High error rates and limited fidelity of quantum gates in near-term quantum devices are the central obstacles to successful execution of the Quantum Approximate Optimization Algorithm (QAOA). In this paper we introduce an application-specific approach for mitigating the errors in QAOA evolution by leveraging the symmetries present in the classical objective function to be optimized. Specifically, the QAOA state is projected into the symmetry-restricted subspace, with projection being performed either at the end of the circuit or throughout the evolution. Our approach improves the fidelity of the QAOA state, thereby increasing both the accuracy of the sample estimate of the QAOA objective and the probability of sampling the binary string corresponding to that objective value. We demonstrate the efficacy of the proposed methods on QAOA applied to the MaxCut problem, although our methods are general and apply to any objective function with symmetries, as well as to the generalization of QAOA with alternative mixers. We experimentally verify the proposed methods on an IBM Quantum processor, utilizing up to 5 qubits. When leveraging a global bit-flip symmetry, our approach leads to a 23% average improvement in quantum state fidelity.
We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an experiment, and develop a zero-cost post-processing protocol which is equivalent to a variant of the quantum subspace expansion. We develop methods for inserting global and local symetries into quantum algorithms, and for adjusting natural symmetries of the problem to boost their mitigation against different error channels. We demonstrate these techniques on two- and four-qubit simulations of the hydrogen…
In the era of quantum computing without full fault-tolerance, it is essential to suppress noise effects via the quantum error mitigation techniques to enhance the computational power of the quantum devices. One of the most effective noise-agnostic error mitigation schemes is the generalized quantum subspace expansion (GSE) method, which unifies various mitigation algorithms under the framework of the quantum subspace expansion. Specifically, the fault-subspace method, a subclass of GSE method, constructs an error-mitigated quantum state with copies of quantum states with different noise levels…
A many-body Hamiltonian can be block-diagonalized by expressing it in terms of symmetry-adapted basis states. Finding the group orbit representatives of these basis states and their corresponding symmetries is currently a memory/computational bottleneck on classical computers during exact diagonalization. We apply Grover's search in the form of a minimization procedure to solve this problem. Our quantum solution provides an exponential reduction in memory, and a quadratic speedup in time over classical methods. We discuss explicitly the full circuit implementation of Grover minimization as app…
Even with the recent rapid developments in quantum hardware, noise remains the biggest challenge for the practical applications of any near-term quantum devices. Full quantum error correction cannot be implemented in these devices due to their limited scale. Therefore instead of relying on engineered code symmetry, symmetry verification was developed which uses the inherent symmetry within the physical problem we try to solve. In this article, we develop a general framework named symmetry expansion which provides a wide spectrum of symmetry-based error mitigation schemes beyond symmetry verifi…
One of the most promising applications of noisy intermediate-scale quantum computers is the simulation of molecular Hamiltonians using the variational quantum eigensolver. We show that encoding symmetries of the simulated Hamiltonian in the VQE ansatz reduces both classical and quantum resources compared to other, widely available ansatze. Through simulations of the H$_2$ molecule, we verify that these improvements persist in the presence of noise. This simulation is performed with IBM software using noise models from real devices. We also demonstrate how these techniques can be used to find m…
Noise mitigation of quantum observables via learning from Hamiltonian symmetry decays
Tecnun - University of Navarra（纳瓦拉理工大学）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IBM Quantum, IBM Thomas J Watson Research Center（IBM量子，IBM托马斯·J·沃森研究中心）；IBM Quantum, IBM Research Europe – Dublin（IBM量子，IBM欧洲研究院都柏林分部）；IBM Quantum, IBM Research Europe – UK（IBM量子，IBM欧洲研究院英国分部）
The success of the current generation of Noisy Intermediate-Scale Quantum (NISQ) hardware shows that quantum hardware may be able to tackle complex problems even without error correction. One outstanding issue is that of coherent errors arising from the increased complexity of these devices. These errors can accumulate through a circuit, making their impact on algorithms hard to predict and mitigate. Iterative algorithms like Quantum Imaginary Time Evolution are susceptible to these errors. This article presents the combination of both noise tailoring using Randomized Compiling and error mitig…
Dynamical decoupling (DD) is a widely-used quantum control technique that takes advantage of temporal symmetries in order to partially suppress quantum errors without the need resource-intensive error detection and correction protocols. This and other open-loop error mitigation techniques are critical for quantum information processing in the era of Noisy Intermediate-Scale Quantum technology. However, despite its utility, dynamical decoupling does not address errors which occur at unstructured times during a circuit, including certain commonly-encountered noise mechanisms such as cross-talk a…
Hardware errors are a major obstacle to demonstrating quantum advantage with the quantum approximate optimization algorithm (QAOA). Recently, symmetry verification has been proposed and empirically demonstrated to boost the quantum state fidelity, the expected solution quality, and the success probability of QAOA on a superconducting quantum processor. Symmetry verification uses parity checks that leverage the symmetries of the objective function to be optimized. We develop a theoretical framework for analyzing this approach under local noise and derive explicit formulas for fidelity improveme…
Robust design under uncertainty in quantum error mitigation
Institute of Theoretical Physics, Jagiellonian University（雅盖隆大学理论物理研究所）；Szkoła Doktorska Nauk Ścisłych i Przyrodniczych, Uniwersytet Jagielloński（雅盖隆大学自然科学博士学院）；Mark Kac Center for Complex Systems Research, Jagiellonian University（雅盖隆大学马克·卡克复杂系统研究中心）；Information Sciences, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室信息科学部）；The Uncertainty Quantification Foundation（不确定性量化基金会）；Quantum Science Center（量子科学中心）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）
Pauli Weight Hamiltonian Term Selection for Optimized Machine Learning Based Quantum Error Mitigation
Bandung Institute of Technology（万隆理工学院）；National Research and Innovation Agency (BRIN)（国家研究与创新署）；National University of Singapore（新加坡国立大学）；Nanyang Technological University（南洋理工大学）
Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One example of such a hybrid quantum-classical approach is the variational quantum eigensolver (VQE) built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed among the candidates for first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can …
Reliable high-accuracy error mitigation for utility-scale quantum circuits
Qedma Quantum Computing（Qedma量子计算）；The Benin School of Computer Science and Engineering, Hebrew University（希伯来大学贝宁计算机科学与工程学苑）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Faculty of Mathematics and Computer Science, Weizmann Institute of Science（魏茨曼科学研究所数学与计算机科学系）
Quantum Error Mitigation with Attention Graph Transformers for Burgers Equation Solvers on NISQ Hardware
Vision-Guided and Intelligent Robotics Lab (ViGIR) - EECS Department - University of Missouri - Columbia（智能机器人实验室（ViGIR）- 电子工程与计算机科学系 - 密苏里大学 - 哥伦比亚）；Department of Mechanical and Aerospace Engineering - University of Missouri - Columbia（机械与航空航天工程系 - 密苏里大学 - 哥伦比亚）
Quantum time dynamics mediated by the Yang-Baxter equation and artificial neural networks
Argonne National Laboratory（阿贡国家实验室）；NVIDIA Corporation（英伟达公司）；Center for Nanoscale Materials, Argonne National Laboratory（阿贡国家实验室纳米级材料中心）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；University of Washington（华盛顿大学）
Noise-Robust Estimation of Quantum Observables in Noisy Hardware
IQM Quantum Computers（IQM量子计算机公司）；Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München（慕尼黑大学物理系与阿诺德·索末菲理论物理中心）
Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved. In the presence of noise, however, the evolution's symmetry could be broken and non-valid states could be sampled at the end of the computation. On the other hand, the restriction to a subspace in the ideal case suggest the possibility of more resource efficient error mitigation techniques for circuits preserving symmetries that are not possible for general …
