Enhancing quantum state reconstruction with structured classical shadows

IF 8.3 1区 物理与天体物理 Q1 PHYSICS, APPLIED
Zhen Qin, Joseph M. Lukens, Brian T. Kirby, Zhihui Zhu
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Abstract

While classical shadows can efficiently predict key quantum state properties, their suitability for certified quantum state tomography remains uncertain. In this paper, we address this challenge by introducing a projected classical shadow (PCS) that extends the standard classical shadow by incorporating a projection step onto the target subspace. For a general quantum state consisting of n qubits, our method requires a minimum of O(4n) total state copies to achieve a bounded recovery error in the Frobenius norm between the reconstructed and true density matrices, reducing to O(2nr) for states of rank r < 2n—meeting information-theoretic optimal bounds in both cases. For matrix product operator states, we demonstrate that the PCS can recover the ground-truth state with O(n2) total state copies, improving upon the previously established Haar-random bound of O(n3). Numerical simulations validate our scaling results and demonstrate the practical accuracy of the proposed PCS method.

Abstract Image

利用结构经典阴影增强量子态重构
虽然经典阴影可以有效地预测关键的量子态特性,但它们对认证量子态层析成像的适用性仍然不确定。在本文中,我们通过引入投影经典阴影(PCS)来解决这一挑战,PCS通过在目标子空间上合并投影步长来扩展标准经典阴影。对于由n个量子比特组成的一般量子态,我们的方法需要至少O(4n)个总状态拷贝才能在重构和真密度矩阵之间的Frobenius范数中实现有界恢复误差,对于秩为r <; 2n的状态,在这两种情况下都满足信息论最优边界,则减少到O(2nr)。对于矩阵积算子状态,我们证明了PCS可以用O(n2)个总状态副本恢复基真状态,改进了先前建立的O(n3)的haar随机界。数值模拟验证了我们的缩放结果,并证明了PCS方法的实用精度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
npj Quantum Information
npj Quantum Information Computer Science-Computer Science (miscellaneous)
CiteScore
13.70
自引率
3.90%
发文量
130
审稿时长
29 weeks
期刊介绍: The scope of npj Quantum Information spans across all relevant disciplines, fields, approaches and levels and so considers outstanding work ranging from fundamental research to applications and technologies.
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