Certifying almost all quantum states with few single-qubit measurements

IF 18.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Hsin-Yuan Huang, John Preskill, Mehdi Soleimanifar
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引用次数: 0

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.

Abstract Image

用很少的单量子位测量来证明几乎所有的量子态
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令人望而却步的资源需求。在这里,我们证明了几乎所有的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,我们的协议只需要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。我们的协议应用于量子系统的基准测试,优化量子电路以生成所需的目标状态,以及仅使用单量子位测量来学习和验证神经网络,张量网络和量子状态的各种其他表示。我们表明,这种经过验证的表示可以用来有效地预测合成状态的高度非局部特性,否则需要对状态进行指数级的测量。我们在多达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。
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来源期刊
Nature Physics
Nature Physics 物理-物理:综合
CiteScore
30.40
自引率
2.00%
发文量
349
审稿时长
4-8 weeks
期刊介绍: Nature Physics is dedicated to publishing top-tier original research in physics with a fair and rigorous review process. It provides high visibility and access to a broad readership, maintaining high standards in copy editing and production, ensuring rapid publication, and maintaining independence from academic societies and other vested interests. The journal presents two main research paper formats: Letters and Articles. Alongside primary research, Nature Physics serves as a central source for valuable information within the physics community through Review Articles, News & Views, Research Highlights covering crucial developments across the physics literature, Commentaries, Book Reviews, and Correspondence.
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