赖特 因果分析

On October 23, 2019 the journal Nature published Quantum Supremacy using a Programmable Superconducting Processor, which describes the breakthrough by Google’s AI Quantum team in building the first quantum processing system capable of clearly demonstrating an advantage over “classical” supercomputers on a particular class of difficult computational problems. But what does this mean, really, and what is its significance? To answer this question, let us first review just what a quantum computer is, and how Google has built theirs.

2019年10月23日,《自然》(Nature)杂志发表了《使用可编程超导处理器的量子至上论 》( Quantum Supremacy) ,该书描述了Google AI量子团队在构建首个量子处理系统方面所取得的突破,该系统能够明显证明在特定类别的困难计算机上优于``经典''超级计算机的优势计算问题。 但是,这实际上意味着什么,它的意义是什么? 为了回答这个问题,让我们首先回顾一下量子计算机是什么,以及谷歌如何制造它们。

为什么要打扰量子计算? (Why Bother with Quantum Computing?)

Quantum computing algorithms have existed since before the first prototype of a quantum processor was built in 1998, but even so, quantum algorithms are in their infancy as a field. One of the earliest quantum algorithms, Shor’s algorithm, from 1994, allows an integer N to be factored on a quantum computer in polynomial time, O((log N)²(log log N)(log log log N)), which is exponentially faster than the best known classical algorithm, the general number field sieve. It is the very “hardness” of factoring integers that underlies RSA and a number of other cryptographic systems. So solving what was once thought of as a theoretical problem in pure mathematics takes on considerable importance.

自1998年建立量子处理器的第一个原型之前,就已经存在量子计算算法,但即便如此,量子算法仍处于起步阶段。 最早的量子算法之一,Shor算法,始于1994年,它允许在整数计算机上以多项式时间O((log N )²(log log N )(log log log N ))分解整数N。指数比最著名的经典算法(通用数字场筛)快得多。 RSA和许多其他密码系统的基础是分解整数的非常“困难”。 因此,解决曾经被认为是纯数学中的理论问题的事物具有相当重要的意义。

Other established quantum algorithms offer fundamental advantages over the best known classical solutions. Some are quite theoretical. Others are more practical. Grover’s search algorithm from 1996 can find an element in an unsorted list of N elements in √N steps, compared to N/2 for a classical scheme. Proposed quantum optimization algorithms offer quadratic to exponential speedups over the best of known classical techniques. Quantum computations are the most natural way to simulate molecules and chemical reactions. But the field is in its infancy. We are only now learning how to build machines to run these algorithms.

其他已建立的量子算法与最著名的经典解决方案相比,具有根本的优势。 有些是很理论的。 其他更实用。 从1996年Grover的搜索算法可以在√N个步骤的N个元素的一个未排序的列表中找到的元素,相比于N / 2为一个传统的方案。 提出的量子优化算法在已知的经典技术中提供了从二次到指数的加速。 量子计算是模拟分子和化学React的最自然方法。 但是这个领域还处于起步阶段。 我们现在仅在学习如何构建运行这些算法的机器。

量子计算基础 (Quantum Computing Basics)

经典二进制数据和量子态 (Classical Binary Data and Quantum States)

Conventional binary digital computers,“classical” computers in the quantum computing idiom, operate on the basis of bits, binary elements of information that are either 0 or 1. That’s only two possible values, but they can be concatenated to represent arbitrarily large value ranges, with each additional bit doubling the range of distinct values. Arithmetic, logical, and other operations can be performed on classical bit values by combining sequences of elements of boolean logic — AND, OR, NOT, etc — to operate on binary values and create new binary values.

传统的二进制数字计算机,即量子计算习语中的“经典”计算机,是基于比特或信息的二进制元素(为0或1)运行的。这只是两个可能的值,但可以将它们组合起来以表示任意大的值范围,每个额外的位使不同值的范围加倍。 通过组合布尔逻辑的元素序列(AND,OR,NOT等)以对二进制值进行运算并创建新的二进制值,可以对经典位值执行算术,逻辑和其他运算。

Quantum computers exploit the fact that quantum particles, such as electrons, photons, or ions, have properties like spin and polarization that can be manipulated to encode and process binary information. These processors operate on quantum bits, or qubits. This quantum information has unusual and counter-intuitive properties that make quantum computing both more powerful and more difficult than classical.

量子计算机利用了这样一个事实,即诸如电子,光子或离子之类的量子粒子具有诸如自旋和极化之类的特性,可以操纵这些特性来编码和处理二进制信息。 这些处理器在量子位或量子位上运行 。 这种量子信息具有非同寻常和违反直觉的特性,这使得量子计算比经典计算更强大,更困难。

A qubit will be represented by the state of a quantum system that can be usefully visualized as a “Bloch sphere”:

量子位将由量子系统的状态表示,该状态可以可视化为“布洛赫球”:

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The quantum state of a qubit may be in a definite 0 state or a definite 1 state, corresponding to the topmost and bottommost points on the Bloch sphere, respectively. But it can also be in a superposed state between them, as is the case for point x,y,z in the diagram. A superposed quantum state between ∣0⧽ and ∣1⧽ does not mean that the qubit has a fractional value greater than 0 and less than 1. Rather, it means that the value will be measured as 0 or as 1, according to the probability distribution described by its position on the Bloch sphere. The probability of it reading as 0 in the example above can be computed as cos(σ/2)². If the state corresponds to a point on the dotted “equator” of the Bloch sphere, it will measure as 0 or 1 with equal likelihood.

量子位的量子态可以是确定的0 状态或确定1状态,分别对应于Bloch球面上的最高点和最低点。 但是它们也可以处于它们之间的叠加状态,就像图中的点x,y,z一样 。 ∣0⧽之间的叠加量子态 和|1⧽ 并不意味着该量子位具有一个分数值大于0且小于1。相反,它意味着该值将作为0或1作为被测量,根据其位置在布洛赫描述的概率分布领域。 在上面的示例中,其读数为0的概率可以计算为cos(σ/ 2)²。 如果状态对应于Bloch球的虚线“赤道”上的某个点,则它将以相等的可能性测量为0或1。

Measurement is a fundamental concept in quantum mechanics. Measurement is not merely an extraction of a value from a qubit, it also affects the quantum state. If the state of the qubit in the Bloch diagram above is measured, and the result is 0, the qubit’s state will thereafter be ∣0⧽, with σ=0, so that further measurements of the qubit will read as 0 until some operation changes the state. Conversely, had the initial measurement yielded 1, the qubit’s state would thereafter be ∣1⧽, while σ would be 𝜋. Measurement collapses superposition. Schrödinger’s famous cat is only both potentially alive and potentially dead until the moment that the box is opened.

测量是量子力学中的一个基本概念。 测量不仅是从量子位中提取值,而且还会影响量子状态。 如果在上面的布洛赫图中测量了量子位的状态,并且结果为0,则此后量子位的状态将为∣0⧽,且σ= 0,因此对该量子位的进一步测量将读取为0,直到某些操作更改状态。 相反,如果初始测量结果为1,则qubit的状态将为∣1⧽,而σ为𝜋。 测量会使叠加崩溃。 Schrödinger着名的猫只有在打开盒子的那一刻才可能活着,也可能死了。

古典与量子加法 (Classical vs. Quantum Addition)

For comparison with its quantum counterpart, consider how two classical bits can be added, producing a 2-bit sum, using AND, OR, and NOT operations in the binary logic circuit below. The two-bit binary output value o[1..0] is the sum of input bits i0 and i1. As there is no “carry” input, the only possible results are 00, 01, and 10.

为了与其量子对应物进行比较,请考虑如何在下面的二进制逻辑电路中使用“与”,“或”和“非”运算将两个经典位相加,产生2位和。 两位二进制输出值o [1..0]是输入位i0和i1的总和。 由于没有“进位”输入,因此唯一可能的结果是00、01和10。

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量子位运算 (Operations on Qubits)

Just as classical binary logic is created by composing simple boolean primitives that can be implemented with a handful of transistors each, and just as one can, in theory, implement all possible binary logic circuits using only NAND gates, quantum computations can be expressed in terms of quantum gates. These have some pretty fundamental differences from their classical counterparts. Unlike binary bits, the full quantum state of a qubit cannot be copied or cloned. A quantum gate computation must be reversible, which requires every gate to have as many outputs as it has inputs. In the case of Google’s quantum technology, the qubits are small, superconducting oscillators, and the gates are applied to them by sending minutely controlled microwave pulses to perturb them. These qubits don’t flow through gates and wires, gates are applied to the qubits.

就像通过组合简单的布尔基元(每个布尔基元可以用几个晶体管来实现)来创建经典的二进制逻辑一样,就如同理论上可以仅使用“与非”门来实现所有可能的二进制逻辑电路一样,量子计算也可以表示为量子门 。 它们与经典版本相比有一些根本的区别。 与二进制位不同,不能复制或克隆量子位的完整量子状态。 量子门的计算必须是可逆的 ,这要求每个门具有与输入一样多的输出。 就Google的量子技术而言,量子位是小型的超导振荡器,通过发送受控制的微波脉冲来扰动它们,从而将栅极加到了它们上。 这些量子位不会流经门和导线,而是应用于量子位。

Where the classical logic model has only one useful unary operation, NOT, much of the richness of quantum computation involves unary operators on individual qubits. Unary gates can generally be visualized as rotations over arcs around the axes of a Bloch sphere. For example, the Hadamard, or H gate, can be thought of as a 180° rotation around the Z axis, followed by a 90° rotation about the Y axis of the Bloch Sphere.

在经典逻辑模型只有一个有用的一元运算的情况下,而不是,量子计算的丰富性涉及单个量子位上的一元运算符。 一元门通常可以可视化为绕Bloch球的轴在圆弧上旋转。 例如,可以将Hadamard或H门视为绕Z轴旋转180°,然后绕Bloch Sphere的Y轴旋转90°。

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When applied to a quantum state that has been prepared to be ∣0⧽ (a definite 0) , a Hadamard gate puts the qubit in a state of equal superposition of potential 0 and 1 values, a common idiom in quantum computing:

当将Hadamard门应用于已准备好为∣0⧽(定为0)的量子状态时,会将量子位置于势能0和1值相等叠加的状态,这是量子计算中的一个常见习语:

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Two-qubit gates are often conditional versions of a unary operator, e.g. CNOT (conditional negation) or CZ (conditional phase inversion). The conditional-conditional-NOT (CCNOT) gate, commonly called a Toffoli gate, is the quantum analog to a NAND gate, the gate out of which one could theoretically construct all possible circuits.

二量子位门通常是一元运算符的条件版本,例如CNOT(条件求反)或CZ(条件相求反)。 有条件-有条件-NOT(CCNOT)门,通常称为Toffoli门,是与非门的量子模拟,从理论上讲,其中的门可以构成所有可能的电路。

Quantum gate model algorithms are graphically depicted as a left-to-right sequence of operations on qubits. A unary operation will be depicted as a labeled box on a given qubit’s time-line. Multi-qubit operations are depicted with vertical connections between points on multiple time-lines.

量子门模型算法以图形方式描绘为对量子位的从左到右的操作序列。 一元运算将被描述为给定qubit时间轴上的标记框。 描绘了多量子位操作,其中在多个时间线上的点之间具有垂直连接。

The basic one-bit add circuit for qubits is:

量子比特的基本一比特加法电路是:

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If the inputs ∣i₀⧽ and ∣i₁⧽ are the basis vectors ∣0⧽ or ∣1⧽, the top and bottom points on the Bloch sphere, then the measurements will be as one might naively expect based on experience with classical logic, i.e, if both are ∣0⧽, both of the output measurements will be zero, no matter how many times one runs the experiment. But, unlike the classical logic circuit, this gate program also manipulates superposed states.

如果输入∣i₀⧽和∣i₁⧽是基向量∣0⧽或∣1⧽,即Bloch球面上的最高点和最低点,那么根据经典逻辑的经验,这些测量将是天真地期望的,即,如果两者均为“ 0”,则无论一个实验进行了多少次,两个输出测量值都将为零。 但是,与经典逻辑电路不同,该门程序还可以处理叠加状态。

As mentioned above, a Hadamard gate, when applied to a qubit in a ∣0⧽ basis state, results in a superposition with equal probabilities of measuring 0 or 1 from the qubit.. Extending the adder example with prepared state inputs and H gates, as depicted below, is in a real sense simultaneously computing all possible 1-bit sums, and the measurements will return 00, 01, or 10, with probabilities of 25%, 50%, and 25% respectively, reflecting the superpositions of the probability amplitudes for ∣00⧽, ∣01⧽, ∣10⧽ and ∣11⧽ as the state vectors of the output qubit pair.

如上所述,将Hadamard门应用于∣0基态的量子位时,将产生叠加,并具有从qubit测得0或1的等概率。.使用准备好的状态输入和H门扩展加法器示例,如下所示,实际上是同时计算所有可能的1位和,并且测量将返回00、01或10,概率分别为25%,50%和25%,反映了概率的叠加∣00⧽,∣01⧽,∣10⧽和∣11⧽的振幅作为输出量子位对的状态向量。

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So while 2 classical bits can contain one of 4 possible values, 2 qubits can represent 4 simultaneous values, in superposition; the probability amplitudes of 00, 01, 10, and 11. Each additional qubit potentially doubles the number of superposed states — which is why simulating systems with more than about 40 qubits with a classical computer is a major challenge. Each additional qubit doubles the memory requirement to classically store the state of the quantum system.

因此,尽管2个经典位可以包含4个可能值之一,但是2个qubit可以表示4个同时值,它们是叠加的; 概率幅度分别为00、01、10和11。每个额外的量子位有可能使叠加状态的数量加倍-这就是为什么用经典计算机模拟大约40量子位以上的系统是一个主要挑战。 每增加一个量子位,内存需求就翻一番,以经典地存储量子系统的状态。

While there is little “quantum advantage” in the example of addition, this quantum parallelism, the ability to operate simultaneously on a potentially large set of superposed values, is the key to most useful quantum algorithms.

尽管加法示例中几乎没有“量子优势”,但这种量子并行性(即同时对一组潜在的大量叠加值进行操作的能力)是最有用的量子算法的关键。

纠缠的比特 (Entangled Qubits)

Qubits can become entangled so that measuring one of an entangled pair determines the value that will be measured from the other. This can seem to result in “spooky action at a distance” as Einstein skeptically referred to it, and is often misrepresented in the popular imagination, but it is a key property for secure communications applications, and it happens inevitably in the course of executing quantum algorithms. Some entanglement is induced in the quantum gate addition program above: If the O₁ bit is measured as 1, the probability of O₀ then also measuring as 1 collapses to zero.

量子位可能会纠缠在一起,因此测量一个纠缠对中的一个将确定要从另一对中测量的值。 正如爱因斯坦怀疑的那样,这似乎会导致“远距离的鬼动作”,并且通常在流行的想象中被误解,但这是安全通信应用的关键特性,并且在执行量子过程中不可避免地发生算法。 在上面的量子门加法程序中会引起一些纠缠:如果将O₁位测量为1,则O₀的概率也将测量为1,变为0。

保真度和退相干性 (Fidelity and Decoherence)

Physical qubits operate at physical scales and energy levels such that errors are not so much a matter of if as a matter of when. Quantum states collapse, not only when measured, but when the qubits interact and entangle with elements of the surrounding system. The simple fact that the quantum system is in enough contact with the rest of the universe to allow deliberate manipulation and measurement implies enough random interaction to eventually cause the qubits to decohere and lose their superposed information. In addition, each gate operation carries an additional risk of inducing an error. Single and multiple-qubit gate operators have a fidelity, which is the likelihood of the operation completing without error.

物理量子物理,在规模和能级这样的错误是没有这么多的问题,如果 的事操作。 量子态不仅在被测量时而且在量子位与周围系统的元素相互作用并纠缠在一起时都崩溃。 一个简单的事实是,量子系统与宇宙的其他部分允许故意操纵和测量足够的接触意味着足够的随机互动,最终导致量比脱散 ,失去他们的叠加信息。 另外,每个门操作都带有引起错误的额外风险。 单和多量子位门运算符具有保真度,这是操作完成而不会出错的可能性。

量子计算的时空体积 (The Space/Time Volume of Quantum Computation)

For any implementation technology, there is a limit to the number of qubits that can be made to operate together in a single quantum computer, and there is a limit to the coherence times and operational fidelities of the qubits in the system. The coherence times and fidelities impose a temporal limit, a maximum number of quantum operations before the errors become inevitable and irrecoverable. The number of available qubits multiplied by the number of operations defines a space/time volume of quantum computations that can be performed on a given machine.

对于任何实施技术,在单个量子计算机中可以一起操作的量子位数量是有限的,并且系统中量子位的相干时间和操作保真度是有限的。 相干时间和保真度施加了时间限制,即在错误变为不可避免和不可恢复之前的最大量子操作数。 可用量子比特数乘以操作数定义了可以在给定机器上执行的量子计算的空间/时间量。

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The history of quantum computing has been one of more and better qubits causing the available volumes to expand, while more sophisticated quantum algorithms reduce the volume required to solve a problem. The point at which the expanding operational envelope intersects the shrinking requirements envelope is the point where quantum computing becomes useful for applications.

量子计算的历史一直是导致可用体积扩展的更多更好的量子位之一,而更复杂的量子算法减少了解决问题所需的体积。 扩展的操作范围与缩小的需求范围相交的点是量子计算对应用有用的点。

构建真实机器 (Building a Real Machine)

Google超导量子位 (Google Superconducting Qubits)

Any two-level quantum mechanical system can act as a qubit — a photon, an electron, an atom or ion, but also macroscopic quantum mechanical systems like oscillating superconducting magnetic fields. The Google team has been working with “Xmon” transmon superconducting qubit designs since 2012, continuing work that had been going on for over a decade at UC Santa Barbara. It may seem counterintuitive, in an industry where performance and value have been driven by driving the size of transistors down to a handful of atoms, but macroscopic qubits are easier to manipulate. Superconducting qubits are relatively easy to engineer, given the scale of research and investment in semiconductor fabrication technology. Google qubits look like this as a planar structure:

任何两级量子力学系统都可以充当量子位(光子,电子,原子或离子),也可以充当宏观量子力学系统,例如振荡超导磁场。 自2012年以来,Google团队就一直在研究“ Xmon”跨子超导量子比特设计,并继续了在圣塔芭芭拉分校进行了十多年的工作。 在通过将晶体管的尺寸减小到几个原子来驱动性能和价值的行业中,这似乎是违反直觉的,但是宏观的量子位更易于操纵。 考虑到半导体制造技术的研究和投资规模,超导量子比特相对容易设计。 Google量子位看起来像是一个平面结构:

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The qubits are instantiated in the blue and green false color shaded “plus” shaped structures, which, at half a millimeter, are visible to the naked eye. The qubit frequency, amplitude, and phase are controlled by microwave pulses arriving from below. Their state can be measured using resonators, the squiggly structure above each qubit, to pick up induced current. With this 1D array of qubits, the Google/UCSB team hit a breakthrough 2-qubit fidelity of 99.4% in 2015. The design efforts since then have focused on how to turn this into 2D scalable designs.

量子位以蓝色和绿色伪彩色阴影的“加号”形状的结构实例化,该结构在肉眼可见的半毫米处。 量子位的频率,幅度和相位由从下方到达的微波脉冲控制。 可以使用谐振器来测量其状态,谐振器是每个量子位上方的弯曲结构,以吸收感应电流。 凭借这一1D量子位阵列,Google / UCSB团队在2015年实现了29.4比特率突破性的99.4%保真度。此后的设计工作一直专注于如何将其转换为2D可缩放设计。

The 22-qubit “Foxtail” and 72-qubit “Bristlecone” quantum processor chips take the Xmon qubit design to a “2.5D” fabrication model, where the qubits are implemented on one piece of silicon in a 2-dimensional array, while the control and measurement elements are symmetrically tiled across a matching 2D silicon carrier. The two pieces of silicon are connected using face-to-face “bump bonding” to make a multi-chip module. The Foxtail carrier and qubit chips are shown below.

22量子位的“ Foxtail”和72量子位的“ Bristlecone”量子处理器芯片将Xmon量子位的设计带入了“ 2.5D”制造模型,其中,量子位以二维阵列的形式在一块硅片上实现,而控制和测量元件对称地铺在匹配的2D硅载体上。 使用面对面的“凸点焊接”连接两个硅片,以制作多芯片模块。 Foxtail载体和qubit芯片如下所示。

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Foxtail, Google’s 22 qubit quantum processor. Image Erik Lucero
谷歌的22位量子处理器Foxtail。 图片Erik Lucero

2D Qubit阵列中的控制和隔离 (Control and Isolation in a 2D Qubit Array)

The operation of multi-qubit Xmon quantum gates requires an electrical coupling between qubits. This can be accomplished by bringing together the oscillating frequencies of neighboring qubits.

多量子位Xmon量子门的操作需要在量子位之间进行电耦合。 这可以通过将相邻量子位的振荡频率汇总在一起来实现。

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While this is relatively straightforward in a 1D array, where each qubit has at most 2 neighbors, the problem becomes more subtle in a 2D array organization. If a 2-qubit operation is to be performed, not only do the frequencies of the qubits involved need to be brought close enough to induce coupling, but the frequencies of the other neighboring qubits need to be taken further away from the coupling frequency. The diagram below shows the 8 qubits directly affected when a 2 qubit operation is set up in a 2D array of superconducting qubits. The qubits being made to couple and entangle are sent to a common frequency (=) while the surrounding qubits are sent to either a higher (+) or lower (-) frequency in a way that reduces the likelihood of their being accidentally affected.

尽管这在一个1D数组中相对简单,其中每个量子位最多具有2个邻居,但是在2D数组组织中,问题变得更加棘手。 如果要执行2量子位运算,不仅需要使所涉及的量子位的频率足够接近以引起耦合,而且还需要使其他相邻量子位的频率远离耦合频率。 下图显示了在2D超导量子比特数组中设置2量子比特操作时直接受影响的8个量子比特。 被耦合和纠缠的量子比特被发送到公共频率(=),而周围的量子比特被发送到更高(+)或更低(-)的频率,从而降低了它们被意外影响的可能性。

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The Foxtail and Bristlecone chip designs used passive capacitive coupling between neighboring qubits, which allows maximum qubit density, and worked quite well in 1D qubit arrays. In parallel to the bring-up of Bristlecone, a new generation of design was under development to move beyond passive coupling.

Foxtail和Bristlecone芯片设计在相邻量子位之间使用了无源电容耦合,从而实现了最大量子位密度,并且在一维量子位阵列中工作得很好。 在推出Bristlecone的同时,正在开发新一代设计,以超越被动耦合。

无花果处理器 (The Sycamore Processor)

The Sycamore processor design makes the trade-off of fewer qubits in the array in return for more control lines and hardware, to provide better operational fidelities. Active, adjustable coupler circuits are added to the chip, with associated external control logic. The number of qubits is reduced to 53 from the Bristlecone processor’s 72, but the overall space/time volume of computation is enhanced. The key is maintaining control, at scale.

Sycamore处理器设计权衡了阵列中较少的量子位,以换取更多的控制线和硬件,以提供更好的操作保真度。 有源,可调耦合器电路以及相关的外部控制逻辑被添加到芯片中。 量子位的数量从Bristlecone处理器的72位减少到53位,但是整体的计算时间/空间量得到了增强。 关键是保持大规模控制。

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While the limits of the quantum computer’s functionality may be defined by the superconducting qubit chip and its readout logic, which must be operated at about 0.01°K, much of the complexity is in the control and readout logic connected to the superconducting qubit module but located higher up in a dilution refrigerator cylinder, where the operating temperature is a warmer 3°K — the temperature of interstellar space. Signals are then routed to and from the top of the refrigerator and the 300°K environment of the machine room, from whence they are routed to conversion, measurement, and control systems in an adjacent rack.

虽然量子计算机功能的限制可以由超导量子位芯片及其读出逻辑来定义,必须在0.01°K左右的温度下运行,但大部分复杂性在于连接至超导量子位模块的控制和读出逻辑,但位于在稀释制冷机圆筒中更高的位置,工作温度为3°K(星际空间的温度)。 然后,信号往返于冰箱顶部和机房的300°K环境,并从那里路由至相邻机架中的转换,测量和控制系统。

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Image: Erik Lucero
图片:埃里克·卢塞罗(Erik Lucero)

The control systems include atomic clocks and signal generators to deliver the precisely timed bursts of microwave energy that modulate the quantum oscillators to implement the gate operations of a quantum program. When appropriate, the readout lines are interrogated, collapsing the superposition of qubits to sets of binary values that are measured, logged, and analysed.

该控制系统包括原子钟和信号发生器,用于传递精确定时的微波能量脉冲,这些脉冲能量调制量子振荡器以实现量子程序的门操作。 在适当的情况下,将对读取行进行查询,从而将qubit的叠加压缩为一组经过测量,记录和分析的二进制值。

NISQ计算机和应用程序 (NISQ Computers and Applications)

Machines such as the Google Foxtail, Bristlecone, and Sycamore machines are often referred to as NISQ computers, for Noisy, Intermediate-Scale Quantum computers. They have enough of a quantum computational volume to run non-trivial programs, but not enough to do so whilst correcting for errors on-the-fly.

机如谷歌谷子,狐尾,和美国梧桐机器通常被称为NISQ计算机,对于N oisy, ntermediate- 小号 Cale的Q uantum计算机。 它们具有足够的量子计算量来运行非平凡的程序,但不足以即时纠正错误。

Given that eventual decoherence of qubits is inevitable and not just bad luck, error correction on quantum computers isn’t just a luxury or an added-cost feature for enterprise-grade systems, it is a necessity for broad classes of applications. However, depending on the degree of correction (e.g. bit-flip only, or bit-flip and phase-flip errors), and the underlying quality of the physical qubits, the number required to implement a single, error-corrected “logical qubit” could range from 10 to 100 to 1000. From a computer science perspective, the most important application of NISQ machines may well be in validating and advancing the theories of quantum error correction. But there are other application areas for which NISQ machines may prove useful.

考虑到量子比特最终的去相干是不可避免的,而不仅仅是运气不佳,量子计算机上的纠错不仅是企业级系统的奢侈功能,也不是增加成本的功能,对于广泛的应用类别而言,这是必需的。 但是,根据校正程度(例如,仅位翻转,位翻转和相位翻转错误)以及物理量子位的基本质量,实现单个经过纠错的“逻辑量子位”所需的数量可能从10到100到1000。从计算机科学的角度来看,NISQ机器最重要的应用很可能是在验证和发展量子误差校正的理论上。 但是,在其他应用领域中,NISQ计算机可能会证明有用。

While quantum information theory has its origins further back in the 20th century, the first proposal to build a quantum computer is generally attributed to Richard Feynman in a 1982 paper entitled “Simulating Physics with Computers”, in which he observed that if physics is fundamentally quantum mechanical, a computer based on quantum principles should logically be the most efficient means of accurately simulating physical systems. And so it is that molecular modeling looks to be one of the first areas where quantum computing may prove to be economically viable. Molecules are relatively simple quantum mechanical systems, but every additional subatomic particle in a molecule doubles the quantum state space, and many “interesting” molecules have too many simultaneous interacting quantum states to be simulated practically by a classical computer. The Google team performed the first scalable simulation of the simplest possible molecule, H₂, with a 5 qubit machine in 2016, but large molecules of heavy atoms will require large, error-corrected quantum computers to fully simulate. NISQ systems should be able to aid in the study and understanding of intermediate-scale molecules of interest, particularly if variational quantum hybrid techniques prove to be effective.

尽管量子信息理论的起源可以追溯到20世纪,但有关建立量子计算机的第一个建议通常归功于Richard Feynman在1982年发表的题为“用计算机模拟物理学”的论文中,他在其中观察到,如果物理学从根本上说是量子的话机械上,基于量子原理的计算机在逻辑上应该是准确模拟物理系统的最有效方法。 因此,分子建模似乎是量子计算可能被证明在经济上可行的最早领域之一。 分子是相对简单的量子力学系统,但是分子中每增加一个亚原子粒子都会使量子态空间加倍,而且许多“有趣的”分子同时相互作用的量子态太多,以致于经典计算机无法实际模拟。 Google团队在2016年使用5量子位机对最简单的分子H 2进行了首次可扩展的仿真 ,但是大分子的重原子将需要经过纠错的大型量子计算机才能完全仿真。 NISQ系统应该能够帮助研究和了解感兴趣的中等规模分子,尤其是在变分量子混合技术被证明有效的情况下。

Other possible areas for useful NISQ applications include optimization and machine learning. Specialized quantum machines have been built to do “quantum annealing” optimization, analogous to simulated annealing algorithms used in classical operations research. These quantum annealing machines are not fully programmable quantum computers, but fully programmable gate-model machines can run adiabatic and other optimization algorithms.

有用的NISQ应用程序的其他可能领域包括优化和机器学习。 已经建立了专门的量子机器来进行“量子退火”优化,类似于经典运筹学中使用的模拟退火算法。 这些量子退火机不是完全可编程的量子计算机,但是完全可编程的门模型机可以运行绝热和其他优化算法。

“量子至上” (“Quantum Supremacy”)

The quest for quantum supremacy is perhaps more usefully thought of as a quest for quantum comparability. As has been seen, quantum computation has some significant advantages, as well as some disadvantages, over classical computation. When and how can one say that a quantum computing technology is “better” than classical? One of the first formulations of quantum supremacy was: when a problem is solved on a quantum machine that could never be solved on a classical computer. The problem there is that designers of classical computers have imaginations, too, and “never” is a very strong statement. A more nuanced definition might be: when a problem is solved on a quantum machine that is infeasible with current classical technology.

对量子至上的追求也许更有用地被认为是对量子可比性的追求。 可以看出,与经典计算相比,量子计算具有一些明显的优点和缺点。 何时,如何说量子计算技术比经典技术“更好”? 量子至高无上的第一个表述是:当问题在量子计算机上解决而经典计算机上永远无法解决。 这里的问题是,古典计算机的设计师也具有想象力,而“从不”是一个非常有力的陈述。 一个更细微的定义可能是:在量子计算机上解决了当前经典技术无法实现的问题时。

Seeking to demonstrate supremacy or advantage requires careful answers to two questions: Advantage doing what, precisely? And if a quantum computation is infeasible for a classical machine to reproduce, how can we verify that the quantum program was completely and correctly run?

寻求证明霸权或优势需要仔细回答以下两个问题:优势究竟在做什么? 如果量子计算对于经典机器而言是不可行的,那么我们如何验证量子程序是否完全正确运行?

Feynman’s original insight, that a quantum computer should be the best way to model quantum mechanics, is at the core of the “supremacy” benchmark proposed by Sergio Boixo et. al. If quantum computers are to be worth building, they must, at the very least, be more effective at running a quantum computer program than a simulation running on a classical machine. The idea is to generate pseudo-random gate-model programs of parametric size and depth, which generate high levels of entanglement across qubits, and randomly apply gates to them. Measurements of such a system provides a distribution of outputs that is not uniformly random, but instead exhibits a specific pattern of quantum interference. The challenge for the classical computer application is, from a given gate program, generate outputs with the same distribution as a quantum device. Classical simulation for programs on small numbers of qubits is quite simple, but for circuits of nontrivial depth, there is no sufficiently accurate classical simulation model that does not double its resource requirements with every additional qubit. Simulating 40–50 qubits to the necessary accuracy is a supercomputing problem.

Feynman最初的观点是,量子计算机应该是建模量子力学的最佳方法,这是Sergio Boixo 等人提出的“至高无上” 基准的核心 。 如果要建造量子计算机,至少它们在运行量子计算机程序方面必须比在经典机器上运行的模拟更有效。 这个想法是生成参数大小和深度的伪随机门模型程序,这些程序会在整个量子位上产生高水平的纠缠,并将门随机应用于它们。 这种系统的测量结果提供的输出分布不是均匀随机的,而是表现出特定的量子干扰模式。 对于经典计算机应用程序而言,挑战在于,从给定的门程序中生成具有与量子设备相同分布的输出。 针对少量量子位的程序的经典仿真非常简单,但是对于非平凡深度的电路,没有足够精确的经典仿真模型,不会使每个额外的量子位使资源需求增加一倍。 将40–50量子比特仿真到必要的精度是一个超级计算问题。

Given that the objective is to demonstrate that the quantum computer has done more than a classical machine, how is it possible to verify that the results are correct? While the correct execution of a random gate program results in a distinctly non-uniform output distribution, the degree of entanglement is such that a single failed gate operator will result in a measured output distribution uncorrelated with the known ideal distribution. The difference between the expected and sampled distributions can be expressed as cross-entropy, a term more commonly used in machine learning. The cross-entropy fidelity of the system is the probability of a run of a given random program to a given depth producing an output bit string from the valid output distribution.

鉴于目标是证明量子计算机比传统机器做得更多,如何验证结果正确? 尽管正确执行随机门程序会导致明显不同的输出分布,但是纠缠程度使得单个失败的门运算符将导致测得的输出分布与已知的理想分布不相关。 预期分布和采样分布之间的差异可以表示为交叉熵 ,它是机器学习中更常用的术语。 系统的交叉熵保真度是将给定随机程序运行到给定深度所产生的概率,该概率从有效输出分布中产生输出位串。

The larger and deeper a quantum gate program, the lower the achievable cross-entropy fidelity. As the fidelities of the constituent gate operations can be measured, they can be used to predict the fidelity of the full system. Even with high constituent fidelities, the multiplication of probabilities represented by a deep quantum gate program will result in a numerically low predicted fidelity. The largest random circuit tested used 53 qubits, and executed 1113 single-qubit gates and 430 two-qubit gates. The predicted fidelity for that circuit was 0.2%, which may seem numerically small, but which is well within the margin of confidence.

量子门程序越大越深,可实现的交叉熵保真度越低。 由于可以测量组成门操作的保真度,因此可以将它们用于预测整个系统的保真度。 即使具有较高的组成保真度,由深量子门程序表示的概率相乘也会导致数值上的预测保真度较低。 测试的最大随机电路使用了53个量子比特,并执行了1113个单量子比特门和430个两个量子比特门。 该电路的预测保真度为0.2%,从数字上看可能很小,但仍在置信范围内。

The experiment was run on the Google Sycamore machine, with simulations on Google servers, at the Jülich supercomputing center, and on the Summit supercomputer at the US Department of Energy’s Oak Ridge National Laboratory. At Google, a series of runs were done which established that measured cross-entropy fidelities tracked their predicted values to the limits of full simulation, and beyond.

该实验在Google Sycamore机器上进行,并在Google服务器,Jülich超级计算中心和美国能源部Oak Ridge国家实验室的Summit超级计算机上进行了仿真。 在Google,进行了一系列运行,确定所测得的交叉熵保真度将其预测值跟踪到完全模拟的极限,甚至更高。

53-qubit benchmark circuits were simulated on the Summit supercomputer to depths of 12 and 14 cycles. The classical computational cost of simulating to the same levels of fidelity increases non-linearly with circuit depth. Simulating one of the circuits for 12-cycles consumed 1.29 hours on 4550 nodes of Summit. The equivalent simulation to 14 cycles would consume 1624 hours, 67.7 days of Summit time. The Sycamore supremacy runs on 53-qubit circuits went to a depth of 20 cycles. Sampling this circuit a million times took 200 seconds on the quantum machine, but would require roughly 10,000 years to simulate on a million-core classical supercomputer. The circuits and the measured output bit strings from the quantum computations were archived, so that future classical simulation algorithms can be benchmarked against the experimental data.

在Summit超级计算机上模拟了53个量子位的基准电路,深度为12和14个循环。 仿真到相同保真度的经典计算成本随着电路深度的增加而非线性增加。 在Summit的4550个节点上,对其中一个电路进行12个周期的仿真消耗了1.29个小时。 相当于14个周期的模拟将花费1624小时,即顶峰时间67.7天。 Sycamore至高无上在53量子位电路上运行了20个循环的深度。 在量子机器上对该电路进行一百万次采样需要200秒,但是在一百万核的经典超级计算机上进行仿真大约需要10,000年的时间。 量子计算的电路和测量的输出位串已存档 ,以便将来的经典仿真算法可与实验数据进行基准比较。

In another ORNL experiment, a program over 49 qubits was simulated for 40 cycles on Summit, completing in 2.44 hours of elapsed time on 27,000 GPUs, or 281 petaflops. The classical run consumed an estimated 21 MWh of power. This compares to roughly 100 seconds (0.027 hours) and 0.00042 MWh on a Google quantum machine.

在另一个ORNL实验中 ,在Summit上模拟了一个49 qubit的程序,进行了40个循环,在27,000个GPU或281 petaflops上花费了2.44个小时。 经典运行消耗的功率估计为21 MWh。 相比之下,在Google量子计算机上大约为100秒(0.027小时)和0.00042 MWh。

The diagram below shows how the operation of the Sycamore machine tracked full simulation (◯) to the limits of practical simulation, and partial simulation (✕, +) beyond.

下图显示了Sycamore机器的运行情况如何将完全模拟(◯)跟踪到实际模拟的极限,以及超出部分模拟(✕,+)的极限。

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量子小鹰 (A Quantum Kittyhawk)

In thinking about the significance of the Google quantum supremacy experiment, I think that there’s a pretty strong analogy to the Wright brothers’ first manned, powered aircraft flights at Kittyhawk, NC in 1903. Not unlike the Google Quantum AI team, the Wright brothers were competing with other teams seeking to create the first practical airplane, including some who were far better known and better financed. Samuel Langley was Secretary of the Smithsonian Institution, with access to substantial US government funding and better engine technology than the Wrights.

考虑到Google量子至上性实验的重要性,我认为这与莱特兄弟1903年在北卡罗来纳州基蒂霍克的首次有人驾驶飞机飞行非常相似。莱特兄弟与Google量子AI团队一样,与其他寻求制造首架实用飞机的团队竞争,其中包括一些知名度更高,资金更充足的飞机。 塞缪尔·兰利(Samuel Langley)是史密森学会(Smithsonian Institution)的秘书,与赖特(Wrights)相比,他可以获得美国政府的大量资助,并拥有更好的发动机技术。

But the Wrights had developed better means to estimate stress and loading, and above all, the Wrights understood that flying was unlike “classical” surface transport in that it requires simultaneous control over three axes, roll, pitch, and yaw. If Langley’s 1903 Aerodrome had survived launch, the pilot would have been in grave danger, as there were simply no mechanisms that could have enabled a landing maneuver.

但是莱特人已经开发出了更好的方法来估算应力和载荷,最重要的是,莱特人理解飞行不同于“经典”的地面运输,因为飞行需要同时控制三个轴(滚动,俯仰和偏航)。 如果兰利(Langley)的1903年机场幸免于发射,飞行员将处于严重危险之中,因为根本没有任何机制可以使飞机降落。

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Image: Library of Congress
图片:国会图书馆

The Wright flyer only made 4 flights on December 17, 1903. None lasted so long as a minute. None covered so much as 1000 feet. The basic Wright airframe design, with the horizontal and vertical stabilizers split fore and aft of the main wings, was proved impractical and abandoned within a few years, even by the Wrights. It was a decade before the first commercial passenger airplane flight. But human-piloted, heavier-than-air, powered flight had been shown to be more than just a dream that refused to die.

赖特(Wright)的传单在1903年12月17日只进行了4次飞行。没有飞行持续一分钟。 没有一个可以覆盖1000英尺。 赖特(Wrights)机体的基本设计,水平和垂直稳定器前后分开主翼,事实证明是不切实际的,并且在几年内就被放弃了。 距商用客机首飞还不到十年。 但是,事实证明,由人类驾驶,比空气重的动力飞行不仅仅只是一个拒绝死亡的梦想。

Somehow, more than a century later, there are echoes of the wind on the North Carolina dunes mixing with the sound of helium pumps in a Santa Barbara lab.

一个多世纪之后的一个月,在圣塔芭芭拉实验室中,北卡罗莱纳州沙丘上的风声与氦泵的声音混合在一起。

翻译自: https://medium.com/discourse/quantum-supremacy-the-wright-stuff-e24d2e9719c7

赖特 因果分析

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