In the lead up to fault tolerance, the utility of quantum computing will be determined by how adequately the effects of noise can be circumvented in quantum algorithms. Hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE) have been designed for the short-term regime. However, as problems scale, VQE results are generally scrambled by noise on present-day hardware. While error mitigation techniques alleviate these issues to some extent, there is a pressing need to develop algorithmic approaches with higher robustness to noise. Here, we explore the robustness properties of the recently introduced quantum computed moments (QCM) approach to ground state energy problems, and show through an analytic example how the underlying energy estimate explicitly filters out incoherent noise. Motivated by this observation, we implement QCM for a model of quantum magnetism on IBM Quantum hardware to examine the noise-filtering effect with increasing circuit depth. We find that QCM maintains a remarkably high degree of error robustness where VQE completely fails. On instances of the quantum magnetism model up to 20 qubits for ultra-deep trial state circuits of up to ~500 CNOTs, QCM is still able to extract reasonable energy estimates. The observation is bolstered by an extensive set of experimental results. To match these results, VQE would need hardware improvement by some 2 orders of magnitude on error rates.
Noise Correlations as a Resource in Pauli-Twirled Circuits
Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Department of Physics and Astronomy, Northwestern University（西北大学物理与天文系）；National Center for Computational Sciences, Oak Ridge National Laboratory（橡树岭国家实验室国家计算科学中心）；IBM Quantum, IBM T.J. Watson Research Center（IBM量子，IBM T.J.沃森研究中心）
Simulating quantum circuits with arbitrary local noise using Pauli Propagation
Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Freie Universität Berlin（柏林自由大学）；Dahlem Center for Complex Quantum Systems, Freie Universität Berlin（柏林自由大学达勒姆复杂量子系统中心）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Diagnosing Quantum Circuits: Noise Robustness, Trainability, and Expressibility
Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）；Yanqi Lake Beijing Institute of Mathematical Sciences and Applications（北京雁栖湖应用数学研究院）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Department of Mathematics, Tsinghua University（清华大学数学系）
Hybrid Gaussian-exponential zero-noise extrapolation for periodic circuits
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学研究所）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学 sciences 国家重点实验室）
Color code thresholds under circuit-level noise beyond the Pauli framework
INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Institute for Complex Quantum Systems, Ulm University（乌尔姆大学复杂量子系统研究所）；Padua Quantum Technologies Research Center, Università degli Studi di Padova（帕多瓦大学帕多瓦量子技术中心）
Laboratoire de Physique Théorique et Modélisation (LPTM), CNRS UMR 8089, CY Cergy Paris Université（CY塞吉-巴黎大学理论物理与建模实验室）；Équipe Traitement de l’Information et Systèmes (ETIS), CNRS UMR 8051, CY Cergy Paris Université（CY塞吉-巴黎大学信息与系统处理团队）
Simulating general noise nearly as cheaply as Pauli noise
National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；University of Chicago（芝加哥大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Entropica Labs（熵实验室）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
A deep learning model for noise prediction on near-term quantum devices
我们提出了一种用于量子线路的深度学习编译器的方法，旨在降低在特定设备上运行的电路的输出噪声。我们在来自量子设备的实验数据上训练卷积神经网络，以学习特定于硬件的噪声模型。然后，编译器使用训练的网络作为噪声预测器，并在电路中插入门序列，以使预期的噪声最小化。我们在IBM 5量子位设备上测试了这种方法，并观察到与Qiskit编译器获得的电路相比，输出噪声降低了12.3%（95%CI [11.5%，13.0%]）。此外，经过训练的噪声模型是特定于硬件的：将在一个设备上训练的噪声模型应用于另一个设备，噪声降低仅为5.2%（95% CI [4.9%，5.6%]）。这些结果表明，使用机器学习的特定于设备的编译器可以产生更高保真的操作，并为噪声模型的设计提供见解。
