Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States

TL;DR

This paper demonstrates that hybrid quantum-classical algorithms, like VQE, can automatically suppress decoherence errors and accurately determine excited states without additional quantum resources.

Contribution

It introduces a model showing variational approaches can mitigate decoherence and fits into a hierarchy improving solution accuracy with classical resources.

Findings

Variational methods can suppress decoherence errors.

Accurate excited state determination achieved.

No extra quantum coherence time needed.

Abstract

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 automatically suppress even non-systematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we show how variational quantum-classical approaches fit in a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions with additional classical resources. We demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error correction codes.