Estimating expectation values is a key subroutine in quantum algorithms. Near-term implementations face two major challenges: a limited number of samples required to learn a large collection of observables, and the accumulation of errors in devices without quantum error correction. To address these challenges simultaneously, we develop a quantum error-mitigation strategy called ``symmetry-adjusted classical shadows,'' by adjusting classical-shadow tomography according to how symmetries are corrupted by device errors. As a concrete example, we highlight global $\mathrm{U(1)}$ symmetry, which manifests in fermions as particle number and in spins as total magnetization, and illustrate their group-theoretic unification with respective classical-shadow protocols. We establish rigorous sampling bounds under readout errors obeying minimal assumptions, and perform numerical experiments with a more comprehensive model of gate-level errors derived from existing quantum processors. Our results reveal symmetry-adjusted classical shadows as a low-cost strategy to mitigate errors from noisy quantum experiments in the ubiquitous presence of symmetry.
Demonstrating and Benchmarking Classical Shadows for Lindblad Tomography
Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所量子设备中心）；Center for the Mathematics of Quantum Theory, MATH Department, University of Copenhagen（哥本哈根大学数学系量子理论数学中心）；NNF Quantum Computing Programme, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所NNF量子计算项目）；Department of Microtechnology and Nanoscience, Chalmers University of Technology（查尔姆斯理工大学微技术和纳米科学系）
Quantum computers have enabled solving problems beyond the current computers' capabilities. However, this requires handling noise arising from unwanted interactions in these systems. Several protocols have been proposed to address efficient and accurate quantum noise profiling and mitigation. In this work, we propose a novel protocol that efficiently estimates the average output of a noisy quantum device to be used for quantum noise mitigation. The multi-qubit system average behavior is approximated as a special form of a Pauli Channel where Clifford gates are used to estimate the average outp…
Sample-efficient quantum error mitigation via classical learning surrogates
Henan Key Laboratory of Quantum Information（量子信息与密码学重点实验室）；College of Computing and Data Science（计算与数据科学学院）；Nanyang Technological University（南洋理工大学）；School of Physical and Mathematical Science（物理与数学科学学院）
Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows
Harvard University（哈佛大学）；IBM Quantum（IBM量子计算部门）；IBM T.J. Watson Research Center（IBM T.J.沃森研究中心）；Berkeley Center for Quantum Information and Computation（伯克利量子信息与计算中心）；University of California San Diego（加利福尼亚大学圣迭戈分校）
Mitigating errors in state preparation and measurement with noncomputational states
IBM Quantum, IBM Research Europe – Zurich（IBM量子，IBM欧洲苏黎世研究部）；Laboratory of Theoretical Physics of Nanosystems, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院纳米系统理论物理实验室）；Theory and Simulation of Materials, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院材料理论与模拟）
