量子比特

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模板:简述。这意味着，通过适当改变坐标，可以消除其中一个自由度。一种可能的选择是 Hopf坐标：

where [math]\displaystyle{ e^{i \phi} }[/math] is the physically significant relative phase.

其中，[math]\displaystyle{ e^{i \phi} }[/math] 是物理上有意义的相对阶段。

[math]\displaystyle{ \begin{align} \alpha &= e^{i \psi} \cos\frac{\theta}{2}, \\ The possible quantum states for a single qubit can be visualised using a Bloch sphere (see diagram). Represented on such a 2-sphere, a classical bit could only be at the "North Pole" or the "South Pole", in the locations where \lt math\gt |0 \rangle }[/math] and [math]\displaystyle{ |1 \rangle }[/math] are respectively. This particular choice of the polar axis is arbitrary, however. The rest of the surface of the Bloch sphere is inaccessible to a classical bit, but a pure qubit state can be represented by any point on the surface. For example, the pure qubit state [math]\displaystyle{ ((|0 \rangle +i|1 \rangle)/{\sqrt{2}}) }[/math] would lie on the equator of the sphere at the positive y-axis. In the classical limit, a qubit, which can have quantum states anywhere on the Bloch sphere, reduces to the classical bit, which can be found only at either poles.

单个量子比特可能的量子态可以用布洛赫球可视化(见图表)。在这样一个2球面上，一个经典的比特只能在“北极”或“南极” ，也就是分别位于 < math > 和 < math > > | 1 rangle </math > 的位置。然而，对极轴的这种特殊选择是任意的。布洛赫球面的其余部分对于传统的比特是不可及的，但是一个纯的量子比特状态可以用表面上的任何点来表示。例如，纯量子比特状态 < math > (| 0 rangle + i | 1 rangle)/{ sqrt {2}}) </math > 将位于球体的赤道正 y 轴上。在经典极限下，一个量子比特可以在布洛赫球面的任何地方具有量子态，它退化为只能在两极找到的经典比特。

\beta &= e^{i (\psi + \phi)} \sin\frac{\theta}{2}.

\end{align}</math>

The surface of the Bloch sphere is a two-dimensional space, which represents the state space of the pure qubit states. This state space has two local degrees of freedom, which can be represented by the two angles [math]\displaystyle{ \phi }[/math] and [math]\displaystyle{ \theta }[/math].

布洛赫球体的表面是一个二维空间，代表纯量子位态的状态空间。这个状态空间有两个局部自由度，可以用两个角度来表示。

Additionally, for a single qubit the overall phase of the state $e i ψ$ has no physically observable consequences, so we can arbitrarily choose $α$ to be real (or $β$ in the case that $α$ is zero), leaving just two degrees of freedom:

此外，对于单个量子比特， $e i ψ$ 状态的整体相位没有物理上可观察的结果，因此我们可以任意选择 $α$ 为实（或者在 $α$ 为零的情况下的 $β$ ），只留下两个自由度：

[math]\displaystyle{ \begin{align} \alpha &= \cos\frac{\theta}{2}, \\ A pure state is one fully specified by a single ket, \lt math\gt | \psi \rangle = \alpha |0 \rangle + \beta |1 \rangle,\, }[/math] a coherent superposition as described above. Coherence is essential for a qubit to be in a superposition state. With interactions and decoherence, it is possible to put the qubit in a mixed state, a statistical combination or incoherent mixture of different pure states. Mixed states can be represented by points inside the Bloch sphere (or in the Bloch ball). A mixed qubit state has three degrees of freedom: the angles [math]\displaystyle{ \phi }[/math] and [math]\displaystyle{ \theta }[/math], as well as the length [math]\displaystyle{ r }[/math] of the vector that represents the mixed state.

一个纯态是由一个单一的量子完全指定的，如上所述，一个相干叠加。量子位处于叠加态时，相干性是必不可少的。通过相互作用和退相干，可以将量子位置置于混合状态，统计组合或不同纯态的非相干混合状态。混合状态可以用布洛赫球内的点(或布洛赫球中的点)来表示。混合量子位状态有三个自由度: 角度 < math > phi </math > 和 < math > theta </math > ，以及表示混合状态的向量的长度 < math > r </math > 。

\beta &= e^{i \phi} \sin\frac{\theta}{2},

\end{align}</math>

where [math]\displaystyle{ e^{i \phi} }[/math] is the physically significant relative phase.

其中，[math]\displaystyle{ e^{i \phi} }[/math] 是物理上有意义的相对阶段。

There are various kinds of physical operations that can be performed on pure qubit states.

有各种各样的物理操作可以在纯量子比特状态下进行。

The possible quantum states for a single qubit can be visualised using a Bloch sphere (see diagram). Represented on such a 2-sphere, a classical bit could only be at the "North Pole" or the "South Pole", in the locations where [math]\displaystyle{ |0 \rangle }[/math] and [math]\displaystyle{ |1 \rangle }[/math] are respectively. This particular choice of the polar axis is arbitrary, however. The rest of the surface of the Bloch sphere is inaccessible to a classical bit, but a pure qubit state can be represented by any point on the surface. For example, the pure qubit state [math]\displaystyle{ ((|0 \rangle +i|1 \rangle)/{\sqrt{2}}) }[/math] would lie on the equator of the sphere at the positive y-axis. In the classical limit, a qubit, which can have quantum states anywhere on the Bloch sphere, reduces to the classical bit, which can be found only at either poles.

单个量子位的可能量子态可以用布洛赫球来可视化（见图表）。在这样一个2-球体上表示，经典位只能位于“北极”或“南极”，分别位于[math]\displaystyle{ | 0\rangle }[/math]和[math]\displaystyle{ | 1\rangle }[/math]的位置。然而，极轴的这种特殊选择是任意的。布洛赫球表面的其余部分是经典位所无法接近的，但是一个纯量子位状态可以用表面上的任何一点来表示。例如，纯量子位态[math]\displaystyle{ （（| 0\rangle+i | 1\rangle）/{\sqrt{2}}） }[/math]将位于正y轴的球体赤道上。在经典极限中，一个量子位元，可以在布洛赫球上的任何地方有量子态，它可以简化为经典位元，而经典位元只能在两极找到。

The surface of the Bloch sphere is a two-dimensional space, which represents the state space of the pure qubit states. This state space has two local degrees of freedom, which can be represented by the two angles [math]\displaystyle{ \phi }[/math] and [math]\displaystyle{ \theta }[/math].

布洛赫球的表面是一个二维空间，它代表了纯量子位态的状态空间。这个状态空间有两个局部自由度，可以用两个角度来表示。

An important distinguishing feature between qubits and classical bits is that multiple qubits can exhibit quantum entanglement. Quantum entanglement is a nonlocal property of two or more qubits that allows a set of qubits to express higher correlation than is possible in classical systems.

量子比特和经典比特的一个重要区别是多个量子比特可以表现出量子纠缠。量子纠缠是两个或多个量子比特的非局域性质，它允许一组量子比特表达比经典系统更高的相关性。

Mixed state混合状态

A pure state is one fully specified by a single ket, [math]\displaystyle{ | \psi \rangle = \alpha |0 \rangle + \beta |1 \rangle,\, }[/math] a coherent superposition as described above. Coherence is essential for a qubit to be in a superposition state. With interactions and decoherence, it is possible to put the qubit in a mixed state, a statistical combination or incoherent mixture of different pure states. Mixed states can be represented by points inside the Bloch sphere (or in the Bloch ball). A mixed qubit state has three degrees of freedom: the angles [math]\displaystyle{ \phi }[/math] and [math]\displaystyle{ \theta }[/math], as well as the length [math]\displaystyle{ r }[/math] of the vector that represents the mixed state.

纯态是一个完全由单个ket指定的态，[math]\displaystyle{ |\psi\rangle=\alpha | 0\rangle+\beta | 1\rangle，\， }[/math]如上所述的相干叠加。相干是量子位元处于叠加态所必需的。通过相互作用和退相干，可以将量子位置于混合态，不同纯态的统计组合或非相干混合。混合状态可以用布洛赫球（或布洛赫球）“内部”的点来表示。混合量子比特态有三个自由度：角[math]\displaystyle{ \phi }[/math]和[math]\displaystyle{ \theta }[/math]，以及表示混合态的向量的长度[math]\displaystyle{ r }[/math]。

The simplest system to display quantum entanglement is the system of two qubits. Consider, for example, two entangled qubits in the [math]\displaystyle{ |\Phi^+\rangle }[/math] Bell state:

显示量子纠缠的最简单的系统是两个量子位的系统。例如，考虑两个处于 < math > | Phi ^ + rangle </math > Bell 态的纠缠量子比特:

Operations on pure qubit states纯量子态的运算

[math]\displaystyle{ \frac{1}{\sqrt{2}} (|00\rangle + |11\rangle). }[/math]

(| 00 rangle + | 11 rangle) . </math >

There are various kinds of physical operations that can be performed on pure qubit states. 有各种各样的物理操作可以在纯量子态上执行。

Quantum logic gates, building blocks for a quantum circuit in a quantum computer, operate on one, two, or three qubits: mathematically, the qubits undergo a (reversible) unitary transformation under the quantum gate. For a single qubit, unitary transformations correspond to rotations of the qubit (unit) vector on the Bloch sphere to specific superpositions. For two qubits, the Controlled NOT gate can be used to entangle or disentangle them.
量子逻辑门s是量子计算机中量子电路的构建块，在一个、两个或三个量子位上运行：从数学上讲，量子位在量子门下经历（可逆的）酉变换。对于单个量子位，幺正变换对应于Bloch球上的量子位（单位）矢量旋转到特定的叠加。对于两个量子比特，受控非门可以用来纠缠或解开它们。

In this state, called an equal superposition, there are equal probabilities of measuring either product state [math]\displaystyle{ |00\rangle }[/math] or [math]\displaystyle{ |11\rangle }[/math], as [math]\displaystyle{ |1/\sqrt{2}|^2 = 1/2 }[/math]. In other words, there is no way to tell if the first qubit has value “0” or “1” and likewise for the second qubit.

在这种被称为等量叠加的状态下，测量乘积态 < math > | 00 rangle </math > 或 < math > | 11 rangle </math > 的概率相等，如 < math > | 1/sqrt {2} | ^ 2 = 1/2 </math > 。换句话说，没有办法知道第一个量子位是“0”还是“1” ，第二个量子位也是如此。

Standard basis measurement is an irreversible operation in which information is gained about the state of a single qubit (and coherence is lost). The result of the measurement will be either [math]\displaystyle{ | 0 \rangle }[/math] (with probability [math]\displaystyle{ |\alpha|^2 }[/math]) or [math]\displaystyle{ | 1 \rangle }[/math] (with probability [math]\displaystyle{ |\beta|^2 }[/math]). Measurement of the state of the qubit alters the magnitudes of α and β. For instance, if the result of the measurement is [math]\displaystyle{ | 1 \rangle }[/math], α is changed to 0 and β is changed to the phase factor [math]\displaystyle{ e^{i \phi} }[/math] no longer experimentally accessible. When a qubit is measured, the superposition state collapses to a basis state (up to a phase) and the relative phase is rendered inaccessible (i.e., coherence is lost). Note that a measurement of a qubit state that is entangled with another quantum system transforms the qubit state, a pure state, into a mixed state (an incoherent mixture of pure states) as the relative phase of the qubit state is rendered inaccessible.

标准基测量是一种不可逆的操作，在这种操作中，获得了关于单个量子比特状态的信息（并且失去了相干性）。测量结果将是[math]\displaystyle{ | 0\rangle }[/math]（概率[math]\displaystyle{ |\alpha | ^2 }[/math]）或[math]\displaystyle{ |1\rangle }[/math]（概率[math]\displaystyle{ |\beta | ^2 }[/math]）。量子位状态的测量改变了α和β的大小。例如，如果测量结果为[math]\displaystyle{ | 1\rangle }[/math]，α变为0，β变为相位因子[math]\displaystyle{ e^{i\phi} }[/math]。当一个量子位被测量时，叠加态坍缩成基态（直到一个相位），相对相位变得不可接近（即，相干性丢失）。注意，对与另一量子系统纠缠的量子位态的测量将量子位态（纯态）转换为混合态（纯态的非相干混合），因为量子位态的相对相位变得不可接近。

Imagine that these two entangled qubits are separated, with one each given to Alice and Bob. Alice makes a measurement of her qubit, obtaining—with equal probabilities—either [math]\displaystyle{ |0\rangle }[/math] or [math]\displaystyle{ |1\rangle }[/math], i.e., she can now tell if her qubit has value “0” or “1”. Because of the qubits' entanglement, Bob must now get exactly the same measurement as Alice. For example, if she measures a [math]\displaystyle{ |0\rangle }[/math], Bob must measure the same, as [math]\displaystyle{ |00\rangle }[/math] is the only state where Alice's qubit is a [math]\displaystyle{ |0\rangle }[/math]. In short, for these two entangled qubits, whatever Alice measures, so would Bob, with perfect correlation, in any basis, however far apart they may be and even though both can not tell if their qubit has value “0” or “1” — a most surprising circumstance that can not be explained by classical physics.

想象一下，这两个纠缠的量子位被分开，每个给爱丽丝和鲍勃一个。爱丽丝对她的量子位进行测量，以相等的概率获得ーー要么是 < math > | 0 rangle </math > ，要么是 < math > | 1 rangle </math > ，也就是说，她现在可以判断她的量子位是值“0”还是“1”。由于量子比特的纠缠，鲍勃现在必须得到与爱丽丝完全相同的测量结果。例如，如果她测量一个 < math > | 0 rangle </math > ，那么 Bob 必须测量相同的值，因为 < math > | 00 rangle </math > 是 Alice 的量子位唯一的状态，其中的量子位是 < math > | 0 rangle </math > 。简而言之，对于这两个纠缠的量子比特，不管 Alice 测量什么，Bob 也会测量，不管它们之间的距离有多远，在任何基础上都有完美的相关性，即使它们都无法判断它们的量子比特值是“0”还是“1”——这是经典物理学无法解释的最令人惊讶的情况。

Quantum entanglement量子纠缠

An important distinguishing feature between qubits and classical bits is that multiple qubits can exhibit quantum entanglement. Quantum entanglement is a nonlocal property of two or more qubits that allows a set of qubits to express higher correlation than is possible in classical systems.

量子比特和经典比特的一个重要区别是，多个量子比特可以表现出量子纠缠。量子纠缠是两个或多个量子比特的非局域性质，它允许一组量子比特表达比经典系统可能更高的相关性。

The simplest system to display quantum entanglement is the system of two qubits. Consider, for example, two entangled qubits in the [math]\displaystyle{ |\Phi^+\rangle }[/math] Bell state:

显示量子纠缠的最简单的系统是两个量子比特的系统。例如，考虑[math]\displaystyle{ |\Phi^+\rangle }[/math]贝尔态中的两个纠缠量子比特：

Controlled gates act on 2 or more qubits, where one or more qubits act as a control for some specified operation. In particular, the controlled NOT gate (or CNOT or cX) acts on 2 qubits, and performs the NOT operation on the second qubit only when the first qubit is [math]\displaystyle{ |1\rangle }[/math], and otherwise leaves it unchanged. With respect to the unentangled product basis [math]\displaystyle{ \{|00\rangle }[/math], [math]\displaystyle{ |01\rangle }[/math], [math]\displaystyle{ |10\rangle }[/math], [math]\displaystyle{ |11\rangle\} }[/math], it maps the basis states as follows:

受控门作用于2个或多个量子位，其中一个或多个量子位用作某些特定操作的控制。特别是，被控制的 NOT 门(或 CNOT 或 cX)作用于2个量子位，并且只有当第一个量子位为 < math > | 1 rangle </math > 时，才对第二个量子位执行 NOT 操作，否则就保持不变。关于不纠缠的产品基础{ | 00 rangle </math > ，< math > | 01 rangle </math > ，< math > | 10 rangle </math > ，< math > | 11 rangle } </math > ，它将基础状态映射如下:

[math]\displaystyle{ | 0 0 \rangle \mapsto | 0 0 \rangle }[/math]

< math > | 00地图 | 00地图 </math >

[math]\displaystyle{ \frac{1}{\sqrt{2}} (|00\rangle + |11\rangle). }[/math]

[math]\displaystyle{ | 0 1 \rangle \mapsto | 0 1 \rangle }[/math]

< math > | 01地图 | 01地图 </math >

[math]\displaystyle{ | 1 0 \rangle \mapsto | 1 1 \rangle }[/math]

< math > | 10个测量点 | 11个测量点

In this state, called an equal superposition, there are equal probabilities of measuring either product state [math]\displaystyle{ |00\rangle }[/math] or [math]\displaystyle{ |11\rangle }[/math], as [math]\displaystyle{ |1/\sqrt{2}|^2 = 1/2 }[/math]. In other words, there is no way to tell if the first qubit has value “0” or “1” and likewise for the second qubit.

在这种被称为“相等叠加”的状态下，测量产品状态[math]\displaystyle{ |00\rangle }[/math] 或 [math]\displaystyle{ |11\rangle }[/math]的概率是相等的，如1/\sqrt{2}^2=1/2</math>。换句话说，无法判断第一个量子位的值是“0”还是“1”，第二个量子位也是如此。

[math]\displaystyle{ | 1 1 \rangle \mapsto | 1 0 \rangle }[/math].

< math > | 11个测量点 | 10个测量点。

Imagine that these two entangled qubits are separated, with one each given to Alice and Bob. Alice makes a measurement of her qubit, obtaining—with equal probabilities—either [math]\displaystyle{ |0\rangle }[/math] or [math]\displaystyle{ |1\rangle }[/math], i.e., she can now tell if her qubit has value “0” or “1”. Because of the qubits' entanglement, Bob must now get exactly the same measurement as Alice. For example, if she measures a [math]\displaystyle{ |0\rangle }[/math], Bob must measure the same, as [math]\displaystyle{ |00\rangle }[/math] is the only state where Alice's qubit is a [math]\displaystyle{ |0\rangle }[/math]. In short, for these two entangled qubits, whatever Alice measures, so would Bob, with perfect correlation, in any basis, however far apart they may be and even though both can not tell if their qubit has value “0” or “1” — a most surprising circumstance that can not be explained by classical physics.

想象一下，这两个纠缠的量子比特是分开的，一个给了爱丽丝和鲍勃。爱丽丝测量她的量子位，以相等的概率获得[math]\displaystyle{ | 0\rangle }[/math]或[math]\displaystyle{ |1\rangle }[/math]，也就是说，她现在可以判断她的量子位值是“0”还是“1”。由于量子比特的纠缠，鲍勃现在必须得到与爱丽丝完全相同的测量值。例如，如果她测量一个[math]\displaystyle{ | 0\rangle }[/math]，Bob必须测量相同的值，因为[math]\displaystyle{ |00\rangle }[/math]是Alice的量子位是[math]\displaystyle{ | 0\rangle }[/math]的唯一状态。简言之，对于这两个纠缠的量子位，无论爱丽丝测量的是什么，无论它们相隔多远，具有“完美”关联的鲍勃也会如此，即使两者都无法分辨它们的量子位值是“0”还是“1”——这是经典物理无法“解释”的最令人惊讶的情况。

A common application of the C_NOT gate is to maximally entangle two qubits into the [math]\displaystyle{ |\Phi^+\rangle }[/math] Bell state. To construct [math]\displaystyle{ |\Phi^+\rangle }[/math], the inputs A (control) and B (target) to the C_NOT gate are:

C_NOT门的一个常见应用是最大限度地将两个量子位纠缠成[math]\displaystyle{ |\Phi^+\rangle }[/math]贝尔态。要构造[math]\displaystyle{ |\Phi^+\rangle }[/math]，到C_NOT门的输入A（控制）和B（目标）是：

Controlled gate to construct the Bell state受控门构造钟态

[math]\displaystyle{ \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)_A }[/math] and [math]\displaystyle{ |0\rangle_B }[/math]

(| 0 rangle + | 1 rangle) a </math > and < math > | 0 rangle _ b </math >

Controlled gates act on 2 or more qubits, where one or more qubits act as a control for some specified operation. In particular, the controlled NOT gate (or CNOT or cX) acts on 2 qubits, and performs the NOT operation on the second qubit only when the first qubit is [math]\displaystyle{ |1\rangle }[/math], and otherwise leaves it unchanged. With respect to the unentangled product basis [math]\displaystyle{ \{|00\rangle }[/math], [math]\displaystyle{ |01\rangle }[/math], [math]\displaystyle{ |10\rangle }[/math], [math]\displaystyle{ |11\rangle\} }[/math], it maps the basis states as follows:

受控门作用于2个或多个量子比特，其中一个或多个量子比特作为某些特定操作的控制。具体而言，controlled NOT gate（或CNOT或cX）作用于2个量子位，并且仅当第一个量子位为[math]\displaystyle{ | 1\rangle }[/math]时才对第二个量子位执行NOT操作，否则保持不变。对于无缠结的产品基[math]\displaystyle{ \{00\rangle }[/math]、[math]\displaystyle{ |01\rangle }[/math]、[math]\displaystyle{ |10\rangle }[/math]、[math]\displaystyle{ |11\rangle\} }[/math]，它将基状态映射如下：

After applying C_NOT, the output is the [math]\displaystyle{ |\Phi^+\rangle }[/math] Bell State: [math]\displaystyle{ \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle) }[/math].

应用 C_NOT 后，输出为 [math]\displaystyle{ |\Phi^+\rangle }[/math] 贝尔态: [math]\displaystyle{ \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle) }[/math]。

[math]\displaystyle{ | 0 0 \rangle \mapsto | 0 0 \rangle }[/math]

[math]\displaystyle{ | 0 1 \rangle \mapsto | 0 1 \rangle }[/math]

[math]\displaystyle{ | 1 0 \rangle \mapsto | 1 1 \rangle }[/math]

[math]\displaystyle{ | 1 1 \rangle \mapsto | 1 0 \rangle }[/math].

The [math]\displaystyle{ |\Phi^+\rangle }[/math] Bell state forms part of the setup of the superdense coding, quantum teleportation, and entangled quantum cryptography algorithms.

贝尔态[math]\displaystyle{ |\Phi^+\rangle }[/math]构成了超稠密编码、量子遥传和纠缠量子密码学算法的一部分。

A common application of the C_NOT gate is to maximally entangle two qubits into the [math]\displaystyle{ |\Phi^+\rangle }[/math] Bell state. To construct [math]\displaystyle{ |\Phi^+\rangle }[/math], the inputs A (control) and B (target) to the C_NOT gate are:

C_NOT门的一个常见应用是最大限度地将两个量子位纠缠到[math]\displaystyle{ |\Phi^+\rangle }[/math]Bell state。要构造[math]\displaystyle{ |\Phi^+\rangle }[/math]，到C_NOT门的输入A（控制）和B（目标）是：

Quantum entanglement also allows multiple states (such as the Bell state mentioned above) to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum computation that cannot be done efficiently on a classical computer. Many of the successes of quantum computation and communication, such as quantum teleportation and superdense coding, make use of entanglement, suggesting that entanglement is a resource that is unique to quantum computation. A major hurdle facing quantum computing, as of 2018, in its quest to surpass classical digital computing, is noise in quantum gates that limits the size of quantum circuits that can be executed reliably.

量子纠缠还允许多个状态(如上面提到的贝尔状态)同时作用，不像传统比特一次只能有一个值。纠缠是任何量子计算的必要组成部分，在经典计算机上无法有效地进行。许多量子计算和通信的成功，例如量子遥传和超密编码，都利用了纠缠，这表明纠缠是量子计算所独有的资源。2018年，量子计算要想超越经典数字计算，量子计算面临的一个主要障碍是量子门中的噪声，这种噪声限制了可靠执行的量子电路的大小。

[math]\displaystyle{ \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)_A }[/math] and [math]\displaystyle{ |0\rangle_B }[/math]

A number of qubits taken together is a qubit register. Quantum computers perform calculations by manipulating qubits within a register. A qubyte (quantum byte) is a collection of eight qubits.

一些量子位元组合在一起就是一个量子位元寄存器。量子计算机通过在寄存器中操纵量子位来执行计算。一个量子字节(quantum byte)是八个量子位的集合。

After applying C_NOT, the output is the [math]\displaystyle{ |\Phi^+\rangle }[/math] Bell State: [math]\displaystyle{ \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle) }[/math].

应用C_NOT之后，输出为 [math]\displaystyle{ |\Phi^+\rangle }[/math] 贝尔态: [math]\displaystyle{ \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle) }[/math]。

Applications应用

Similar to the qubit, the qutrit is the unit of quantum information that can be realized in suitable 3-level quantum systems. This is analogous to the unit of classical information trit of ternary computers. Note, however, that not all 3-level quantum systems are qutrits. The term "qu-d-it" (quantum d-git) denotes the unit of quantum information that can be realized in suitable d-level quantum systems. In 2017, scientists at the National Institute of Scientific Research constructed a pair of qudits with 10 different states each, giving more computational power than 6 qubits.

与量子位类似，量子树是可以在合适的三能级量子系统中实现的量子信息单位。这类似于三元计算机的经典信息树trit单位。然而，请注意，并非所有的三能级量子系统都是量子系统。术语“qu-d-it”（量子d-git）表示可以在合适的d级量子系统中实现的量子信息单元。2017年，美国国家科学研究院（National Institute of Scientific Research）的科学家构建了一对分别具有10种不同状态的量子数，其计算能力超过了6个量子位。

The [math]\displaystyle{ |\Phi^+\rangle }[/math] Bell state forms part of the setup of the superdense coding, quantum teleportation, and entangled quantum cryptography algorithms.

[math]\displaystyle{ |\Phi^+\rangle }[/math]Bell态是密集编码、量子通信和纠缠量子密码术算法设置的一部分。

Quantum entanglement also allows multiple states (such as the Bell state mentioned above) to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum computation that cannot be done efficiently on a classical computer. Many of the successes of quantum computation and communication, such as quantum teleportation and superdense coding, make use of entanglement, suggesting that entanglement is a resource that is unique to quantum computation.^[1] A major hurdle facing quantum computing, as of 2018, in its quest to surpass classical digital computing, is noise in quantum gates that limits the size of quantum circuits that can be executed reliably.^[2]

量子纠缠还允许同时作用于多个态（例如上面提到的贝尔态），不像经典比特一次只能有一个值。纠缠是任何量子计算的必要组成部分，在经典计算机上无法有效地完成。量子计算和通信的许多成功，如量子隐形传态和超密集编码，都利用了纠缠，这表明纠缠是量子计算所特有的资源。^[3] 截至2018年，量子计算在寻求超越经典数字计算的过程中面临的一个主要障碍是量子门中的噪声，它限制了能够可靠执行的量子电路的大小。^[2]

Any two-level quantum-mechanical system can be used as a qubit. Multilevel systems can be used as well, if they possess two states that can be effectively decoupled from the rest (e.g., ground state and first excited state of a nonlinear oscillator). There are various proposals. Several physical implementations that approximate two-level systems to various degrees were successfully realized. Similarly to a classical bit where the state of a transistor in a processor, the magnetization of a surface in a hard disk and the presence of current in a cable can all be used to represent bits in the same computer, an eventual quantum computer is likely to use various combinations of qubits in its design.

任何两能级的量子力学系统都可以用作量子位。如果多电平系统具有两种可以有效地与其他状态解耦的状态(例如，非线性振荡器的基态和第一激发态) ，那么多电平系统也可以被应用。有各种各样的建议。成功地实现了几种不同程度近似两能级系统的物理实现。与处理器中晶体管的状态、硬盘表面的磁化和电缆中电流的存在都可以用来表示同一台计算机中的位相类似，最终的量子计算机可能会在其设计中使用不同的量子位组合。

Quantum register量子寄存器

The following is an incomplete list of physical implementations of qubits, and the choices of basis are by convention only.

下面是量子比特物理实现的一个不完整的列表，其基础设定依照惯例。

A number of qubits taken together is a qubit register. Quantum computers perform calculations by manipulating qubits within a register. A qubyte (quantum byte) is a collection of eight quits.

一些量子位元合在一起就是量子位元寄存器。量子计算机通过操纵寄存器中的量子位来执行计算。“量子字节”（quantum byte）是八个量子比特的集合。^[4]模板:Verification failed

! scope="col" style="background: white;" | [math]\displaystyle{ |1 \rangle }[/math]

!“白色背景” | < math > | 1 rangle </math >

|-

Variations of the qubit量子位的变化

| rowspan=3 |Photon

3 | Photon

Similar to the qubit, the qutrit is the unit of quantum information that can be realized in suitable 3-level quantum systems. This is analogous to the unit of classical information trit of ternary computers. Note, however, that not all 3-level quantum systems are qutrits.^[5] The term "qu-d-it" (quantum d-git) denotes the unit of quantum information that can be realized in suitable d-level quantum systems.^[6] In 2017, scientists at the National Institute of Scientific Research constructed a pair of qudits with 10 different states each, giving more computational power than 6 qubits.^[7]

与量子位类似，量子树qutrit是可以在合适的三能级量子系统中实现的量子信息单位。这类似于三元计算机的经典信息单位树trit。^[8] 术语 "qu-d-it" (quantum d-git)表示可在适当的“d”级量子系统中实现的量子信息单位。^[9] 2017年，国家科学研究院的科学家们构建了一对qudit量子数，每个量子数qudit有10种不同的状态，计算能力超过了6个量子比特。^[10]

| Polarization encoding

| 偏振编码

| Polarization of light

| 光的偏振

Physical implementations物理实现

| Horizontal

| 横向

| Vertical

Any two-level quantum-mechanical system can be used as a qubit. Multilevel systems can be used as well, if they possess two states that can be effectively decoupled from the rest (e.g., ground state and first excited state of a nonlinear oscillator). There are various proposals. Several physical implementations that approximate two-level systems to various degrees were successfully realized. Similarly to a classical bit where the state of a transistor in a processor, the magnetization of a surface in a hard disk and the presence of current in a cable can all be used to represent bits in the same computer, an eventual quantum computer is likely to use various combinations of qubits in its design.

任何二能级量子力学系统都可以用作量子位。如果多电平系统具有两个能有效地与其他状态解耦的状态（例如，非线性振荡器的基态和第一激发态），则也可以使用多电平系统。有各种各样的建议。成功地实现了几种不同程度近似于两级系统的物理实现。类似于经典位，处理器中晶体管的状态，[[硬盘]中表面的磁化和电缆中电流的存在都可以用来表示同一台计算机中的位，最终的量子计算机可能会在其设计中使用各种量子位的组合。

|-

| Number of photons

| 光子数

The following is an incomplete list of physical implementations of qubits, and the choices of basis are by convention only.

下面是量子比特物理实现的一个不完整的列表，其基础设定依惯例。

| Fock state

| 福克州

| Vacuum

| 真空

Single photon state	单光子态
Physical support	Time-bin encoding	时间容器编码	Name	Time of arrival	抵达时间	Information support	Early 早期	[math]\displaystyle{ \|0 \rangle }[/math]	Late 迟到	[math]\displaystyle{ \|1 \rangle }[/math]
Coherent state of light 光的相干态	Photon	Squeezed light 压缩光	Polarization encoding	Quadrature	正交	Polarization of light	Amplitude-squeezed state	振幅压缩态	Horizontal	Phase-squeezed state	相压缩态	Vertical
Electrons 2 \| 电子		Number of photons	Electronic spin	电子自旋	Fock state	Spin 旋转	Vacuum	Up 起来	Single photon state	Down 下来
Electrons 2 \| 电子		Time-bin encoding	Electron number	电子数	Time of arrival	Charge	费用	Early	No electron 没有电子	Late	One electron 一个电子
Coherent state of light	Nucleus 纽核力	Squeezed light	Nuclear spin addressed through NMR 核自旋通过 NMR 处理	Quadrature 模板:Clarify	Spin 旋转	Amplitude-squeezed state	Up 起来	Phase-squeezed state	Down 下来
Electrons	Optical lattices	光学晶格	Electronic spin	Atomic spin 原子自旋	Spin	Spin 旋转	Up	Up 起来	Down	Down 下来
Electrons	Electron number	Josephson junction 3 \| Josephson junction	Charge	电荷	Superconducting charge qubit	超导电荷量子位	No electron	没有电子	Charge	费用	One electron	单电子	Uncharged superconducting island (Q=0)	无电荷超导岛(q = 0)
Charged superconducting island (Q=2e, one extra Cooper pair)	带电超导岛(q = 2e，多一对库珀)		Nucleus	原子核
Nuclear spin addressed through NMR	【核自旋】通过【核磁共振】		Superconducting flux qubit	超导磁通量子位	Spin	Current	目前	Up	Clockwise current	顺时针方向电流	Down	Counterclockwise current 逆时针方向电流
Optical lattices	Superconducting phase qubit	超导相量子位	Atomic spin	Energy	能源	Spin	Ground state	基态	Up	First excited state	第一激发态	Down
Singly charged quantum dot pair 单电荷量子点对	Josephson junction	Electron localization	电子定位	Superconducting charge qubit	Charge	费用	Charge	Electron on left dot 左点上的电子	Uncharged superconducting island (Q=0)	Electron on right dot	右点上的电子	Charged superconducting island (Q=2e, one extra Cooper pair)
Quantum dot		量子点	Superconducting flux qubit	Dot spin 点旋转	Current	Spin 旋转	Clockwise current	Down 下来	Counterclockwise current	Up 起来
Superconducting phase qubit		Gapped topological system	间隙拓扑系统	Energy	能量	Non-abelian anyons	非阿贝尔任意子	Non-abelian anyons	非阿贝尔任意子	Ground state	基态	Braiding of Excitations	编织激发	First excited state	第一激发态	Depends on specific topological system 依赖于特定的拓扑系统
Depends on specific topological system 依赖于特定的拓扑系统	Singly charged quantum dot pair	单电荷量子点对
Electron localization	电子局域化	van der Waals heterostructure 范德华异质结构	Charge	Electron localization	电子定位	Electron on left dot	左点上的电子	Charge	费用	Electron on right dot	右点上的电子	Electron on bottom sheet	底片上的电子
Electron on top sheet	电子在最上面的表格	Quantum dot	量子点

|}

| Dot spin

| Spin

| Down

| Up

In a paper entitled "Solid-state quantum memory using the ³¹P nuclear spin", published in the October 23, 2008, issue of the journal Nature, a team of scientists from the U.K. and U.S. reported the first relatively long (1.75 seconds) and coherent transfer of a superposition state in an electron spin "processing" qubit to a nuclear spin "memory" qubit. This event can be considered the first relatively consistent quantum data storage, a vital step towards the development of quantum computing. Recently, a modification of similar systems (using charged rather than neutral donors) has dramatically extended this time, to 3 hours at very low temperatures and 39 minutes at room temperature. Room temperature preparation of a qubit based on electron spins instead of nuclear spin was also demonstrated by a team of scientists from Switzerland and Australia.

在《自然》杂志2008年10月23日发表的一篇题为“使用 ³¹P 核自旋的固态量子存储器”的论文中，一组来自英国和美国的科学家报告了第一个相对较长(1.75秒)的电子自旋中叠加态的“处理”量子位到核自旋“存储器”量子位的相干转移。这次事件可以被认为是第一次相对一致的量子数据存储，是量子计算发展的重要一步。最近，一种类似系统的改进(使用带电的而不是中性的捐赠者)已经戏剧性地延长了这个时间，在极低温度下3小时，在室温下39分钟。来自瑞士和澳大利亚的一组科学家也演示了基于电子自旋而不是核自旋的量子比特的室温准备。

|-

|van der Waals heterostructure

|范德华异质结构 ^[11]

|Electron localization |电子局域化 |Charge |充电 Category:Quantum computing

类别: 量子计算

|Electron on bottom sheet |底片上的电子 Category:Quantum information science

类别: 量子信息科学

|Electron on top sheet

Category:Quantum states

类别: 量子态

|}

Category:Teleportation

分类: 瞬间移动

Category:Units of information

类别: 信息单位

Qubit storage量子位存储

Category:Australian inventions

分类: 澳大利亚的发明

This page was moved from wikipedia:en:Qubit. Its edit history can be viewed at 量子比特/edithistory

此页摘自维基百科：英文：量子比特。其编辑历史记录可在量子比特/历史记录查阅

↑ Horodecki, Ryszard; et al. (2009). "Quantum entanglement". Reviews of Modern Physics. 81 (2): 865–942. arXiv:quant-ph/0702225. Bibcode:2009RvMP...81..865H. doi:10.1103/RevModPhys.81.865. S2CID 59577352.
↑ ^2.0 ^2.1 Preskill, John (2018). "Quantum Computing in the NISQ era and beyond". Quantum. 2: 79. arXiv:1801.00862. doi:10.22331/q-2018-08-06-79. S2CID 44098998.
↑ Horodecki, Ryszard; et al. (2009). "Quantum entanglement". Reviews of Modern Physics. 81 (2): 865–942. arXiv:quant-ph/0702225. Bibcode:2009RvMP...81..865H. doi:10.1103/RevModPhys.81.865. S2CID 59577352.
↑ R. Tanburn {; E. Okada; N. S. Dattani ! scope="col" (2015 ! scope="col"). [https://archive.org/details/arxiv-1508.04816 ! scope="col" style="background: white;" "Reducing multi-qubit interactions in adiabatic quantum computation without adding auxiliary qubits. Part 1: The "deduc-reduc" method and its application to quantum factorization of numbers ! scope="col""]. arXiv:1508.04816 [wikitable” align = “ center” “ wikitable” align = “ center”]. Bibcode:2015arXiv150804816T. {{cite journal}}: Cite journal requires |journal= (help); Check |url= value (help); Check date values in: |year= (help); Text "-" ignored (help); Text "-" ignored (help); Text "0 rangle </math >" ignored (help); Text "< math >" ignored (help); Text "Name" ignored (help); Text "信息支持" ignored (help); Text "物理支持" ignored (help); line feed character in |author3= at position 14 (help); line feed character in |author= at position 11 (help); line feed character in |title= at position 189 (help); line feed character in |url= at position 45 (help); line feed character in |year= at position 5 (help)
↑ "Quantum systems: three-level vs qutrit". Physics Stack Exchange. Retrieved 2018-07-25.
↑ Nisbet-Jones, Peter B. R.; Dilley, Jerome; Holleczek, Annemarie; Barter, Oliver; Kuhn, Axel (2013). "Photonic qubits, qutrits and ququads accurately prepared and delivered on demand". New Journal of Physics (in English). 15 (5): 053007. arXiv:1203.5614. Bibcode:2013NJPh...15e3007N. doi:10.1088/1367-2630/15/5/053007. ISSN 1367-2630. S2CID 110606655.
↑ "Qudits: The Real Future of Quantum Computing?". IEEE Spectrum (in English). 2017-06-28. Retrieved 2017-06-29.
↑ "Quantum systems: three-level vs qutrit". Physics Stack Exchange. Retrieved 2018-07-25.
↑ Nisbet-Jones, Peter B. R.; Dilley, Jerome; Holleczek, Annemarie; Barter, Oliver; Kuhn, Axel (2013). "Photonic qubits, qutrits and ququads accurately prepared and delivered on demand". New Journal of Physics (in English). 15 (5): 053007. arXiv:1203.5614. Bibcode:2013NJPh...15e3007N. doi:10.1088/1367-2630/15/5/053007. ISSN 1367-2630. S2CID 110606655.
↑ "Qudits: The Real Future of Quantum Computing?". IEEE Spectrum (in English). 2017-06-28. Retrieved 2017-06-29.
↑ B. Lucatto; et al. (2019). "Charge qubit in van der Waals heterostructures". Physical Review B. 100 (12): 121406. arXiv:1904.10785. doi:10.1103/PhysRevB.100.121406. S2CID 129945636.

[1] Horodecki, Ryszard; et al. (2009). "Quantum entanglement". Reviews of Modern Physics. 81 (2): 865–942. arXiv:quant-ph/0702225. Bibcode:2009RvMP...81..865H. doi:10.1103/RevModPhys.81.865. S2CID 59577352.

[preskill2018-2] 2.0 ^2.1 Preskill, John (2018). "Quantum Computing in the NISQ era and beyond". Quantum. 2: 79. arXiv:1801.00862. doi:10.22331/q-2018-08-06-79. S2CID 44098998.

[3] Horodecki, Ryszard; et al. (2009). "Quantum entanglement". Reviews of Modern Physics. 81 (2): 865–942. arXiv:quant-ph/0702225. Bibcode:2009RvMP...81..865H. doi:10.1103/RevModPhys.81.865. S2CID 59577352.

[4] R. Tanburn {; E. Okada; N. S. Dattani ! scope="col" (2015 ! scope="col"). [https://archive.org/details/arxiv-1508.04816 ! scope="col" style="background: white;" "Reducing multi-qubit interactions in adiabatic quantum computation without adding auxiliary qubits. Part 1: The "deduc-reduc" method and its application to quantum factorization of numbers ! scope="col""]. arXiv:1508.04816 [wikitable” align = “ center” “ wikitable” align = “ center”]. Bibcode:2015arXiv150804816T. {{cite journal}}: Cite journal requires |journal= (help); Check |url= value (help); Check date values in: |year= (help); Text "-" ignored (help); Text "-" ignored (help); Text "0 rangle </math >" ignored (help); Text "< math >" ignored (help); Text "Name" ignored (help); Text "信息支持" ignored (help); Text "物理支持" ignored (help); line feed character in |author3= at position 14 (help); line feed character in |author= at position 11 (help); line feed character in |title= at position 189 (help); line feed character in |url= at position 45 (help); line feed character in |year= at position 5 (help)

[5] "Quantum systems: three-level vs qutrit". Physics Stack Exchange. Retrieved 2018-07-25.

[6] Nisbet-Jones, Peter B. R.; Dilley, Jerome; Holleczek, Annemarie; Barter, Oliver; Kuhn, Axel (2013). "Photonic qubits, qutrits and ququads accurately prepared and delivered on demand". New Journal of Physics (in English). 15 (5): 053007. arXiv:1203.5614. Bibcode:2013NJPh...15e3007N. doi:10.1088/1367-2630/15/5/053007. ISSN 1367-2630. S2CID 110606655.

[7] "Qudits: The Real Future of Quantum Computing?". IEEE Spectrum (in English). 2017-06-28. Retrieved 2017-06-29.

[8] "Quantum systems: three-level vs qutrit". Physics Stack Exchange. Retrieved 2018-07-25.

[9] Nisbet-Jones, Peter B. R.; Dilley, Jerome; Holleczek, Annemarie; Barter, Oliver; Kuhn, Axel (2013). "Photonic qubits, qutrits and ququads accurately prepared and delivered on demand". New Journal of Physics (in English). 15 (5): 053007. arXiv:1203.5614. Bibcode:2013NJPh...15e3007N. doi:10.1088/1367-2630/15/5/053007. ISSN 1367-2630. S2CID 110606655.

[10] "Qudits: The Real Future of Quantum Computing?". IEEE Spectrum (in English). 2017-06-28. Retrieved 2017-06-29.

[11] B. Lucatto; et al. (2019). "Charge qubit in van der Waals heterostructures". Physical Review B. 100 (12): 121406. arXiv:1904.10785. doi:10.1103/PhysRevB.100.121406. S2CID 129945636.

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