内容来源：https://research.google/blog/a-verifiable-quantum-advantage/

内容总结：

谷歌量子AI团队在《自然》杂志发表封面文章，宣布实现可验证的量子计算优势。这项名为"量子回声"的创新算法通过测量"时序关联函数"，首次在量子可观测量的验证性计算中突破经典计算极限。

研究团队在"柳树"量子芯片上使用103个量子比特展开实验。该技术通过前向与反向量子演化，观测到类似蝴蝶效应的量子混沌现象。实验数据显示，二阶时序关联函数产生的量子干涉效应，使经典计算机需耗时约13000倍才能完成同等计算任务。

该研究突破了2019年量子霸权演示中随机电路采样的局限性，将量子计算导向具有实际应用价值的可验证路径。团队已开展核磁共振领域的应用探索，通过模拟有机分子在液晶环境中的量子行为，成功提升了分子结构建模精度。这项突破为量子计算机在分子结构解析等现实问题中的应用开辟了可行路径。

这项成果凝聚了谷歌量子AI、DeepMind与加州大学伯克利分校等机构的集体智慧，标志着量子计算正从理论优势迈向实际应用的新阶段。

中文翻译：

可验证的量子优势
2025年10月22日
谷歌量子人工智能研究科学家 肖米、科斯佳京·凯切吉

在最新发表于《自然》杂志的论文中，我们提出了一种测量时序关联函数（OTOC）的新型量子计算任务。这项研究不仅展示了可验证的量子优势，更为解决核磁共振中的哈密顿量学习等现实问题开辟了道路。

快速链接

自然界充满混沌现象，其核心特征在于系统对微小扰动的高度敏感性。宏观世界中，天气系统就是典型混沌系统——初始条件的细微变化会随时间推移导致截然不同的结果（即“蝴蝶效应”）；种群动态同样如此，局部种群的微小波动最终可能影响整个生态系统。量子系统中的混沌现象同样普遍，例如原子核在时变磁场作用下的磁化动力学，以及高温超导体中的电子流动。

由于计算成本呈指数级增长，模拟量子混沌系统对经典计算构成巨大挑战，这也使得量子计算机成为实现量子优势的理想平台。2019年，我们通过从高度混沌的量子比特态中采样比特串，首次实现了超越经典计算能力的量子计算。但随机线路采样方案存在局限性：在大型量子系统中，相同比特串永远不会重复出现，这限制了其提取有效信息的能力。

在登上《自然》封面的论文《在量子遍历性边缘观测相长干涉》中，我们提出并实验演示了名为“量子回波”的创新算法。该算法核心在于测量被称为时序关联函数（OTOC）的量子可观测量。OTOC及其高阶推广构成了描述量子动力学混沌特性的新型观测量家族。与比特串不同，量子期望值（如电流、速度、磁化强度和密度）具有可验证性——在不同量子计算机上运行会获得相同结果。期望值的普适性与可验证性相结合，为利用OTOC解决经典计算机无法应对的现实问题指明了方向。值得注意的是，我们在Willow量子芯片上运行量子回波算法时，针对基准量子线路组已实现超越经典计算的能力。

时序关联函数实践

实际操作中，OTOC表征着经历系列量子操作后单个量子比特的终态。在Willow芯片的实验中，共有103个量子比特通过随机量子线路形式经历“正向”（U）与“反向”（U†）演化。当所有量子比特处于独立状态时，正向演化会使系统进入高度混沌态，形成全量子比特关联。在两次时间演化之间，我们对某个量子比特施加单比特操作B作为扰动，后续再施加单比特探针操作M。重复此过程一至两次，可分别获得一阶或二阶OTOC。若未引入扰动B，正反向演化将使系统回归初始独立状态；而扰动B会触发蝴蝶效应——经过扰动后的正反向演化，系统将陷入与初始状态截然不同的混沌态。

实验中的重要发现是：高阶OTOC展现出类似传统干涉仪的复杂量子干涉效应，即多体干涉。这意味着众多粒子的量子态会相互干涉，如同水波干涉产生复杂整体效应。其中扰动操作B和M如同非理想反射镜，改变着系统轨迹。随着“往返”演化次数增加（轨迹在B和M间反射），高阶OTOC对扰动愈发敏感。当满足共振条件（即U†恰好是U的逆演化）时，相长干涉会从混沌态的全部关联中放大特定量子关联子集。具体而言，这种干涉测量揭示了演化U如何在操作B和M作用的两个量子比特间建立关联，可作为表征U演化的精密仪器。

量子优势的干涉根基

OTOC的干涉特性带来两个对实现量子优势至关重要的结果。首先，正反向演化能部分逆转混沌效应并放大终端测量的量子信号。我们在OTOC信号中观测到这种放大特征：OTOC信号强度（以随机线路集合中OTOC值分布宽度为表征）随时间呈负幂律衰减，而无反向演化的量子信号则呈指数衰减。这种缓慢的幂律衰减表明，在量子计算机上测量OTOC比经典模拟效率显著更高——后者成本随时间呈指数增长。

量子与经典处理器的算力鸿沟

多体干涉的第二个结果是经典计算复杂度问题。量子计算的核心任务之一是界定特定计算任务中量子与经典计算机的计算成本差异。我们通过双重路径验证：(1)结合理论分析与实验，揭示经典算法在复现Willow芯片OTOC计算结果时面临的根本障碍；(2)通过直接实现与成本评估，测试九种经典模拟算法的性能。

在第一路径中，我们确认量子干涉是经典计算的主要障碍。量子力学的显著特征在于：预测实验结果需分析概率幅而非经典力学中的概率。著名案例如光量子纠缠现象（2022年诺贝尔物理学奖）与超导电路中的宏观量子隧穿效应（2025年诺贝尔物理学奖）。

我们的二阶OTOC数据（经历两次正反向线路循环）揭示了概率与概率幅的本质差异。关键在于概率为非负数，而概率幅可具任意符号并由复数描述。这些特性意味着概率幅承载着更复杂的信息集合。我们的实验涉及65个量子比特的指数大空间中的概率幅，精确描述此类量子系统需在内存中存储处理2^65个复数，这已超越超级计算机容量。此外，线路中的量子混沌确保每个概率幅均至关重要，因此采用压缩描述的算法所需内存与处理时间也超出超算极限。

进一步理论实验分析表明：必须精确计算概率幅的符号相位才能通过数值计算预测实验数据。这对曾成功描述大尺度量子现象（如液氦-4超流性）的高效经典算法——量子蒙特卡罗方法构成重大障碍。该类算法基于概率描述，而我们的分析证明此类方法将导致计算输出出现不可控误差。

通过对压缩表示与量子蒙特卡罗算法的直接实现，我们确认经典算法无法预测二阶OTOC数据。Willow芯片仅用2小时完成的实验，经典超算预计需多耗费13,000倍时间。这一结论源自我们投入约10人年对量子结果进行的经典验证，累计实施了九种经典模拟算法。

OTOC线路的实际应用

在确立OTOC的超越经典复杂度后，我们开始探索其解决实际问题的应用场景。为此提出哈密顿量学习方案：通过量子计算机模拟自然界物理系统（如参数未知的分子）的OTOC信号，将其与真实物理系统数据比对，寻找最佳吻合点。通过这种匹配，我们有望获得比其他技术更精确的系统参数估计。

为实现该方案，需要寻找能执行量子回波算法的自然系统，并在量子硬件上模拟这些系统。作为迈向该目标的一步，在预印本《通过多体核自旋回波的分子几何结构量子计算》中，我们展示了利用核磁共振谱学验证此概念的实验。核磁共振通过大磁场中核自旋进动来解析分子与材料结构，如人体蛋白质或手机电池组件。核自旋遵循量子力学规律，在特定条件（如固体或类固体材料）下会呈现前述量子混沌行为，使其成为OTOC协议的理想载体。

在这篇待同行评审的预印本中，我们在加州大学伯克利分校派恩斯磁共振中心，测量了溶解于液晶的两种有机分子的OTOC，随后在Willow芯片上模拟该实验，最终获得改进的分子结构模型。尽管受现实系统模拟复杂度与当前芯片性能限制，这项初步演示尚未超越经典能力，但结果展现出对分子细节的灵敏度，我们确信这条路径将引领量子计算迈向首批实用应用。

结论

我们完成了首个测量量子观测值的量子计算实验，该观测量既可通过其他量子计算机或自然量子系统验证，又超越已知经典算法的模拟能力。这一突破得益于我们近期的硬件进展，为量子计算机在探测分子等物理系统微观结构方面实现首次实际应用铺平道路。

致谢

本项工作汇聚量子AI团队众多成员，以及谷歌DeepMind、加州大学伯克利分校、达特茅斯学院、QSimulate和英伟达的外部合作者。

英文来源：

A verifiable quantum advantage
October 22, 2025
Xiao Mi and Kostyantyn Kechedzhi, Research Scientists, Google Quantum AI
In our latest Nature publication, we introduce a new quantum computational task measuring Out-of-Time-Order Correlators (OTOCs). This work demonstrates a verifiable quantum advantage and paves the way for solving real-world problems like Hamiltonian learning in Nuclear Magnetic Resonance (NMR).
Quick links
Nature is brimming with chaos, a phenomenon characterized by the high sensitivity of a system toward small perturbations. In the macroscopic world, notable examples of chaotic systems include weather patterns, wherein a small change in initial conditions leads to vastly different outcomes over time (often dubbed “the butterfly effect”), and population dynamics, where small shifts in local populations may eventually affect the entire ecosystem. Chaos is similarly abundant in quantum systems, with examples including the dynamics of magnetization of atomic nuclei when subjected to a time-varying magnetic field, and the flow of electrons in high-temperature superconductors.
Simulating quantum-chaotic systems is challenging for classical computation due to exponentially scaling computational cost, making quantum computers ideal for achieving quantum advantage. In 2019, we demonstrated the first beyond-classical quantum computation by sampling bitstrings from a highly chaotic quantum state of qubits. However, this random circuit sampling approach has limited practical utility since the same bitstring never appears twice in a large quantum system, restricting its ability to reveal useful information.
In “Observation of constructive interference at the edge of quantum ergodicity”, featured on the cover of Nature, we introduce and experimentally demonstrate a quantum algorithm which we call Quantum Echoes. The heart of the algorithm is measuring the expectation value of a quantum observable, called the out-of-time-order correlator (OTOC). OTOC and its higher order generalizations are a new family of observables that describe how quantum dynamics become chaotic. Unlike bitstrings, quantum expectation values, e.g., current, velocity, magnetization and density, are verifiable computational outcomes that remain the same when run on different quantum computers. The wide relevance of expectation values combined with their verifiability indicates a direct path toward using OTOCs to solve real-world problems using quantum computers, which are not possible to solve on classical computers. Remarkably, we show that running the Quantum Echoes algorithm on the Willow quantum chip is already in the beyond-classical regime for a set of benchmarking quantum circuits.
Out-of-time-order correlator
In practice, OTOC represents the state of a single qubit at the end of a series of quantum operations. In our experiments running Quantum Echoes on Willow, a total of 103 qubits underwent both “forward” (U) and “backward” (U†) evolutions in the form of random quantum circuits. A forward evolution applied to a state where all qubits are independent from each other brings the system to a highly chaotic state with quantum correlations across all qubits. A perturbation, a one-qubit operation B, is applied to a qubit in between the two time evolutions. This circuit is followed by another probe, a one-qubit operation M. Repeating this process once or twice leads to an OTOC of first or second order. In absence of B the forward and backward evolution returns the system to the initial state, where all qubits are independent. Inclusion of the perturbation B sets off a butterfly effect: after such perturbed forward and backward evolution, the whole system ends in a chaotic state with quantum correlations across all qubits that is very different from the initial state.
A crucial insight we obtained from our experiments is that higher-order OTOCs exhibit complex quantum interference effects analogous to a traditional interferometer. This is known as many-body interference, meaning the quantum states of many particles interfere with each other, much like waves of water might interfere, leading to complex overall effects. Here the perturbations, B and M, act as imperfect mirrors that modify the system’s trajectories. Higher order OTOCs become more sensitive to the perturbation due to increasing number of “round trip” evolutions, where the trajectories bounce off of B and M. When a resonance condition is satisfied, which corresponds to evolution U† being the exact inverse of U, the interference is constructive and it amplifies the subset of quantum correlations from the totality of those present in the chaotic state. More specifically, this interferometry reveals how the evolution U generates correlations between the two qubits where operations B and M were applied. It can be used as a sensitive instrument to characterize the evolution of U.
The interference nature of the OTOC leads to two consequences crucial for attaining quantum advantage. First, the forward and backward evolutions partially reverse the effects of chaos and amplify the quantum signal measured at the end. We observed the signature of this amplification in OTOC signals. More specifically, OTOC signal magnitude, characterized by the width of the distribution of OTOC values over the ensemble of random circuits, scales as a negative power of time, whereas quantum signals measured without back evolutions decay exponentially. The slow power law decay of OTOCs suggests that measuring these quantities on a quantum computer is significantly more efficient than classical simulations, where costs increase exponentially over time.
The computational gap between quantum and classical processors
The second consequence of many-body interference is classical complexity. A central task for quantum computing is to identify the computational cost gap between quantum and classical computers on specific computational tasks. We approached this in two ways: (1) through a combination of theoretical analysis and experiments, we revealed the fundamental obstacles to known classical algorithms in achieving the same outcome as our OTOC calculations on Willow, and (2) we tested the performance of nine relevant classical simulation algorithms by direct implementation and cost estimation.
In the first approach we identified that quantum interference is an obstacle for classical computation. A distinct characteristic of quantum mechanics is that predicting an outcome of an experiment requires analyzing probability amplitudes rather than probabilities as in classical mechanics. A well known example is the entanglement of light that manifests in quantum correlations between photons, elementary particles of light, that persist over long distances (2022 Physics Nobel Laureates) or macroscopic quantum tunneling phenomena in superconducting circuits (2025 Physics Nobel Laureates).
The interference in our second order OTOC data (i.e., an OTOC that runs through the backward and forward circuit loop twice) reveals a similar distinction between probabilities and probability amplitudes. Crucially, probabilities are non-negative numbers, whereas probability amplitudes can be of an arbitrary sign and are described by complex numbers. Taken together, these features mean they contain a much more complex collection of information. Instead of a pair of photons or a single superconducting junction, our experiment is described by probability amplitudes across an exponentially large space of 65 qubits. An exact description of such a quantum mechanical system requires storing and processing 265 complex numbers in memory, which is beyond the capacity of supercomputers. Moreover, quantum chaos in our circuits ensures that every amplitude is equally important, and therefore algorithms using a compressed description of the system require memory and processing time beyond the capacity of supercomputers.
Our further theoretical and experimental analysis revealed that carefully accounting for the signs of the probability amplitudes is necessary to predict our experimental data by a numerical calculation. This presents a significant barrier for a class of efficient classical algorithms, quantum Monte Carlo, that have been successful at describing quantum phenomena in a large quantum mechanical space (e.g., superfluidity of liquid Helium-4). These algorithms rely on description in terms of probabilities, yet our analysis demonstrates that such approaches would result in an uncontrollable error in the computation output.
Our direct implementation of algorithms relying on both compressed representation and efficient quantum Monte Carlo confirmed the impossibility of predicting second-order OTOC data. Our experiments on Willow took approximately 2 hours, a task estimated to require 13,000 times longer on a classical supercomputer. This conclusion was reached after an estimated 10 person years spent in classical red teaming of our quantum result, implementing a total of nine classical simulation algorithms as a result.
Practical application of OTOC circuits
Having established the beyond-classical complexity of OTOCs, we began exploring how they could be applied to solving real-world problems of practical interest. To this end, we proposed Hamiltonian learning, a scheme where the quantum computer simulates OTOC signals from a physical system in nature, such as molecules, whose system parameters are not fully known. Then, we compare the quantum computer OTOC signals against real-world data about the physical system and observe when they best agree. By looking for this agreement, we aim to obtain a more precise estimate of system parameters than what is possible through other techniques.
To make this scheme practical, we have to find systems in nature that can perform our Quantum Echoes algorithm, and simulate these systems on our quantum hardware. As a step toward this goal, in "Quantum computation of molecular geometry via many-body nuclear spin echoes”, we show that we tested this concept using nuclear magnetic resonance (NMR) spectroscopy. In NMR, one uses the precession of nuclear spins in a large magnetic field to learn the structure of molecules and materials, like the proteins in your body or the battery components in your phone. Nuclear spins obey the laws of quantum mechanics, and under certain conditions (namely in solids or solid-like materials) they demonstrate the same quantum-chaotic behavior described above. This makes them a perfect candidate for the OTOC protocol.
In this pre-print, which will be submitted for peer review, we measured OTOCs on two organic molecules dissolved in liquid crystal at the Pines Magnetic Resonance Center at UC Berkeley. This experiment was then simulated on our Willow chip, resulting in improved models of the molecular structure. Due to the inherent complexity of simulating real-world systems and performance limits of our current chip, this initial demonstration is not yet beyond classical. However, our results demonstrate sensitivity to molecular details and we're confident that this path will lead to some of the first useful applications of quantum computation.
Conclusion
We have performed the first quantum computing experiment measuring a quantum observable that is both verifiable through another quantum computer or a natural quantum system, and beyond the simulation capacity of known classical algorithms. This experiment was made possible by our recent hardware advancement, and paves the way toward the first real-world application of quantum computers in probing the microscopic structures of physical systems such as molecules.
Acknowledgements
This work involved many members of the Quantum AI team, along with Google DeepMind and external collaborators at UC Berkeley, Dartmouth College, QSimulate, and NVIDIA.