Efficiently estimating fermionic Hamiltonian expectation values is vital for simulating various physical systems. Classical shadow (CS) algorithms offer a solution by reducing the number of quantum state copies needed, but noise in quantum devices poses challenges. We propose an error-mitigated CS algorithm assuming gate-independent, time-stationary, and Markovian (GTM) noise. For n-qubit systems, our algorithm, which employs the easily prepared initial state \(\left\vert {0}^{n}\right\rangle \,\left\langle {0}^{n}\right\vert\) assumed to be noiseless, efficiently estimates k-RDMs with \(\widetilde{{{{\mathcal{O}}}}}(k{n}^{k})\) state copies and \(\widetilde{{{{\mathcal{O}}}}}(\sqrt{n})\) calibration measurements for GTM noise with constant fidelities. We show that our algorithm is robust against noise types like depolarizing, damping, and X-rotation noise with constant strengths, showing scalings akin to prior CS algorithms for fermions but with better noise resilience. Numerical simulations confirm our algorithm’s efficacy in noisy settings, suggesting its viability for near-term quantum devices.

有效估计费米子哈密顿期望值对于模拟各种物理系统至关重要。经典影子 (CS) 算法通过减少所需的量子态副本数量提供了解决方案，但量子设备中的噪声带来了挑战。我们提出了一种误差减轻 CS 算法，假设与门无关、时间平稳和马尔可夫 (GTM) 噪声。对于n量子位系统，我们的算法采用容易准备的初始状态\(\left\vert {0}^{n}\right\rangle \,\left\langle {0}^{n}\right\vert \)假设是无噪声的，用\(\widetilde{{{{\mathcal{O}}}}}(k{n}^{k})\)状态副本和\ (\widetilde{ {{{\mathcal{O}}}}}(\sqrt{n})\)具有恒定保真度的 GTM 噪声校准测量。我们表明，我们的算法对于去极化、阻尼和X旋转噪声等噪声类型具有鲁棒性，并且具有恒定的强度，显示出类似于之前的费米子 CS 算法的缩放，但具有更好的噪声恢复能力。数值模拟证实了我们的算法在噪声环境中的有效性，表明其对于近期量子设备的可行性。