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The [[Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers.]]

The [[Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers.]]

[[布洛赫球体是量子计算机的基本构件——量子比特的表示。]]

[[布洛赫球体是量子计算机的基本构件——量子比特的表示模型。]]

A memory consisting of <math display="inline">n</math> bits of information has <math display="inline">2^n</math> possible states. A vector representing all memory states thus has <math display="inline">2^n</math> entries (one for each state). This vector is viewed as a probability vector and represents the fact that the memory is to be found in a particular state.

A memory consisting of <math display="inline">n</math> bits of information has <math display="inline">2^n</math> possible states. A vector representing all memory states thus has <math display="inline">2^n</math> entries (one for each state). This vector is viewed as a probability vector and represents the fact that the memory is to be found in a particular state.

一个由<math display="inline">n</math> 比特信息组成的内存有 <math display="inline">2^n</math> 种可能的状态。因此，一个代表所有内存状态的向量具有 <math display="inline">2^n</math> 个条目(每个状态一个)。这个向量被看作是一个概率向量，它表达这样一个事实——内存总是被发现处在一个特定的状态下。

一个由<math display="inline">n</math> 比特信息组成的内存有 <math display="inline">2^n</math> 种可能的状态。因此，一个代表所有内存状态的向量具有 <math display="inline">2^n</math> 个条目(每个状态一个)。这个向量被看作是一个概率向量，它代表这样一个事实——内存总是在某个特定的状态下被访问。

In quantum mechanics, probability vectors are generalized to density operators. This is the technically rigorous mathematical foundation for quantum logic gates, but the intermediate quantum state vector formalism is usually introduced first because it is conceptually simpler. This article focuses on the quantum state vector formalism for simplicity.

In quantum mechanics, probability vectors are generalized to density operators. This is the technically rigorous mathematical foundation for quantum logic gates, but the intermediate quantum state vector formalism is usually introduced first because it is conceptually simpler. This article focuses on the quantum state vector formalism for simplicity.

在<font color="#ff8000"> 量子力学</font>中，概率向量被推广到'''<font color="#ff8000"> 密度算子Density operators</font>'''。这是技术上严格的'''<font color="#ff8000"> 量子逻辑门的数学基础</font>'''，但中间量子态向量形式通常首先被介绍，因为它在概念上比较简单。为了简单起见，本文着重讨论量子态向量形式。

在<font color="#ff8000"> 量子力学</font>中，概率向量被推广到'''<font color="#ff8000"> 密度算子Density operators</font>'''。它是技术上严格的'''<font color="#ff8000"> 量子逻辑门的数学基础</font>'''，但介绍的时候通常首先引入中间量子态的向量形式，因为它在概念上比较简单。为了简单起见，本文着重讨论量子态向量形式。

We begin by considering a simple memory consisting of only one bit. This memory may be found in one of two states: the zero state or the one state. We may represent the state of this memory using Dirac notation so that

We begin by considering a simple memory consisting of only one bit. This memory may be found in one of two states: the zero state or the one state. We may represent the state of this memory using Dirac notation so that

我们首先考虑一个只包含一个位的简单内存。这种记忆可以在两种状态中的一种中找到: 零状态或一状态。我们可以用'''<font color="#ff8000"> 狄拉克符号Dirac notation</font>'''来表示这段记忆的状态，因此

我们首先考虑一个只有1位的简单内存。这种内存只有0或1两种状态。我们可以用'''<font color="#ff8000"> 狄拉克符号Dirac notation</font>'''来表示这段内存的状态，因此

<math display="block">

<math display="block">

A quantum memory may then be found in any quantum superposition <math display="inline">|\psi\rangle</math> of the two classical states <math display="inline">|0\rangle</math> and <math display="inline">|1\rangle</math>:

A quantum memory may then be found in any quantum superposition <math display="inline">|\psi\rangle</math> of the two classical states <math display="inline">|0\rangle</math> and <math display="inline">|1\rangle</math>:

一个量子内存可能会在任何一个经典状态下的量子态叠加原理中被发现:

一个量子内存可能处在两种经典状态的量子叠加态中的任意一种状态:

<math display="block">

<math display="block">

In general, the coefficients <math display="inline">\alpha</math> and <math display="inline">\beta</math> are complex numbers. In this scenario, one qubit of information is said to be encoded into the quantum memory. The state <math display="inline">|\psi\rangle</math> is not itself a probability vector but can be connected with a probability vector via a measurement operation. If the quantum memory is measured to determine if the state is <math display="inline">|0\rangle</math> or <math display="inline">|1\rangle</math> (this is known as a computational basis measurement), the zero state would be observed with probability <math display="inline">|\alpha|^2</math> and the one state with probability <math display="inline">|\beta|^2</math>. The numbers <math display="inline">\alpha</math> and <math display="inline">\beta</math> are called quantum amplitudes.

In general, the coefficients <math display="inline">\alpha</math> and <math display="inline">\beta</math> are complex numbers. In this scenario, one qubit of information is said to be encoded into the quantum memory. The state <math display="inline">|\psi\rangle</math> is not itself a probability vector but can be connected with a probability vector via a measurement operation. If the quantum memory is measured to determine if the state is <math display="inline">|0\rangle</math> or <math display="inline">|1\rangle</math> (this is known as a computational basis measurement), the zero state would be observed with probability <math display="inline">|\alpha|^2</math> and the one state with probability <math display="inline">|\beta|^2</math>. The numbers <math display="inline">\alpha</math> and <math display="inline">\beta</math> are called quantum amplitudes.

一般来说，系数 <math display="inline">\alpha</math> 和 <math display="inline">\beta</math>都是'''<font color="#ff8000"> 复数</font>'''。在这种情况下，一个量子比特的信息被称为被编码到量子存储器中。状态<math display="inline">|\psi\rangle</math>本身不是一个概率向量，但可以通过一个测量操作与一个概率向量相连。如果量子内存被测量以确定其状态是否为 <math display="inline">|0\rangle</math> 或<math display="inline">|1\rangle</math>(这被称为计算基础测量) ，那么零状态将被观察到概率 <math display="inline">|\alpha|^2</math>和概率 <math display="inline">|\beta|^2</math> 。数字 <math display="inline">\alpha</math> 和 <math display="inline">\beta</math>被称为'''<font color="#ff8000"> 量子幅值Quantum amplitudes</font>'''。

一般来说，系数 <math display="inline">\alpha</math> 和 <math display="inline">\beta</math>都是'''<font color="#ff8000"> 复数</font>'''。在这种情况下，信息的一个量子比特被编码到量子内存中。状态<math display="inline">|\psi\rangle</math>本身不是一个概率向量，但可以通过测量操作与概率向量相连。如果量子内存被测量以确定其状态是 <math display="inline">|0\rangle</math> 还是<math display="inline">|1\rangle</math>(这被称为计算基础测量) ，那么0状态将以概率 <math display="inline">|\alpha|^2</math>被观测到，而1状态将以概率 <math display="inline">|\beta|^2</math>被观测到。数字 <math display="inline">\alpha</math> 和 <math display="inline">\beta</math>被称为'''<font color="#ff8000"> 量子幅值Quantum amplitudes</font>'''。

The state of this one-qubit quantum memory can be manipulated by applying quantum logic gates, analogous to how classical memory can be manipulated with classical logic gates. One important gate for both classical and quantum computation is the NOT gate, which can be represented by a matrix

The state of this one-qubit quantum memory can be manipulated by applying quantum logic gates, analogous to how classical memory can be manipulated with classical logic gates. One important gate for both classical and quantum computation is the NOT gate, which can be represented by a matrix

这种单比特量子存储器的状态可以通过'''<font color="#ff8000"> 量子逻辑门</font>'''来控制，类似于用'''<font color="#ff8000"> 经典逻辑门</font>'''来控制经典存储器。对经典和量子计算都重要的一个门是'''<font color="#ff8000"> 非门NOT gate</font>'''，它可以用矩阵表示

这种单比特量子存储器的状态可以通过'''<font color="#ff8000"> 量子逻辑门</font>'''来控制，类似于用'''<font color="#ff8000"> 经典逻辑门</font>'''来控制经典存储器。对经典和量子计算都很重要的门是'''<font color="#ff8000"> 非门NOT gate</font>'''，它可以用矩阵表示

<math display="block">X := \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}.</math>

<math display="block">X := \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}.</math>

Mathematically, the application of such a logic gate to a quantum state vector is modelled with matrix multiplication. Thus <math display="inline">X|0\rangle = |1\rangle</math> and <math display="inline">X|1\rangle = |0\rangle</math>.

Mathematically, the application of such a logic gate to a quantum state vector is modelled with matrix multiplication. Thus <math display="inline">X|0\rangle = |1\rangle</math> and <math display="inline">X|1\rangle = |0\rangle</math>.

在数学上，这种逻辑门应用于'''<font color="#ff8000">量子态向量</font>'''是用矩阵乘法模型来建模的。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'''<font color="#ff8000">量子态向量</font>'''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>。

The mathematics of single qubit gates can be extended to operate on multiqubit quantum memories in two important ways. One way is simply to select a qubit and apply that gate to the target qubit whilst leaving the remainder of the memory unaffected. Another way is to apply the gate to its target only if another part of the memory is in a desired state. These two choices can be illustrated using another example. The possible states of a two-qubit quantum memory are

The mathematics of single qubit gates can be extended to operate on multiqubit quantum memories in two important ways. One way is simply to select a qubit and apply that gate to the target qubit whilst leaving the remainder of the memory unaffected. Another way is to apply the gate to its target only if another part of the memory is in a desired state. These two choices can be illustrated using another example. The possible states of a two-qubit quantum memory are

<math display="block">

<math display="block">

As a mathematical consequence of this definition, <math display="inline">CNOT|00\rangle = |00\rangle</math>, <math display="inline">CNOT|01\rangle = |01\rangle</math>, <math display="inline">CNOT|10\rangle = |11\rangle</math>, and <math display="inline">CNOT|11\rangle = |10\rangle</math>. In other words, the CNOT applies a NOT gate (<math display="inline">X</math> from before) to the second qubit if and only if the first qubit is in the state <math display="inline">|1\rangle</math>. If the first qubit is <math display="inline">|0\rangle</math>, nothing is done to either qubit.

As a mathematical consequence of this definition, <math display="inline">CNOT|00\rangle = |00\rangle</math>, <math display="inline">CNOT|01\rangle = |01\rangle</math>, <math display="inline">CNOT|10\rangle = |11\rangle</math>, and <math display="inline">CNOT|11\rangle = |10\rangle</math>. In other words, the CNOT applies a NOT gate (<math display="inline">X</math> from before) to the second qubit if and only if the first qubit is in the state <math display="inline">|1\rangle</math>. If the first qubit is <math display="inline">|0\rangle</math>, nothing is done to either qubit.

作为这个定义的数学推论，<math display="inline">CNOT|00\rangle = |00\rangle</math>, <math display="inline">CNOT|01\rangle = |01\rangle</math>, <math display="inline">CNOT|10\rangle = |11\rangle</math>, 和<math display="inline">CNOT|11\rangle = |10\rangle</math>。换句话说，当且仅当第一个量子位处于状态 <math display="inline">|1\rangle</math> 时，CNOT 对第二个量子位应用 非NOT 门(<math display="inline">X</math>)。如果第一个量子位是 <math display="inline">|0\rangle</math>，则对任何一个量子位都不做处理。

作为这个定义的数学推论，<math display="inline">CNOT|00\rangle = |00\rangle</math>, <math display="inline">CNOT|01\rangle = |01\rangle</math>, <math display="inline">CNOT|10\rangle = |11\rangle</math>, 和<math display="inline">CNOT|11\rangle = |10\rangle</math>。换句话说，当且仅当第一个量子位处于状态 <math display="inline">|1\rangle</math> 时，CNOT 才对第二个量子位应用 非门(<math display="inline">X</math>)。如果第一个量子位是 <math display="inline">|0\rangle</math>，则对任何一个量子位都不做处理。

In summary, a quantum computation can be described as a network of quantum logic gates and measurements. Any measurement can be deferred to the end of a quantum computation, though this deferment may come at a computational cost. Because of this possibility of deferring a measurement, most quantum circuits depict a network consisting only of quantum logic gates and no measurements. More information can be found in the following articles: universal quantum computer, Shor's algorithm, Grover's algorithm, Deutsch–Jozsa algorithm, amplitude amplification, quantum Fourier transform, quantum gate, quantum adiabatic algorithm and quantum error correction.

In summary, a quantum computation can be described as a network of quantum logic gates and measurements. Any measurement can be deferred to the end of a quantum computation, though this deferment may come at a computational cost. Because of this possibility of deferring a measurement, most quantum circuits depict a network consisting only of quantum logic gates and no measurements. More information can be found in the following articles: universal quantum computer, Shor's algorithm, Grover's algorithm, Deutsch–Jozsa algorithm, amplitude amplification, quantum Fourier transform, quantum gate, quantum adiabatic algorithm and quantum error correction.

总之，'''<font color="#ff8000"> 量子计算</font>'''可以描述为一个由量子逻辑门和测量组成的网络。任何测量都可以推迟到'''<font color="#ff8000"> 量子计算</font>'''结束时进行，尽管这种推迟可能会带来计算成本。由于这种延迟测量的可能性，大多数量子电路描述的网络只有量子逻辑门而没有测量。更多信息可以在以下文章中找到: '''<font color="#ff8000"> 通用量子计算机，Shor 算法，Grover 算法，Deutsch-Jozsa 算法，振幅放大，量子傅里叶变换Quantum Fourier transform，量子门，量子绝热算法和量子误差修正Quantum error correction</font>'''。

总之，'''<font color="#ff8000"> 量子计算</font>'''可以描述为一个由量子逻辑门和测量组成的网络。任何测量都可以推迟到'''<font color="#ff8000"> 量子计算</font>'''结束时进行，尽管这种推迟可能会带来计算成本。由于这种延迟测量的可能性，大多数量子电路描述的网络只有量子逻辑门而没有测量。更多信息可以参考以下文章: '''<font color="#ff8000"> 通用量子计算机，Shor 算法，Grover 算法，Deutsch-Jozsa 算法，振幅放大，量子傅里叶变换Quantum Fourier transform，量子门，量子绝热算法和量子误差修正Quantum error correction</font>'''。

Any quantum computation can be represented as a network of quantum logic gates from a fairly small family of gates. A choice of gate family that enables this construction is known as a universal gate set. One common such set includes all single-qubit gates as well as the CNOT gate from above. This means any quantum computation can be performed by executing a sequence of single-qubit gates together with CNOT gates. Though this gate set is infinite, it can be replaced with a finite gate set by appealing to the Solovay-Kitaev theorem. The representation of multiple qubits can be shown as Qsphere.  

Any quantum computation can be represented as a network of quantum logic gates from a fairly small family of gates. A choice of gate family that enables this construction is known as a universal gate set. One common such set includes all single-qubit gates as well as the CNOT gate from above. This means any quantum computation can be performed by executing a sequence of single-qubit gates together with CNOT gates. Though this gate set is infinite, it can be replaced with a finite gate set by appealing to the Solovay-Kitaev theorem. The representation of multiple qubits can be shown as Qsphere.  

任何'''<font color="#ff8000"> 量子计算</font>'''都可以表示为一个量子逻辑门网络，它来自一个相当小的量子门家族。使这种结构成为可能的门系列的选择被称为通用门系列。一个常见的这样的集合包括所有的单量子比特门以及上面的 量子受控非门CNOT 门。这意味着任何量子计算都可以通过执行一系列带有 <font color="#ff8000"> 量子受控非门CNOT 门</font>的单量子比特门来完成。虽然这个门集合是无限的，但是它可以通过引用 Solovay-Kitaev 定理用一个有限的门集合来代替。多个量子位的表示可以用 Qsphere 来表示。

任何'''<font color="#ff8000"> 量子计算</font>'''都可以表示为一个量子逻辑门网络，量子逻辑门是门中的一个小类。使这种结构成为可能的一类门的被称为通用门集合。常见的这种集合包括所有的单量子比特门以及上面的 量子受控非门CNOT 门。这意味着任何量子计算都可以通过执行一系列带有 <font color="#ff8000"> 量子受控非门CNOT 门</font>的单量子比特门来完成。虽然这个门集合是无限的，但是它可以通过引用 Solovay-Kitaev 定理被一个有限的门集合来代替。多个量子位可以用 Qsphere 来表示。

== Potential applications 潜在应用==

== Potential applications 潜在应用==

Integer factorization, which underpins the security of public key cryptographic systems, is believed to be computationally infeasible with an ordinary computer for large integers if they are the product of few prime numbers (e.g., products of two 300-digit primes). By comparison, a quantum computer could efficiently solve this problem using Shor's algorithm to find its factors. This ability would allow a quantum computer to break many of the cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for solving the problem. In particular, most of the popular public key ciphers are based on the difficulty of factoring integers or the discrete logarithm problem, both of which can be solved by Shor's algorithm. In particular, the RSA, Diffie–Hellman, and elliptic curve Diffie–Hellman algorithms could be broken. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security.

Integer factorization, which underpins the security of public key cryptographic systems, is believed to be computationally infeasible with an ordinary computer for large integers if they are the product of few prime numbers (e.g., products of two 300-digit primes). By comparison, a quantum computer could efficiently solve this problem using Shor's algorithm to find its factors. This ability would allow a quantum computer to break many of the cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for solving the problem. In particular, most of the popular public key ciphers are based on the difficulty of factoring integers or the discrete logarithm problem, both of which can be solved by Shor's algorithm. In particular, the RSA, Diffie–Hellman, and elliptic curve Diffie–Hellman algorithms could be broken. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security.

'''<font color="#ff8000"> 整数因式分解Integer factorization</font>'''是'''<font color="#ff8000"> 公钥密码系统Public key cryptographic systems</font>'''安全性的基础，如果大的整数是几个素数的乘积（例如，两个300位素数的乘积），那么在普通计算机上计算大整数是做不到的。相比之下，量子计算机可以有效地解决这个问题，使用'''<font color="#ff8000"> 肖尔Shor算法</font>'''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，在这个意义上，将有一个<font color="#ff8000">多项式时间（整数位数）算法</font>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整数的因式分解困难或离散对数问题，这两个问题都可以用'''<font color="#ff8000"> 肖尔Shor算法</font>'''来解决。特别是'''<font color="#ff8000"> RSA、Diffie-Hellman和椭圆曲线Diffie-Hellman算法</font>'''可能会被打破。它们用于保护安全网页、加密电子邮件和许多其他类型的数据。破坏这些将对电子隐私和安全产生重大影响。

'''<font color="#ff8000"> 整数因式分解Integer factorization</font>'''是'''<font color="#ff8000"> 公钥密码系统Public key cryptographic systems</font>'''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），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'''<font color="#ff8000"> 肖尔Shor算法</font>'''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</font>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'''<font color="#ff8000"> 肖尔Shor算法</font>'''来解决。尤其是'''<font color="#ff8000"> RSA、Diffie-Hellman和椭圆曲线Diffie-Hellman算法</font>'''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。

However, other cryptographic algorithms do not appear to be broken by those algorithms. Some public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to which Shor's algorithm applies, like the McEliece cryptosystem based on a problem in coding theory. Lattice-based cryptosystems are also not known to be broken by quantum computers, and finding a polynomial time algorithm for solving the dihedral hidden subgroup problem, which would break many lattice based cryptosystems, is a well-studied open problem. It has been proven that applying Grover's algorithm to break a symmetric (secret key) algorithm by brute force requires time equal to roughly 2^n/2 invocations of the underlying cryptographic algorithm, compared with roughly 2ⁿ in the classical case, meaning that symmetric key lengths are effectively halved: AES-256 would have the same security against an attack using Grover's algorithm that AES-128 has against classical brute-force search (see Key size).

However, other cryptographic algorithms do not appear to be broken by those algorithms. Some public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to which Shor's algorithm applies, like the McEliece cryptosystem based on a problem in coding theory. Lattice-based cryptosystems are also not known to be broken by quantum computers, and finding a polynomial time algorithm for solving the dihedral hidden subgroup problem, which would break many lattice based cryptosystems, is a well-studied open problem. It has been proven that applying Grover's algorithm to break a symmetric (secret key) algorithm by brute force requires time equal to roughly 2^n/2 invocations of the underlying cryptographic algorithm, compared with roughly 2ⁿ in the classical case, meaning that symmetric key lengths are effectively halved: AES-256 would have the same security against an attack using Grover's algorithm that AES-128 has against classical brute-force search (see Key size).

然而，其他密码算法似乎并没有被这些算法破解。有些公钥算法是基于除整数分解和离散对数问题以外的问题，'''<font color="#ff8000"> 肖尔Shor算法</font>'''适用于这些问题，例如McEliece密码体制基于编码理论中的一个问题。基于格的密码体制也不能被量子计算机破解，寻找一个多项式时间算法来解决<font color="#ff8000"> 二面体隐子群问题Dihedral hidden subgroup problem</font>，这将打破许多基于<font color="#ff8000"> 格</font>的密码体制，是一个研究得很好的开放性问题。已经证明，应用'''<font color="#ff8000"> Grover算法</font>'''以暴力破解对称（密钥）算法所需的时间大约相当于基础加密算法的2次调用^n/2，而在经典情况下大约需要2ⁿ，这意味着对称密钥长度有效地减半：AES-256对于使用'''<font color="#ff8000"> Grover算法</font>'''的攻击的安全性与AES-128针对经典暴力搜索的安全性相同（参见密钥大小）。

然而，其他密码算法似乎并没有被那些算法破解。有些公钥算法是基于除整数分解和离散对数问题以外的问题，'''<font color="#ff8000"> 肖尔Shor算法</font>'''并不适用于这些问题，例如McEliece密码体制基于编码理论中的一个问题。基于格的密码体制也不能被量子计算机破解，寻找一个多项式时间算法来解决<font color="#ff8000"> 二面体隐子群问题Dihedral hidden subgroup problem</font>，将打破许多基于<font color="#ff8000"> 格</font>的密码体制，这是一个充分研究的开放性问题。已经证明，用'''<font color="#ff8000"> Grover算法</font>'''来暴力破解对称（密钥）算法所需的时间大约相当于基础加密算法的2^n/2次调用，而在经典情况下大约需要2ⁿ，这意味着对称密钥长度将有效地减半：AES-256应对使用'''<font color="#ff8000"> Grover算法</font>'''的攻击的安全性与AES-128应对经典暴力搜索的安全性相同（参见密钥大小）。

Quantum cryptography could potentially fulfill some of the functions of public key cryptography. Quantum-based cryptographic systems could, therefore, be more secure than traditional systems against quantum hacking.

Quantum cryptography could potentially fulfill some of the functions of public key cryptography. Quantum-based cryptographic systems could, therefore, be more secure than traditional systems against quantum hacking.

'''<font color="#ff8000"> 量子密码学Quantum cryptography</font>'''可以实现公开密钥加密的一些功能。因此，基于量子的加密系统可能比传统系统更安全，可以抵御量子黑客攻击。

'''<font color="#ff8000"> 量子密码学Quantum cryptography</font>'''可以实现公开密钥加密的一些功能。因此，面对量子黑客攻击时，基于量子的加密系统可能比传统系统更安全。

=== Quantum search 量子搜索===

=== Quantum search 量子搜索===

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 polynomials, 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. However, quantum computers offer polynomial speedup for some problems. The most well-known example of this is quantum database search, which can be solved by Grover's algorithm using quadratically fewer queries to the database than that are required by classical algorithms. In this case, the advantage is not only provable but also optimal, it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups. Several other examples of provable quantum speedups for query problems have subsequently been discovered, such as for finding collisions in two-to-one functions and evaluating NAND trees.

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 polynomials, 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. However, quantum computers offer polynomial speedup for some problems. The most well-known example of this is quantum database search, which can be solved by Grover's algorithm using quadratically fewer queries to the database than that are required by classical algorithms. In this case, the advantage is not only provable but also optimal, it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups. Several other examples of provable quantum speedups for query problems have subsequently been discovered, such as for finding collisions in two-to-one functions and evaluating NAND trees.

除了因式分解和离散对数外，在很多问题上发现，量子算法比最著名的经典算法提供了超过多项式的加速度，其中包括从化学和固态物理模拟量子物理过程，'''<font color="#ff8000"> 琼斯多项式Jones polynomials</font>'''的近似，和解'''<font color="#ff8000"> 佩尔方程Pell's equation</font>'''。目前还没有发现数学上的证明可证明同样快速的经典算法无法被发现，尽管这被认为是不可能的。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 </font>'''来解决，使用比经典算法所需的查询更少的数据库查询。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。随后又发现了其他几个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，其中包括化学和固态物理方面的量子物理过程仿真，'''<font color="#ff8000"> 琼斯多项式Jones polynomials</font>'''的近似，以及'''<font color="#ff8000"> 佩尔方程Pell's equation</font>'''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 </font>'''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。

|date=2009-06-19  

|date=2009-06-19  

Problems that can be addressed with Grover's algorithm have the following properties:

Problems that can be addressed with Grover's algorithm have the following properties:{{citation needed|date=May 2020}}

可以通过 '''<font color="#ff8000">格罗夫Grover算法 </font>'''解决的问题有以下属性:

可以通过 '''<font color="#ff8000">格罗夫Grover算法 </font>'''解决的问题有以下属性:

}}{{self-published inline|date=May 2020}}</ref> However, quantum computers offer polynomial speedup for some problems. The most well-known example of this is ''quantum database search'', which can be solved by [[Grover's algorithm]] using quadratically fewer queries to the database than that are required by classical algorithms. In this case, the advantage is not only provable but also optimal, it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups. Several other examples of provable quantum speedups for query problems have subsequently been discovered, such as for finding collisions in two-to-one functions and evaluating NAND trees.{{citation needed|date=May 2020}}

}}{{self-published inline|date=May 2020}}</ref> However, quantum computers offer polynomial speedup for some problems. The most well-known example of this is ''quantum database search'', which can be solved by [[Grover's algorithm]] using quadratically fewer queries to the database than that are required by classical algorithms. In this case, the advantage is not only provable but also optimal, it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups. Several other examples of provable quantum speedups for query problems have subsequently been discovered, such as for finding collisions in two-to-one functions and evaluating NAND trees.{{citation needed|date=May 2020}}

}}{{self-published inline|date=May 2020}}</ref>然而，量子计算机为某些问题提供了多项式加速。这方面最著名的例子是“量子数据库搜索”，它可以通过[[格罗夫算法]]使用比经典算法要求的更少的对数据库的查询来解决。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查询提供了找到所需元素的最大可能概率。随后又发现了其他几个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。{{citation needed|date=May 2020}}

}}{{self-published inline|date=May 2020}}</ref>然而，量子计算机为某些问题提供了多项式加速。这方面最著名的例子是“量子数据库搜索”，它可以通过[[格罗夫算法]]使用比经典算法要求的查询次数少二次方的查询次数来解决。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查询提供了找到所需元素的最大可能概率。随后又发现了其他几个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。{{citation needed|date=May 2020}}

There is no searchable structure in the collection of possible answers,

There is no searchable structure in the collection of possible answers,

要检查的可能答案的数量与算法的输入数量相同，以及

要检查的可能答案的数量与算法的输入数量相同，以及

There exists a boolean function which evaluates each input and determines whether it is the correct answer

There exists a boolean function which evaluates each input and determines whether it is the correct answer

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 cracker that attempts to guess the password or secret key for an encrypted file or system. Symmetric ciphers such as Triple DES and AES are particularly vulnerable to this kind of attack. This application of quantum computing is a major interest of government agencies.

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 cracker that attempts to guess the password or secret key for an encrypted file or system. Symmetric ciphers such as Triple DES and AES are particularly vulnerable to this kind of attack. This application of quantum computing is a major interest of government agencies.

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<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> 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>

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<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> 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[[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的主要兴趣。

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[[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。

{{Main|Quantum simulator}}

{{Main|Quantum simulator}}

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.<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>

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.

 

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>

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.

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.

'''<font color="#ff8000"> 量子退火或绝热量子计算</font>'''依赖于绝热定理进行计算。对于一个简单的'''<font color="#ff8000"> 哈密顿量</font>'''，一个系统被放置在'''<font color="#ff8000"> 基态</font>'''，这个'''<font color="#ff8000"> 哈密顿量</font>'''慢慢演化成一个更复杂的哈密顿量，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'''<font color="#ff8000"> 基态</font>'''。

'''<font color="#ff8000"> 量子退火或绝热量子计算</font>'''依赖于绝热定理进行计算。在一个简单的'''<font color="#ff8000"> 哈密顿体系</font>'''中，系统处于'''<font color="#ff8000"> 基态</font>'''，这个'''<font color="#ff8000"> 哈密顿体系</font>'''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'''<font color="#ff8000"> 基态</font>'''。

=== 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 ===

[[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.

[[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.

[[量子退火]]或[[绝热量子计算]]依赖绝热定理进行计算。一个系统被置于基态，简单的哈密顿量慢慢演化成一个更复杂的哈密顿量，其基态代表问题的解决方案。绝热定理指出，如果进化足够慢，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。

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.

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.

以其发现者 '''<font color="#ff8000"> 哈罗Harrow，哈西迪姆Hassidim和劳埃德Lloyd</font>'''命名的线性方程组的量子算法，或称'''<font color="#ff8000"> “ HHL 算法”</font>'''，预计将提供比经典算法更快的速度。

以其发现者 '''<font color="#ff8000"> 哈罗Harrow，哈西迪姆Hassidim和劳埃德Lloyd</font>'''命名的线性方程组的量子算法，或称'''<font color="#ff8000"> “ HHL 算法”</font>'''，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===

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.

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.

约翰 · 普雷斯基尔提出了'''<font color="#ff8000"> 量子优势Quantum supremacy</font>'''这一术语，指的是量子计算机在某一领域相对于经典计算机的假设加速优势。谷歌在2017年宣布，它希望在今年年底前实现'''<font color="#ff8000"> 量子优势</font>'''，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'''<font color="#ff8000"> 量子优势</font>'''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，其计算速度是顶峰计算机的300万倍以上，顶峰计算机被公认为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。认为一台400量子位的计算机甚至会与全息原理宇宙理论暗示的宇宙学信息发生冲突。

约翰 · 普雷斯基尔提出了'''<font color="#ff8000"> 量子优势Quantum supremacy</font>'''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'''<font color="#ff8000"> 量子优势</font>'''，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'''<font color="#ff8000"> 量子优势</font>'''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。

=== Quantum supremacy 量子至上===

=== Quantum supremacy 量子至上===

{{Main|Quantum supremacy}}

{{Main|Quantum supremacy}}

[[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.<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]] 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.<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> Although skeptics like [[Gil Kalai]] doubt that quantum supremacy will ever be achieved,<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> in October 2019, a [[Sycamore processor]] created in conjunction with Google AI Quantum was reported to have achieved quantum supremacy,<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> with calculations more than 3,000,000 times as fast as those of [[Summit (supercomputer)|Summit]], generally considered the world's fastest computer.<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> [[Bill Unruh]] doubted the practicality of quantum computers in a paper published back in 1994.<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]] argued that a 400-qubit computer would even come into conflict with the cosmological information bound implied by the [[holographic principle]].<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]] 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]].

[[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。[[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。尽管像[[Gil Kalai]]这样的怀疑论者怀疑量子霸权是否会实现，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，它的计算速度是世界上最快的计算机[[Summit（supercomputer）| Summit]]的300多万倍。[[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。

[[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>

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:

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:

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下列要求:

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==

There are a number of technical challenges in building a large-scale quantum computer.<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> Physicist [[David P. DiVincenzo|David DiVincenzo]] has listed the following [[DiVincenzo's criteria|requirements]] for a practical quantum computer:<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>

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。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]] ：

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

* Scalable physically to increase the number of qubits

*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

* Qubits that can be initialized to arbitrary values

* Qubits that can be initialized to arbitrary values

*可以初始化为任意值的量子位

*可以初始化为随机值的量子位

* Quantum gates that are faster than [[decoherence]] time

* Quantum gates that are faster than [[decoherence]] time

*比[[退相干]]时间快的量子门

*比[[退相干]]时间快的量子门