Estimating Coherent Contributions to the Error Profile Using Cycle Error Reconstruction

Abstract

Mitigation and calibration schemes are central to maximize the computational reach of today's Noisy Intermediate Scale Quantum (NISQ) hardware, but these schemes are often specialized to exclusively address either coherent or decoherent error sources. Quantifying the two types of errors hence constitutes a desirable feature when it comes to benchmarking error suppression tools. In this paper, we present a scalable and cycle-centric methodology for obtaining a detailed estimate of the coherent contribution to the error profile of a hard computing cycle. The protocol that we suggest is based on Cycle Error Reconstruction (CER), also known as K-body Noise Reconstruction (KNR). This protocol is similar to Cycle Benchmarking (CB) in that it provides a cycle-centric diagnostic based on Pauli fidelity estimation \cite{erhard2019characterizing}. We introduce an additional hyper-parameter in CER by allowing the hard cycles to be folded multiple times before being subject to Pauli twirling. Performing CER for different values of our added hyper-parameter allows estimating the coherent error contributions through a generalization of the fidelity decay formula. We confirm the accuracy of our method through numerical simulations on a quantum simulator, and perform proof-of-concept experiments on three IBM chips, namely $\texttt{ibmq_guadalupe}$, $\texttt{ibmq_manila}$, and $\texttt{ibmq_montreal}$. In all three experiments, we measure substantial coherent errors biased in Z.