更改

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.   

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>

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}}   

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}}   

多量子比特系统的控制需要产生和协调大量的电信号，并且具有严格和确定的时序分辨率。这导致了[[量子控制器]]的发展，这种控制器可以连接量子比特。扩展这些系统以支持数量不断增长的量子比特是量子计算机扩展的另一个挑战。{{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===

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 T₂ (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.

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 T₂ (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.

构建量子计算机的最大挑战之一是控制或移除'''<font color="#ff8000"> 量子退相干Quantum decoherence</font>'''。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去中心化。然而，也存在其他的消相干源。例如'''<font color="#ff8000"> 量子门，晶格振动</font>'''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'''<font color="#ff8000"> 非酉Non-unitary</font>'''的，如果不能避免的话，通常应该高度控制。对于候选系统，尤其是横向弛豫时间T₂（对于核磁共振和核磁共振技术，也称为去相时间），在低温下通常在纳秒和秒之间。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，宇宙射线等电离辐射仍然可以导致某些系统在毫秒范围内发生衰变。

构建量子计算机的最大挑战之一是控制或消除'''<font color="#ff8000"> 量子退相干Quantum decoherence</font>'''。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'''<font color="#ff8000"> 量子门，晶格振动</font>'''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'''<font color="#ff8000"> 非酉Non-unitary</font>'''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T₂（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。

{{Main|Quantum decoherence}}

{{Main|Quantum decoherence}}

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.

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''₂ (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>

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''₂ (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>

建造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去中心化。然而，也存在其他的消相干源。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，因为它实际上是非幺正的，如果不能避免的话，通常是应该高度控制的。候选系统的退相干时间，特别是横向弛豫时间“T”₂（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”₂（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>

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.

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.

 

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 10⁻³, assuming the noise is depolarizing.

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 10⁻³, assuming the noise is depolarizing.

正如量子阈值定理所描述的那样，如果误差率足够小，人们认为可以利用量子误差修正来抑制误差和退相干。这使得总计算时间比消相干时间更长，如果纠错方案能够比消相干引入的误差更快地纠正误差。假设噪声是去极化的，容错计算中每个门所需的错误率经常被引用的数字是10⁻³。

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10⁻³。

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.

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.

这些问题对于光学方法来说更为困难，因为时间尺度短一个数量级，而克服这些问题的常用方法是光学[[脉冲成形]]。错误率通常与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。

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 L², 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 10⁴ bits without error correction. With error correction, the figure would rise to about 10⁷ bits. Computation time is about L² or about 10⁷ steps and at 1&nbsp;MHz, about 10 seconds.

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 L², 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 10⁴ bits without error correction. With error correction, the figure would rise to about 10⁷ bits. Computation time is about L² or about 10⁷ steps and at 1&nbsp;MHz, about 10 seconds.

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仍然是多项式的，并且被认为在L和L²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10⁴位没有纠错。通过纠错，这个数字将上升到大约10⁷位。计算时间约为L² 或约 10⁷步，在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L²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10⁴位没有纠错。通过纠错，这个数字将上升到大约10⁷位。计算时间约为L² 或约 10⁷步，在主频为1兆赫时，大约10秒。

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 10⁻³, assuming the noise is depolarizing.

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 10⁻³, assuming the noise is depolarizing.

如[[量子阈值定理]]所述，如果错误率足够小，则可以使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，则允许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^-3。

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^-3。

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.

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.

稳定性退相干问题的另一种不同的方法是用'''<font color="#ff8000"> 任意子、准粒子Anyons, Quasi-particles</font>'''作为线程，依靠'''<font color="#ff8000"> 辫子理论Braid theory</font>'''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'''<font color="#ff8000"> 任意子、准粒子Anyons, Quasi-particles</font>'''作为线程，依靠'''<font color="#ff8000"> 辫子理论Braid theory</font>'''形成稳定的逻辑门，创建一个拓扑量子计算机。

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''², 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 10⁴ bits without error correction.<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> With error correction, the figure would rise to about 10⁷ bits. Computation time is about ''L''² or about 10⁷ steps and at 1&nbsp;MHz, about 10 seconds.

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''², 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 10⁴ bits without error correction. With error correction, the figure would rise to about 10⁷ bits. Computation time is about ''L''² or about 10⁷ steps and at 1&nbsp;MHz, about 10 seconds.

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:

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.<ref>{{cite journal

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.

稳定退相干问题的一个非常不同的方法是用[[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

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

"So the number of continuous parameters describing the state of such a useful quantum computer at any given moment must be... about 10³⁰⁰... Could we ever learn to control the more than 10³⁰⁰ continuously variable parameters defining the quantum state of such a system? My answer is simple. No, never."

"So the number of continuous parameters describing the state of such a useful quantum computer at any given moment must be... about 10³⁰⁰... Could we ever learn to control the more than 10³⁰⁰ continuously variable parameters defining the quantum state of such a system? My answer is simple. No, never."

“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10³⁰⁰ ... ... 我们能否学会控制定义这样一个系统的量子态的超过10³⁰⁰ 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10³⁰⁰ ... ... 我们能否学会控制定义这样一个系统的量子态的超过10³⁰⁰ 个连续可变参数？我的答案很简单。不，永远不会。”

  | last1 = Freedman | first1 = Michael H. | author1-link = Michael Freedman

  | last1 = Freedman | first1 = Michael H. | author1-link = Michael Freedman

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.

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.

量子图灵机在理论上是重要的，但是这个模型的实际实施是不可行的。所有四种计算模型都被证明是等价的; 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。

  | pages = 31–38

  | pages = 31–38

:"So the number of continuous parameters describing the state of such a useful quantum computer at any given moment must be... about 10³⁰⁰... Could we ever learn to control the more than 10³⁰⁰ continuously variable parameters defining the quantum state of such a system? My answer is simple. ''No, never.''"<ref>{{cite web |last1=Dyakonov |first1=Mikhail |title=The Case Against Quantum Computing |url=https://spectrum.ieee.org/computing/hardware/the-case-against-quantum-computing |website=IEEE Spectrum |accessdate=3 December 2019}}</ref><ref>{{cite book |last1=Dyakonov |first1=Mikhail |title=Will We Ever Have a Quantum Computer? |date=24 March 2020 |url=https://www.springer.com/gp/book/9783030420185 |publisher=Springer |isbn=9783030420185 |accessdate=22 May 2020}}{{page needed|date=May 2020}}</ref>

:"So the number of continuous parameters describing the state of such a useful quantum computer at any given moment must be... about 10³⁰⁰... Could we ever learn to control the more than 10³⁰⁰ continuously variable parameters defining the quantum state of such a system? My answer is simple. ''No, never.''"<ref>{{cite web |last1=Dyakonov |first1=Mikhail |title=The Case Against Quantum Computing |url=https://spectrum.ieee.org/computing/hardware/the-case-against-quantum-computing |website=IEEE Spectrum |accessdate=3 December 2019}}</ref><ref>{{cite book |last1=Dyakonov |first1=Mikhail |title=Will We Ever Have a Quantum Computer? |date=24 March 2020 |url=https://www.springer.com/gp/book/9783030420185 |publisher=Springer |isbn=9783030420185 |accessdate=22 May 2020}}{{page needed|date=May 2020}}</ref>

：“因此，描述这种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10³⁰⁰... 我们能不能学会控制定义这样一个系统量子态的超过10³⁰⁰连续可变的参数？我的回答很简单“不，从来没有”。

：“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10³⁰⁰... 我们能不能学会控制定义这样一个系统量子态的超过10³⁰⁰个连续可变的参数？我的回答很简单“不，永远不会”。

== Developments 发展==

== Developments 发展==

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:

* [[quantum circuit|Quantum gate array]] (computation decomposed into a sequence of few-qubit [[quantum gate]]s)

* [[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]])

* [[One-way quantum computer]] (computation decomposed into a sequence of one-qubit measurements applied to a highly entangled initial state or [[cluster state]])

*[[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]]）

* [[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)<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>

* [[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)

*[[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）

* [[Topological quantum computer]]<ref name="Nayaketal2008">{{cite journal

* [[Topological quantum computer]]

*[[拓扑量子计算机]]<ref name="Nayaketal2008">{{cite journal

|arxiv = 0707.1889

|arxiv = 0707.1889

A large number of candidates demonstrates that quantum computing, despite rapid progress, is still in its infancy.

A large number of candidates demonstrates that quantum computing, despite rapid progress, is still in its infancy.

|last3 = Stern

|last3 = Stern

Any computational problem solvable by a classical computer is also solvable by a quantum computer. 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.

Any computational problem solvable by a classical computer is also solvable by a quantum computer. 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.

任何经典计算机可解的计算问题也可以用量子计算机来解。直观地说，这是因为人们相信所有的物理现象，包括经典计算机的运算，都可以用量子计算机运算的基础---- 量子力学来描述。

任何经典计算机可解的计算问题也可以用量子计算机来解。直观地说，这是因为人们相信所有的物理现象（包括经典计算机的运算），都可以用量子计算机运算的基础----量子力学来描述。

|issue = 3 |s2cid = 119628297

|issue = 3 |s2cid = 119628297

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.

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.

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，例如停机问题和量子计算机的存在并不能否定'''<font color="#ff8000"> 丘奇-图灵论点Church–Turing thesis</font>'''。

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'''<font color="#ff8000"> 丘奇-图灵论点Church–Turing thesis</font>'''。

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.

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.

[[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。所有四个计算模型都被证明是等价的；每一个都可以用不超过多项式的开销来模拟另一个。

[[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。

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.

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.

=== Physical realizations 物理实现===

=== Physical realizations 物理实现===

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.

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>

*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>

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.

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.

有界误差的量子计算机能有效地解决的一类问题称为<font color="#ff8000"> BQP</font>，即“有界误差，量子，多项式时间”。更正式地说，<font color="#ff8000"> BQP</font>是一类可以用多项式时间量子图灵机求解的问题，其错误概率最大为1/3。作为一类概率问题，<font color="#ff8000"> BQP</font>是<font color="#ff8000"> BPP</font>（“有界误差，概率，多项式时间”）的量子对应物，BPP是一类可由具有有界误差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性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<font color="#ff8000"> BQP</font>，即“有界误差，量子，多项式时间”。更正式地说，<font color="#ff8000"> BQP</font>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，<font color="#ff8000"> BQP</font>是<font color="#ff8000"> BPP</font>（“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。

*[[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

*[[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

*[[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，并用无线电波探测

*[[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

The suspected relationship of BQP to several classical complexity classes.

The suspected relationship of BQP to several classical complexity classes.

BQP 与几个经典复杂类的可疑关系。

BQP 与几个经典复杂性类的可疑关系。

*Solid-state NMR [[Kane quantum computer]]s (qubit realized by the nuclear spin state of [[phosphorus]] [[Electron donor|donors]] in [[silicon]])

*Solid-state NMR [[Kane quantum computer]]s (qubit realized by the nuclear spin state of [[phosphorus]] [[Electron donor|donors]] in [[silicon]])

*固态NMR[[Kane量子计算机]]s（由[[磷]][[电子施主|施主]]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）

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).

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).

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有效解决的问题也能被量子计算机有效地解决，所有能被量子计算机有效解决的问题，也能用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，这意味着量子计算机可以有效地解决一些问题，而确定性经典计算机却不能有效地解决这些问题。例如，整数因式分解和离散对数问题已知位于BQP中，并且被怀疑位于P之外。关于BQP与NP的关系，除了一些被认为不在P中的NP问题也在BQP中（整数因式分解和离散对数问题都在NP中）之外，人们知之甚少，例如），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硬度NP-hardness</font>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<font color="#32CD32">NP困难问题NP-hardness</font>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）

*[[Cavity quantum electrodynamics]] (CQED) (qubit provided by the internal state of trapped atoms coupled to high-finesse cavities)

*[[Cavity quantum electrodynamics]] (CQED) (qubit provided by the internal state of trapped atoms coupled to high-finesse cavities)

*[[腔量子电动力学]]（CQED）（由与高精细腔耦合的囚禁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）

<!-- Summary of relationship to essential complexity classes -->

<!-- Summary of relationship to essential complexity classes -->

It is also known that BQP is contained in the complexity class #P (or more precisely in the associated class of decision problems P^#P), 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.

It is also known that BQP is contained in the complexity class #P (or more precisely in the associated class of decision problems P^#P), 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.

众所周知，BQP包含在复杂性类P中（或者更准确地说，在相关的决策问题类P^#P）中，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开放的问题；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^#P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。

*[[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>

*[[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>

A large number of candidates demonstrates that quantum computing, despite rapid progress, is still in its infancy.{{citation needed|date=May 2020}}

A large number of candidates demonstrates that quantum computing, despite rapid progress, is still in its infancy.{{citation needed|date=May 2020}}

大量的候选者表明，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==

==Relation to computability and complexity theory与可计算性和复杂性理论的关系==

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.

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.

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，包括经典计算机的操作，都可以用[[量子力学]]来描述，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。

Category:Models of computation

Category:Models of computation

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>

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>

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]]方面没有比经典计算机更强大的能力。这意味着量子计算机不能解决[[不可判定的问题]]像[[停止问题]]一样，量子计算机的存在并不能反驳[[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]]。

Category:Information theory

Category:Information 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.

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.

到目前为止，量子计算机还不能满足[[丘奇-图灵理论|强大的教会理论]]。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，因此还没有一台量子计算机能够满足强大的教会理论。

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。

Category:Classes of computers

Category:Classes of computers