Title: Quantum error mitigation for Fourier moment computation Show Chinese title

Title: 量子误差缓解用于傅里叶矩计算

Abstract: Hamiltonian moments in Fourier space - expectation values of the unitary evolution operator under a Hamiltonian at different times - provide a convenient framework to understand quantum systems. They offer insights into the energy distribution, higher-order dynamics, response functions, correlation information and physical properties. This paper focuses on the computation of Fourier moments within the context of a nuclear effective field theory on superconducting quantum hardware. The study integrates echo verification and noise renormalization into Hadamard tests using control reversal gates. These techniques, combined with purification and error suppression methods, effectively address quantum hardware decoherence. The analysis, conducted using noise models, reveals a significant reduction in noise strength by two orders of magnitude. Moreover, quantum circuits involving up to 266 CNOT gates over five qubits demonstrate high accuracy under these methodologies when run on IBM superconducting quantum devices. Show Chinese abstract

Abstract: 哈密顿量在傅里叶空间中的矩——在不同时间下哈密顿量作用下的单位演化算符的期望值——提供了一个方便的框架来理解量子系统。它们提供了关于能量分布、高阶动力学、响应函数、相关信息和物理性质的见解。本文重点研究了在超导量子硬件上的核有效场理论中傅里叶矩的计算。该研究将回波验证和噪声归一化集成到使用控制反转门的Hadamard测试中。这些技术结合纯化和误差抑制方法，有效地解决了量子硬件退相干问题。通过噪声模型进行的分析显示，噪声强度显著降低了两个数量级。此外，在IBM超导量子设备上运行的涉及五个量子比特最多266个CNOT门的量子电路，在这些方法下表现出高精度。