近日，美国加州理工学院Mehdi Soleimanifar团队实现了用很少的单量子位测量来证明几乎所有的量子态。该项研究成果发表在2025年9月8日出版的《自然—物理学》杂志上。

证明实验室合成的n量子比特状态接近给定的目标状态是量子信息科学的一项基本任务。然而，现有的适用于一般目标状态的严格协议在深度量子电路或指数级多单量子位测量的形式中都有潜在的禁止电阻要求。

研究组证明了几乎所有的n-量子比特目标态，包括那些具有指数电路复杂度的目标态，可以只用O（n²）个单量子比特测量来证明。给定对目标状态振幅的访问，他们的协议只需要O（n³）个经典计算。这一结果是通过一种将证明与随机漫步的混合时间联系起来的技术建立起来的。该协议应用于对量子系统进行基准测试，优化量子电路以产生所需的目标状态，以及学习和验证神经网络，张量网络以及仅以单量子位测量为主题的量子状态的各种其他表示。

研究组表明，这种验证的表示可以被主题化，以有效地预测合成状态的高度非局域属性，否则需要对状态进行指数级的测量。研究组在多达120个量子位的数值实验中展示了这些应用，并观察到与现有方法（如交叉熵基准测试）相比的优势。

附：英文原文

Title: Certifying almost all quantum states with few single-qubit measurements

Author: Huang, Hsin-Yuan, Preskill, John, Soleimanifar, Mehdi

Issue&Volume: 2025-09-08

Abstract: Certifying that an n-qubit state synthesized in the laboratory is close to a given target state is a fundamental task in quantum information science. However, existing rigorous protocols applicable to general target states have potentially prohibitive resource requirements in the form of either deep quantum circuits or exponentially many single-qubit measurements. Here we prove that almost all n-qubit target states, including those with exponential circuit complexity, can be certified from only O(n2) single-qubit measurements. Given access to the target state’s amplitudes, our protocol requires only O(n3) classical computation. This result is established by a technique that relates certification to the mixing time of a random walk. Our protocol has applications for benchmarking quantum systems, for optimizing quantum circuits to generate a desired target state and for learning and verifying neural networks, tensor networks and various other representations of quantum states using only single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties of a synthesized state that would otherwise require an exponential number of measurements on the state. We demonstrate these applications in numerical experiments with up to 120 qubits and observe an advantage over existing methods such as cross-entropy benchmarking.

DOI: 10.1038/s41567-025-03025-1

Source: https://www.nature.com/articles/s41567-025-03025-1