |title=Quantum Annealing and Analog Quantum Computation | journal=[[Reviews of Modern Physics|Rev. Mod. Phys.]] |volume=80 |issue=3 |pages=1061–1081 |year=2008 |doi=10.1103/RevModPhys.80.1061 |bibcode=2008RvMP...80.1061D|citeseerx=10.1.1.563.9990 |arxiv=0801.2193 |s2cid=14255125 }}</ref>
*[[拓扑量子计算机]]<ref name="Nayaketal2008">{{cite journal
*[[拓扑量子计算机]]<ref name="Nayaketal2008">{{cite journal
|arxiv = 0707.1889
|arxiv = 0707.1889
}}</ref> (computation decomposed into the braiding of [[anyon]]s in a 2D lattice)
}}</ref> (computation decomposed into the braiding of [[anyon]]s in a 2D lattice)
相反，任何量子计算机可以解决的问题也可以用经典计算机来解决; 或者更正式地说，任何量子计算机都可以用图灵机来模拟。换句话说，就可计算性而言，量子计算机并不比传统计算机提供额外的能力。这意味着量子计算机不能解决不可判定的问题，例如停机问题，而且量子计算机的存在并不能否定'''丘奇-图灵论点Church–Turing thesis'''。
相反，任何量子计算机可以解决的问题也可以用经典计算机来解决; 或者更正式地说，任何量子计算机都可以用图灵机来模拟。换句话说，就可计算性而言，量子计算机并不比传统计算机提供额外的能力。这意味着量子计算机不能解决不可判定的问题，例如停机问题，而且量子计算机的存在并不能否定'''丘奇-图灵论点Church–Turing thesis'''。
[[量子图灵机]]理论上很重要，但是这个模型的物理实现是不可行的。所有四种计算模型被证明是等价的; 每种模型只需要不超过多项式的开销就可以模拟另一种模型。
[[量子图灵机]]理论上很重要，但是这个模型的物理实现是不可行的。所有四种计算模型被证明是等价的; 每种模型只需要不超过多项式的开销就可以模拟另一种模型。
到目前为止，量子计算机还不能满足强丘奇理论。虽然假想的机器已经被实现，但是通用的量子计算机还有待物理构造。切奇论点的更强版本需要一台物理计算机实体，因此现在没有量子计算机能够满足强丘奇理论。
到目前为止，量子计算机还不能满足强丘奇理论。虽然假想的机器已经被实现，但是通用的量子计算机还有待物理构造。切奇论点的更强版本需要一台物理计算机实体，因此现在没有量子计算机能够满足强丘奇理论。
=== Physical realizations 物理实现===
=== Physical realizations 物理实现===
对于量子计算机的物理实现，人们正在寻找许多不同的候选方案，其中包括（以实现量子比特的物理系统为区别）：
对于量子计算机的物理实现，人们正在寻找许多不同的候选方案，其中包括（以实现量子比特的物理系统为区别）：
*[[Superconducting quantum computing]]<ref name="ClarkeWilhelm2008">{{cite journal |last1=Clarke |first1=John |last2=Wilhelm |first2=Frank K. |title=Superconducting quantum bits |journal=Nature |date=18 June 2008 |volume=453 |issue=7198 |pages=1031–1042 |doi=10.1038/nature07128 |pmid=18563154 |bibcode=2008Natur.453.1031C |s2cid=125213662 |url=https://www.semanticscholar.org/paper/7ee1053ce63f33a62f2ea555547c514ce5f21054 }}</ref><ref>{{cite journal |last1=Kaminsky |first1=William M. |last2=Lloyd |first2=Seth |last3=Orlando |first3=Terry P. |title=Scalable Superconducting Architecture for Adiabatic Quantum Computation |arxiv=quant-ph/0403090 |date=12 March 2004 |bibcode=2004quant.ph..3090K }}</ref> (qubit implemented by the state of small superconducting circuits ([[Josephson junctions]])
*[[Superconducting quantum computing]]<ref name="ClarkeWilhelm2008">{{cite journal |last1=Clarke |first1=John |last2=Wilhelm |first2=Frank K. |title=Superconducting quantum bits |journal=Nature |date=18 June 2008 |volume=453 |issue=7198 |pages=1031–1042 |doi=10.1038/nature07128 |pmid=18563154 |bibcode=2008Natur.453.1031C |s2cid=125213662 |url=https://www.semanticscholar.org/paper/7ee1053ce63f33a62f2ea555547c514ce5f21054 }}</ref><ref>{{cite journal |last1=Kaminsky |first1=William M. |last2=Lloyd |first2=Seth |last3=Orlando |first3=Terry P. |title=Scalable Superconducting Architecture for Adiabatic Quantum Computation |arxiv=quant-ph/0403090 |date=12 March 2004 |bibcode=2004quant.ph..3090K }}</ref> (qubit implemented by the state of small superconducting circuits ([[Josephson junctions]])
*[[超导量子计算]]<ref name="ClarkeWilhelm2008">{{cite journal |last1=Clarke |first1=John |last2=Wilhelm |first2=Frank K. |title=Superconducting quantum bits |journal=Nature |date=18 June 2008 |volume=453 |issue=7198 |pages=1031–1042 |doi=10.1038/nature07128 |pmid=18563154 |bibcode=2008Natur.453.1031C |s2cid=125213662 |url=https://www.semanticscholar.org/paper/7ee1053ce63f33a62f2ea555547c514ce5f21054 }}</ref><ref>{{cite journal |last1=Kaminsky |first1=William M. |last2=Lloyd |first2=Seth |last3=Orlando |first3=Terry P. |title=Scalable Superconducting Architecture for Adiabatic Quantum Computation |arxiv=quant-ph/0403090 |date=12 March 2004 |bibcode=2004quant.ph..3090K }}</ref>（由小型超导电路状态实现的量子比特（[[约瑟夫森结]])
*[[超导量子计算]]<ref name="ClarkeWilhelm2008">{{cite journal |last1=Clarke |first1=John |last2=Wilhelm |first2=Frank K. |title=Superconducting quantum bits |journal=Nature |date=18 June 2008 |volume=453 |issue=7198 |pages=1031–1042 |doi=10.1038/nature07128 |pmid=18563154 |bibcode=2008Natur.453.1031C |s2cid=125213662 |url=https://www.semanticscholar.org/paper/7ee1053ce63f33a62f2ea555547c514ce5f21054 }}</ref><ref>{{cite journal |last1=Kaminsky |first1=William M. |last2=Lloyd |first2=Seth |last3=Orlando |first3=Terry P. |title=Scalable Superconducting Architecture for Adiabatic Quantum Computation |arxiv=quant-ph/0403090 |date=12 March 2004 |bibcode=2004quant.ph..3090K }}</ref>（由小型超导电路状态实现的量子比特（[[约瑟夫森结]])
< ! -- 量子计算机的能力和极限 -- >
< ! -- 量子计算机的能力和极限 -- >
*[[束缚离子量子计算机]]（由束缚离子的内部状态实现的量子比特）
*[[束缚离子量子计算机]]（由束缚离子的内部状态实现的量子比特）
虽然量子计算机不能解决任何传统计算机已经不能解决的问题，人们怀疑它们能比传统计算机更快地解决许多问题。例如，众所周知量子计算机可以高效地对整数进行因子分解，而经典计算机则不然。可是，量子计算机加速经典算法的能力具有严格的上限，绝大多数经典计算不能被量子计算机加速。
虽然量子计算机不能解决任何传统计算机已经不能解决的问题，人们怀疑它们能比传统计算机更快地解决许多问题。例如，众所周知量子计算机可以高效地对整数进行因子分解，而经典计算机则不然。可是，量子计算机加速经典算法的能力具有严格的上限，绝大多数经典计算不能被量子计算机加速。
*[[光学晶格]]s中的中性原子（由被困在光学晶格中的中性原子的内部状态实现的量子比特）<ref>{{Cite journal|last1=Khazali|first1=Mohammadsadegh|last2=Mølmer|first2=Klaus|date=2020-06-11|title=Fast Multiqubit Gates by Adiabatic Evolution in Interacting Excited-State Manifolds of Rydberg Atoms and Superconducting Circuits|journal=Physical Review X|volume=10|issue=2|pages=021054|doi=10.1103/PhysRevX.10.021054|bibcode=2020PhRvX..10b1054K|doi-access=free}}</ref><ref>{{Cite journal|last1=Henriet|first1=Loic|last2=Beguin|first2=Lucas|last3=Signoles|first3=Adrien|last4=Lahaye|first4=Thierry|last5=Browaeys|first5=Antoine|last6=Reymond|first6=Georges-Olivier|last7=Jurczak|first7=Christophe|date=2020-06-22|title=Quantum computing with neutral atoms|journal=Quantum|volume=4|page=327|doi=10.22331/q-2020-09-21-327|arxiv=2006.12326|s2cid=219966169}}</ref>
*[[光学晶格]]s中的中性原子（由被困在光学晶格中的中性原子的内部状态实现的量子比特）<ref>{{Cite journal|last1=Khazali|first1=Mohammadsadegh|last2=Mølmer|first2=Klaus|date=2020-06-11|title=Fast Multiqubit Gates by Adiabatic Evolution in Interacting Excited-State Manifolds of Rydberg Atoms and Superconducting Circuits|journal=Physical Review X|volume=10|issue=2|pages=021054|doi=10.1103/PhysRevX.10.021054|bibcode=2020PhRvX..10b1054K|doi-access=free}}</ref><ref>{{Cite journal|last1=Henriet|first1=Loic|last2=Beguin|first2=Lucas|last3=Signoles|first3=Adrien|last4=Lahaye|first4=Thierry|last5=Browaeys|first5=Antoine|last6=Reymond|first6=Georges-Olivier|last7=Jurczak|first7=Christophe|date=2020-06-22|title=Quantum computing with neutral atoms|journal=Quantum|volume=4|page=327|doi=10.22331/q-2020-09-21-327|arxiv=2006.12326|s2cid=219966169}}</ref>
*[[量子点]]计算机，基于自旋（例如[[Divencenzo损失差额量子计算机]]<ref>{{cite journal |last1=Imamog¯lu |first1=A. |last2=Awschalom |first2=D. D. |last3=Burkard |first3=G. |last4=DiVincenzo |first4=D. P. |last5=Loss |first5=D. |last6=Sherwin |first6=M. |last7=Small |first7=A. |title=Quantum Information Processing Using Quantum Dot Spins and Cavity QED |journal=Physical Review Letters |date=15 November 1999 |volume=83 |issue=20 |pages=4204–4207 |doi=10.1103/PhysRevLett.83.4204 |bibcode=1999PhRvL..83.4204I |arxiv=quant-ph/9904096 |s2cid=18324734 }}</ref>)（量子比特由俘获电子的自旋态给出）
*[[量子点]]计算机，基于自旋（例如[[Divencenzo损失差额量子计算机]]<ref>{{cite journal |last1=Imamog¯lu |first1=A. |last2=Awschalom |first2=D. D. |last3=Burkard |first3=G. |last4=DiVincenzo |first4=D. P. |last5=Loss |first5=D. |last6=Sherwin |first6=M. |last7=Small |first7=A. |title=Quantum Information Processing Using Quantum Dot Spins and Cavity QED |journal=Physical Review Letters |date=15 November 1999 |volume=83 |issue=20 |pages=4204–4207 |doi=10.1103/PhysRevLett.83.4204 |bibcode=1999PhRvL..83.4204I |arxiv=quant-ph/9904096 |s2cid=18324734 }}</ref>)（量子比特由俘获电子的自旋态给出）
< ! -- BQP 的基本定义 -- >
< ! -- BQP 的基本定义 -- >
*基于空间的量子点计算机（由双量子点中的电子位置给出的量子比特）<ref>{{cite journal |last1=Fedichkin |first1=L. |last2=Yanchenko |first2=M. |last3=Valiev |first3=K. A. |title=Novel coherent quantum bit using spatial quantization levels in semiconductor quantum dot |journal=Quantum Computers and Computing |date=June 2000 |volume=1 |page=58 |bibcode=2000quant.ph..6097F |arxiv=quant-ph/0006097 }}</ref>
*基于空间的量子点计算机（由双量子点中的电子位置给出的量子比特）<ref>{{cite journal |last1=Fedichkin |first1=L. |last2=Yanchenko |first2=M. |last3=Valiev |first3=K. A. |title=Novel coherent quantum bit using spatial quantization levels in semiconductor quantum dot |journal=Quantum Computers and Computing |date=June 2000 |volume=1 |page=58 |bibcode=2000quant.ph..6097F |arxiv=quant-ph/0006097 }}</ref>
误差有界的量子计算机能高效解决的一类问题称为'''BQP'''，即“有界误差，量子，多项式时间”。更正式地说，'''BQP'''是一类可以用多项式时间量子图灵机求解（其错误概率最大为1/3）的问题。作为一类概率问题，'''BQP'''是'''BPP'''（“有界误差，概率，多项式时间”）的量子对应物，BPP是一类可由误差有界的多项式时间概率图灵机求解的问题。众所周知，BPP<math>\subseteq</math>BQP，并被广泛怀疑为BQP<math>\nsubseteq</math>BPP，这直观地意味着量子计算机在时间复杂度方面比经典计算机更强大。
误差有界的量子计算机能高效解决的一类问题称为'''BQP'''，即“有界误差，量子，多项式时间”。更正式地说，'''BQP'''是一类可以用多项式时间量子图灵机求解（其错误概率最大为1/3）的问题。作为一类概率问题，'''BQP'''是'''BPP'''（“有界误差，概率，多项式时间”）的量子对应物，BPP是一类可由误差有界的多项式时间概率图灵机求解的问题。众所周知，BPP<math>\subseteq</math>BQP，并被广泛怀疑为BQP<math>\nsubseteq</math>BPP，这直观地意味着量子计算机在时间复杂度方面比经典计算机更强大。
*使用工程量子阱进行量子计算，原则上可以建造在室温下工作的量子计算机<ref>{{cite journal |last1=Ivády |first1=Viktor |last2=Davidsson |first2=Joel |last3=Delegan |first3=Nazar |last4=Falk |first4=Abram L. |last5=Klimov |first5=Paul V. |last6=Whiteley |first6=Samuel J. |last7=Hruszkewycz |first7=Stephan O. |last8=Holt |first8=Martin V. |last9=Heremans |first9=F. Joseph |last10=Son |first10=Nguyen Tien |last11=Awschalom |first11=David D. |last12=Abrikosov |first12=Igor A. |last13=Gali |first13=Adam |title=Stabilization of point-defect spin qubits by quantum wells |journal=Nature Communications |date=6 December 2019 |volume=10 |issue=1 |page=5607 |doi=10.1038/s41467-019-13495-6 |pmid=31811137 |pmc=6898666 |arxiv=1905.11801 |bibcode=2019NatCo..10.5607I }}</ref><ref>{{cite news |title=Scientists Discover New Way to Get Quantum Computing to Work at Room Temperature |url=https://interestingengineering.com/scientists-discover-new-way-to-get-quantum-computing-to-work-at-room-temperature |work=interestingengineering.com |date=24 April 2020 }}</ref>
*使用工程量子阱进行量子计算，原则上可以建造在室温下工作的量子计算机<ref>{{cite journal |last1=Ivády |first1=Viktor |last2=Davidsson |first2=Joel |last3=Delegan |first3=Nazar |last4=Falk |first4=Abram L. |last5=Klimov |first5=Paul V. |last6=Whiteley |first6=Samuel J. |last7=Hruszkewycz |first7=Stephan O. |last8=Holt |first8=Martin V. |last9=Heremans |first9=F. Joseph |last10=Son |first10=Nguyen Tien |last11=Awschalom |first11=David D. |last12=Abrikosov |first12=Igor A. |last13=Gali |first13=Adam |title=Stabilization of point-defect spin qubits by quantum wells |journal=Nature Communications |date=6 December 2019 |volume=10 |issue=1 |page=5607 |doi=10.1038/s41467-019-13495-6 |pmid=31811137 |pmc=6898666 |arxiv=1905.11801 |bibcode=2019NatCo..10.5607I }}</ref><ref>{{cite news |title=Scientists Discover New Way to Get Quantum Computing to Work at Room Temperature |url=https://interestingengineering.com/scientists-discover-new-way-to-get-quantum-computing-to-work-at-room-temperature |work=interestingengineering.com |date=24 April 2020 }}</ref>
*耦合的[[量子线|量子线]]（量子比特由一对量子线实现，量子线通过一对量子线耦合[[量子点接触|量子点接触]]）<ref>{{cite journal |last1=Bertoni |first1=A. |last2=Bordone |first2=P. |last3=Brunetti |first3=R. |last4=Jacoboni |first4=C. |last5=Reggiani |first5=S. |title=Quantum Logic Gates based on Coherent Electron Transport in Quantum Wires |journal=Physical Review Letters |date=19 June 2000 |volume=84 |issue=25 |pages=5912–5915 |doi=10.1103/PhysRevLett.84.5912 |pmid=10991086 |bibcode=2000PhRvL..84.5912B |hdl=11380/303796|hdl-access=free }}</ref><ref>{{cite journal |last1=Ionicioiu |first1=Radu |last2=Amaratunga |first2=Gehan |last3=Udrea |first3=Florin |title=Quantum Computation with Ballistic Electrons |journal=International Journal of Modern Physics B |date=20 January 2001 |volume=15 |issue=2 |pages=125–133 |doi=10.1142/S0217979201003521 |arxiv=quant-ph/0011051 |bibcode=2001IJMPB..15..125I |citeseerx=10.1.1.251.9617 |s2cid=119389613 }}</ref><ref>{{cite journal |last1=Ramamoorthy |first1=A |last2=Bird |first2=J P |last3=Reno |first3=J L |title=Using split-gate structures to explore the implementation of a coupled-electron-waveguide qubit scheme |journal=Journal of Physics: Condensed Matter |date=11 July 2007 |volume=19 |issue=27 |pages=276205 |doi=10.1088/0953-8984/19/27/276205 |bibcode=2007JPCM...19A6205R }}</ref>
*耦合的[[量子线|量子线]]（量子比特由一对量子线实现，量子线通过一对量子线耦合[[量子点接触|量子点接触]]）<ref>{{cite journal |last1=Bertoni |first1=A. |last2=Bordone |first2=P. |last3=Brunetti |first3=R. |last4=Jacoboni |first4=C. |last5=Reggiani |first5=S. |title=Quantum Logic Gates based on Coherent Electron Transport in Quantum Wires |journal=Physical Review Letters |date=19 June 2000 |volume=84 |issue=25 |pages=5912–5915 |doi=10.1103/PhysRevLett.84.5912 |pmid=10991086 |bibcode=2000PhRvL..84.5912B |hdl=11380/303796|hdl-access=free }}</ref><ref>{{cite journal |last1=Ionicioiu |first1=Radu |last2=Amaratunga |first2=Gehan |last3=Udrea |first3=Florin |title=Quantum Computation with Ballistic Electrons |journal=International Journal of Modern Physics B |date=20 January 2001 |volume=15 |issue=2 |pages=125–133 |doi=10.1142/S0217979201003521 |arxiv=quant-ph/0011051 |bibcode=2001IJMPB..15..125I |citeseerx=10.1.1.251.9617 |s2cid=119389613 }}</ref><ref>{{cite journal |last1=Ramamoorthy |first1=A |last2=Bird |first2=J P |last3=Reno |first3=J L |title=Using split-gate structures to explore the implementation of a coupled-electron-waveguide qubit scheme |journal=Journal of Physics: Condensed Matter |date=11 July 2007 |volume=19 |issue=27 |pages=276205 |doi=10.1088/0953-8984/19/27/276205 |bibcode=2007JPCM...19A6205R }}</ref>
< ! -- BQP 与基本复杂类的关系 -- >
< ! -- BQP 与基本复杂类的关系 -- >
*[[核磁共振量子计算机]]（NMRQC）利用溶液中分子的[[核磁共振]]来实现，其中量子比特由溶解分子中的[[核自旋]]s提供，并被无线电波探测
*[[核磁共振量子计算机]]（NMRQC）利用溶液中分子的[[核磁共振]]来实现，其中量子比特由溶解分子中的[[核自旋]]s提供，并被无线电波探测
BQP 与几个经典复杂性类的可疑关系。
BQP 与几个经典复杂性类的可疑关系。
*固态NMR[[Kane量子计算机]]s（由[[磷]][[电子供体|供体]]在[[硅]]中的核自旋态实现的量子比特）
*固态NMR[[Kane量子计算机]]s（由[[磷]][[电子供体|供体]]在[[硅]]中的核自旋态实现的量子比特）
BQP与P、NP和PSPACE的确切关系尚不清楚。然而，众所周知P<math>\subseteq</math>BQP<math>\subseteq</math>PSPACE，即所有能被确定性经典计算机高效解决的问题也能被量子计算机高效地解决，所有能被量子计算机有效解决的问题，也能用有多项式空间资源的确定性经典计算机来求解。人们进一步怀疑BQP是P的严格超集，这意味着一些问题能被量子计算机有效地解决，但无法靠确定性经典计算机有效地解决。例如，整数因式分解和离散对数问题属于BQP，但被怀疑不属于P。关于BQP与NP的关系，除了知道一些NP问题不在P中但在BQP中（比如整数因式分解和离散对数问题都属于NP）之外，人们知之甚少。有人怀疑NP<math>\nsubseteq</math>BQP；也就是说，人们相信存在着量子计算机无法有效解决的有效可检查问题。作为这种观点的直接结果，人们还怀疑BQP与NP完全问题类不相交（如果一个NP完全问题在BQP中，那么从<font color="#32CD32">NP困难问题NP-hardness'''可以看出NP中的所有问题都在BQP中）。
BQP与P、NP和PSPACE的确切关系尚不清楚。然而，众所周知P<math>\subseteq</math>BQP<math>\subseteq</math>PSPACE，即所有能被确定性经典计算机高效解决的问题也能被量子计算机高效地解决，所有能被量子计算机有效解决的问题，也能用有多项式空间资源的确定性经典计算机来求解。人们进一步怀疑BQP是P的严格超集，这意味着一些问题能被量子计算机有效地解决，但无法靠确定性经典计算机有效地解决。例如，整数因式分解和离散对数问题属于BQP，但被怀疑不属于P。关于BQP与NP的关系，除了知道一些NP问题不在P中但在BQP中（比如整数因式分解和离散对数问题都属于NP）之外，人们知之甚少。有人怀疑NP<math>\nsubseteq</math>BQP；也就是说，人们相信存在着量子计算机无法有效解决的有效可检查问题。作为这种观点的直接结果，人们还怀疑BQP与NP完全问题类不相交（如果一个NP完全问题在BQP中，那么从NP困难问题NP-hardness'''可以看出NP中的所有问题都在BQP中）。
*量子计算机上的电子（量子比特是电子的自旋）
*量子计算机上的电子（量子比特是电子的自旋）
*[[腔量子电动力学]]（CQED）（由与高精细腔耦合的被俘获原子的内部状态提供的量子比特）
*[[腔量子电动力学]]（CQED）（由与高精细腔耦合的被俘获原子的内部状态提供的量子比特）
< ! -- 本质复杂性类的关系总结 -- >
< ! -- 本质复杂性类的关系总结 -- >
*[[单分子磁体|分子磁体]]（量子比特由自旋态给出）<ref>{{cite journal |last1=Leuenberger |first1=Michael N. |last2=Loss |first2=Daniel |title=Quantum computing in molecular magnets |journal=Nature |date=April 2001 |volume=410 |issue=6830 |pages=789–793 |doi=10.1038/35071024 |pmid=11298441 |arxiv=cond-mat/0011415 |bibcode=2001Natur.410..789L |s2cid=4373008 }}</ref>
*[[单分子磁体|分子磁体]]（量子比特由自旋态给出）<ref>{{cite journal |last1=Leuenberger |first1=Michael N. |last2=Loss |first2=Daniel |title=Quantum computing in molecular magnets |journal=Nature |date=April 2001 |volume=410 |issue=6830 |pages=789–793 |doi=10.1038/35071024 |pmid=11298441 |arxiv=cond-mat/0011415 |bibcode=2001Natur.410..789L |s2cid=4373008 }}</ref>
BQP 与基本经典复杂性类的关系可以概括如下:
BQP 与基本经典复杂性类的关系可以概括如下:
*基于[[富勒烯]]的[[电子顺磁共振| ESR]]<ref>{{cite journal |last1=Harneit |first1=Wolfgang |title=Fullerene-based electron-spin quantum computer |journal= Physical Review A|date=27 February 2002 |volume=65 |issue=3 |page=032322 |doi=10.1103/PhysRevA.65.032322 |bibcode=2002PhRvA..65c2322H }}https://www.researchgate.net/publication/257976907_Fullerene-based_electron-spin_quantum_computer</ref>量子计算机（基于[[内表面富勒烯|被富勒烯包围的原子或分子的电子自旋的量子比特]）
*基于[[富勒烯]]的[[电子顺磁共振| ESR]]<ref>{{cite journal |last1=Harneit |first1=Wolfgang |title=Fullerene-based electron-spin quantum computer |journal= Physical Review A|date=27 February 2002 |volume=65 |issue=3 |page=032322 |doi=10.1103/PhysRevA.65.032322 |bibcode=2002PhRvA..65c2322H }}https://www.researchgate.net/publication/257976907_Fullerene-based_electron-spin_quantum_computer</ref>量子计算机（基于[[内表面富勒烯|被富勒烯包围的原子或分子的电子自旋的量子比特]）
<math>\mathsf{P \subseteq BPP \subseteq BQP \subseteq PP \subseteq PSPACE}</math>
<math>\mathsf{P \subseteq BPP \subseteq BQP \subseteq PP \subseteq PSPACE}</math>
{ p subseteq BPP subseteq subseteq PP subseteq PSPACE } </math >
{ p subseteq BPP subseteq subseteq PP subseteq PSPACE } </math >
*[[光学量子计算|非线性光学量子计算机]]（通过线性和[[非线性光学|非线性]]元件处理光的不同[[正常模式|模式]]状态实现的量子比特）<ref name="qc1988">K. Igeta and Y. Yamamoto. "Quantum mechanical computers with single atom and photon fields." International Quantum Electronics Conference (1988) https://www.osapublishing.org/abstract.cfm?uri=IQEC-1988-TuI4</ref><ref name="chuang1995">I.L. Chuang and Y. Yamamoto. "Simple quantum computer." Physical Review A 52, 5, 3489 (1995) https://doi.org/10.1103/PhysRevA.52.3489</ref>
*[[光学量子计算|非线性光学量子计算机]]（通过线性和[[非线性光学|非线性]]元件处理光的不同[[正常模式|模式]]状态实现的量子比特）<ref name="qc1988">K. Igeta and Y. Yamamoto. "Quantum mechanical computers with single atom and photon fields." International Quantum Electronics Conference (1988) https://www.osapublishing.org/abstract.cfm?uri=IQEC-1988-TuI4</ref><ref name="chuang1995">I.L. Chuang and Y. Yamamoto. "Simple quantum computer." Physical Review A 52, 5, 3489 (1995) https://doi.org/10.1103/PhysRevA.52.3489</ref>
众所周知，BQP属于复杂性类P（或者更准确地说，属于决策问题类P<sup>#P</sup>的相关类），量子引力理论，如M理论和环路量子引力，可以使计算机的速度更快。然而，由于时间问题，在这些理论中定义计算是一个未解决问题；也就是说，在这些物理理论中，目前没有明显的方法来描述观察者在一个时间点向计算机提交输入，然后在以后的时间点接收输出意味着什么。
众所周知，BQP属于复杂性类P（或者更准确地说，属于决策问题类P<sup>#P</sup>的相关类），量子引力理论，如M理论和环路量子引力，可以使计算机的速度更快。然而，由于时间问题，在这些理论中定义计算是一个未解决问题；也就是说，在这些物理理论中，目前没有明显的方法来描述观察者在一个时间点向计算机提交输入，然后在以后的时间点接收输出意味着什么。
*[[线性光学量子计算|线性光学量子计算机]]（通过线性元件（如反射镜、[[分束器]]和[[相移模块|移相器]]处理光的不同[[正常模式|模式]]状态实现的量子比特）<ref name="KLM2001">{{cite journal |last1=Knill |first1=G. J. |last2=Laflamme |last3=Milburn |title=A scheme for efficient quantum computation with linear optics |journal=Nature |year=2001 |volume=409 |doi=10.1038/35051009 |bibcode = 2001Natur.409...46K |first2=R. |first3=G. J. |issue=6816 |pmid=11343107 |pages=46–52 |s2cid=4362012 |url=https://www.semanticscholar.org/paper/054b680165a7325569ca6e63028ca9cee7f3ac9a }}</ref>
*[[线性光学量子计算|线性光学量子计算机]]（通过线性元件（如反射镜、[[分束器]]和[[相移模块|移相器]]处理光的不同[[正常模式|模式]]状态实现的量子比特）<ref name="KLM2001">{{cite journal |last1=Knill |first1=G. J. |last2=Laflamme |last3=Milburn |title=A scheme for efficient quantum computation with linear optics |journal=Nature |year=2001 |volume=409 |doi=10.1038/35051009 |bibcode = 2001Natur.409...46K |first2=R. |first3=G. J. |issue=6816 |pmid=11343107 |pages=46–52 |s2cid=4362012 |url=https://www.semanticscholar.org/paper/054b680165a7325569ca6e63028ca9cee7f3ac9a }}</ref>
*[[金刚石量子计算机]]<ref name="Nizovtsevetal2004">{{cite journal
*[[金刚石量子计算机]]<ref name="Nizovtsevetal2004">{{cite journal
|journal = Optics and Spectroscopy
|journal = Optics and Spectroscopy
< ! -- 新链接请按字母顺序排列 -- >
< ! -- 新链接请按字母顺序排列 -- >
}}</ref> (qubit realized by the electronic or nuclear spin of [[nitrogen-vacancy center]]s in diamond)
}}</ref> (qubit realized by the electronic or nuclear spin of [[nitrogen-vacancy center]]s in diamond)
*基于[[玻色-爱因斯坦凝聚体|玻色-爱因斯坦凝聚体]]的量子计算机<ref>{{cite journal |last1=Anderlini |first1=Marco |last2=Lee |first2=Patricia J. |last3=Brown |first3=Benjamin L. |last4=Sebby-Strabley |first4=Jennifer |last5=Phillips |first5=William D. |last6=Porto |first6=J. V. |title=Controlled exchange interaction between pairs of neutral atoms in an optical lattice |journal=Nature |date=July 2007 |volume=448 |issue=7152 |pages=452–456 |doi=10.1038/nature06011 |pmid=17653187 |lay-url=https://www.nist.gov/news-events/news/2007/07/thousands-atoms-swap-spins-partners-quantum-square-dance |arxiv=0708.2073 |bibcode=2007Natur.448..452A |s2cid=4410355 }}</ref>
*基于[[玻色-爱因斯坦凝聚体|玻色-爱因斯坦凝聚体]]的量子计算机<ref>{{cite journal |last1=Anderlini |first1=Marco |last2=Lee |first2=Patricia J. |last3=Brown |first3=Benjamin L. |last4=Sebby-Strabley |first4=Jennifer |last5=Phillips |first5=William D. |last6=Porto |first6=J. V. |title=Controlled exchange interaction between pairs of neutral atoms in an optical lattice |journal=Nature |date=July 2007 |volume=448 |issue=7152 |pages=452–456 |doi=10.1038/nature06011 |pmid=17653187 |lay-url=https://www.nist.gov/news-events/news/2007/07/thousands-atoms-swap-spins-partners-quantum-square-dance |arxiv=0708.2073 |bibcode=2007Natur.448..452A |s2cid=4410355 }}</ref>
*基于晶体管的量子计算机——使用静电阱夹带正空穴的串量子计算机
*基于晶体管的量子计算机——使用静电阱夹带正空穴的串量子计算机
*稀土金属离子掺杂无机晶体量子计算机<ref name="Ohlsson2002">{{cite journal
*稀土金属离子掺杂无机晶体量子计算机<ref name="Ohlsson2002">{{cite journal
|journal = Opt. Commun.
|journal = Opt. Commun.
}}</ref> (qubit realized by the internal electronic state of [[dopant]]s in [[optical fiber]]s)
}}</ref> (qubit realized by the internal electronic state of [[dopant]]s in [[optical fiber]]s)
*基于类金属碳纳米球的量子计算机<ref name="Nafradi2016">{{cite journal |last1=Náfrádi |first1=Bálint |last2=Choucair |first2=Mohammad |last3=Dinse |first3=Klaus-Peter |last4=Forró |first4=László |title=Room temperature manipulation of long lifetime spins in metallic-like carbon nanospheres |journal=Nature Communications |date=18 July 2016 |volume=7 |issue=1 |page=12232 |doi=10.1038/ncomms12232 |pmid=27426851 |pmc=4960311 |arxiv=1611.07690 |bibcode=2016NatCo...712232N }}</ref>
*基于类金属碳纳米球的量子计算机<ref name="Nafradi2016">{{cite journal |last1=Náfrádi |first1=Bálint |last2=Choucair |first2=Mohammad |last3=Dinse |first3=Klaus-Peter |last4=Forró |first4=László |title=Room temperature manipulation of long lifetime spins in metallic-like carbon nanospheres |journal=Nature Communications |date=18 July 2016 |volume=7 |issue=1 |page=12232 |doi=10.1038/ncomms12232 |pmid=27426851 |pmc=4960311 |arxiv=1611.07690 |bibcode=2016NatCo...712232N }}</ref>
大量的候选方案表明，尽管量子计算技术发展迅速，但仍处于初级阶段。{{citation needed|date=May 2020}}
大量的候选方案表明，尽管量子计算技术发展迅速，但仍处于初级阶段。{{citation needed|date=May 2020}}
==Relation to computability and complexity theory与可计算性和复杂性理论的关系==
==与可计算性和复杂性理论的关系==
===Computability theory可计算性理论===
===可计算性理论===
{{See also|Computability theory}}
{{See also|Computability theory}}
{{另见可计算性理论}}
{{另见可计算性理论}}
经典计算机可以解决的任何[[计算问题]]也可以由量子计算机解决。<ref>Nielsen, p. 29</ref>直觉上，这是因为人们相信，所有物理现象（包括经典计算机的运行），都可以用[[量子力学]]来描述，而这是量子计算机操作的基础。
经典计算机可以解决的任何[[计算问题]]也可以由量子计算机解决。<ref>Nielsen, p. 29</ref>直觉上，这是因为人们相信，所有物理现象（包括经典计算机的运行），都可以用[[量子力学]]来描述，而这是量子计算机操作的基础。
类别: 计算模型
类别: 计算模型
类别: 量子密码学
类别: 量子密码学
相反，量子计算机可以解决的任何问题也可以用经典计算机来解决；或者更正式地说，任何量子计算机都可以用[[图灵机]]<来模拟！--增加关于[[量子虚拟机]]的介绍，它可以在经典的量子计算机-->上模拟量子计算机。换句话说，量子计算机在[[可计算性]]方面没有比传统计算机多提供额外的优势。这意味着量子计算机不能解决像[[停止问题]]一样的[[不可判定问题]]，量子计算机的存在也并不能否定[[丘奇-图灵论点]]。
相反，量子计算机可以解决的任何问题也可以用经典计算机来解决；或者更正式地说，任何量子计算机都可以用[[图灵机]]<来模拟！--增加关于[[量子虚拟机]]的介绍，它可以在经典的量子计算机-->上模拟量子计算机。换句话说，量子计算机在[[可计算性]]方面没有比传统计算机多提供额外的优势。这意味着量子计算机不能解决像[[停止问题]]一样的[[不可判定问题]]，量子计算机的存在也并不能否定[[丘奇-图灵论点]]。
范畴: 信息论
范畴: 信息论
类别: 计算复杂性理论
类别: 计算复杂性理论
到目前为止，量子计算机还不能满足[[丘奇-图灵理论|强丘奇理论]]。虽然假想的机器已经实现，但一个通用的量子计算机还没有被物理构造出来。丘奇理论的强版本需要一台物理计算机实体，所以还没有一台量子计算机能够满足强大的丘奇理论。
到目前为止，量子计算机还不能满足[[丘奇-图灵理论|强丘奇理论]]。虽然假想的机器已经实现，但一个通用的量子计算机还没有被物理构造出来。丘奇理论的强版本需要一台物理计算机实体，所以还没有一台量子计算机能够满足强大的丘奇理论。
类别: 理论计算机科学
类别: 理论计算机科学