Quantum error mitigation by hidden inverses protocol in superconducting quantum devices

TL;DR

This paper introduces a hidden inverses error mitigation protocol for superconducting quantum devices that reduces coherent errors in variational algorithms, leading to more stable and efficient quantum computations.

Contribution

It proposes a novel error mitigation method using hidden inverses to cancel noise in quantum circuits, demonstrated on superconducting hardware for VQE.

Findings

Reduces energy fluctuations in VQE on superconducting hardware

Decreases the number of iterations needed for convergence

Explains hardware performance through detailed noise modeling and simulations

Abstract

We present a method to improve the convergence of variational algorithms based on hidden inverses to mitigate coherent errors. In the context of error mitigation, this means replacing the on hardware implementation of certain Hermitian gates with their inverses. Doing so results in noise cancellation and a more resilient quantum circuit. This approach improves performance in a variety of two-qubit error models where the noise operator also inverts with the gate inversion. We apply the mitigation scheme on superconducting quantum processors running the variational quantum eigensolver (VQE) algorithm to find the H$_{\rm 2}$ ground-state energy. When implemented on superconducting hardware we find that the mitigation scheme effectively reduces the energy fluctuations in the parameter learning path in VQE, reducing the number of iterations for a converged value. We also provide a detailed numerical simulation of VQE performance under different noise models and explore how hidden inverses \& randomized compiling affect the underlying loss landscape of the learning problem. These simulations help explain our experimental hardware outcomes, helping to connect lower-level gate performance to application-specific behavior in contrast to metrics like fidelity which often do not provide an intuitive insight into observed high-level performance.