Compare Papers

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.

Open paper

Paper 2

Non-Hermitian spectral flows and Berry-Chern monopoles

Lucien Jezequel, Pierre Delplace

Year

2022

Journal

arXiv preprint

DOI

arXiv:2209.03876

arXiv

2209.03876

We propose a non-Hermitian generalization of the correspondence between the spectral flow and the topological charges of band crossing points (Berry-Chern monopoles). A class of non-Hermitian Hamiltonians that display a complex-valued spectral flow is built by deforming an Hermitian model while preserving its analytical index. We relate those spectral flows to a generalized Chern number that we show to be equal to that of the Hermitian case, provided a line gap exists. We demonstrate the homotopic invariance of both the non-Hermitian Chern number and the spectral flow index, making explicit their topological nature. In the absence of a line gap, our system still displays a spectral flow whose topology can be captured by exploiting an emergent pseudo-Hermitian symmetry.

Open paper