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Paper 1

Purity-Assisted Zero-Noise Extrapolation for Quantum Error Mitigation

Tian-Ren Jin, Yun-Hao Shi, Zheng-An Wang, Tian-Ming Li, Kai Xu, Heng Fan

Year

2023

Journal

arXiv preprint

DOI

arXiv:2310.10037

arXiv

2310.10037

Quantum error mitigation aims to reduce errors in quantum systems and improve accuracy. Zero-noise extrapolation (ZNE) is a commonly used method, where noise is amplified, and the target expectation is extrapolated to a noise-free point. However, ZNE relies on assumptions about error rates based on the error model. In this study, a purity-assisted zero-noise extrapolation (pZNE) method is utilized to address limitations in error rate assumptions and enhance the extrapolation process. The pZNE is based on the Pauli diagonal error model implemented using the Pauli twirling technique. Although this method does not significantly reduce the bias of routine ZNE, it extends its effectiveness to a wider range of error rates where routine ZNE may face limitations. In addition, the practicality of the pZNE method is verified through numerical simulations and experiments on the online quantum computation platform, Quafu. Comparisons with routine ZNE and virtual distillation methods show that biases in extrapolation methods increase with error rates and may become divergent at high error rates. The bias of pZNE is slightly lower than routine ZNE, while its error rate threshold surpasses that of routine ZNE. Furthermore, for full density matrix information, the pZNE method is more efficient than the routine ZNE.

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Paper 2

Quantum optimization with arbitrary connectivity using Rydberg atom arrays

Minh-Thi Nguyen, Jin-Guo Liu, Jonathan Wurtz, Mikhail D. Lukin, Sheng-Tao Wang, Hannes Pichler

Year

2022

Journal

arXiv preprint

DOI

arXiv:2209.03965

arXiv

2209.03965

Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of quantum optimization algorithms [Ebadi et al., Science, 376, 1209 (2022)] with hundreds of qubits. In particular, the maximum independent set problem on so-called unit-disk graphs, was shown to be efficiently encodable in such a quantum system. Here, we extend the classes of problems that can be efficiently encoded in Rydberg arrays by constructing explicit mappings from a wide class of problems to maximum weighted independent set problems on unit-disk graphs, with at most a quadratic overhead in the number of qubits. We analyze several examples, including: maximum weighted independent set on graphs with arbitrary connectivity, quadratic unconstrained binary optimization problems with arbitrary or restricted connectivity, and integer factorization. Numerical simulations on small system sizes indicate that the adiabatic time scale for solving the mapped problems is strongly correlated with that of the original problems. Our work provides a blueprint for using Rydberg atom arrays to solve a wide range of combinatorial optimization problems with arbitrary connectivity, beyond the restrictions imposed by the hardware geometry.

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