Noise Resilience and Robust Convergence Guarantees for the Variational Quantum Eigensolver

TL;DR

This paper investigates how noise impacts the convergence and optimality of the Variational Quantum Eigensolver, providing theoretical insights and numerical validation for noise resilience in quantum algorithms.

Contribution

It characterizes the effects of various noise processes on VQE convergence and optimal parameters, extending theoretical guarantees to noisy quantum circuits.

Findings

Noise affects the optimal parameters and cost in VQE.

Convergence guarantees can be extended to noisy quantum circuits.

Numerical simulations validate theoretical insights.

Abstract

Variational Quantum Algorithms (VQAs) are a class of hybrid quantum-classical algorithms that leverage on classical optimization tools to find the optimal parameters for a parameterized quantum circuit. One relevant application of VQAs is the Variational Quantum Eigensolver (VQE), which aims at steering the output of the quantum circuit to the ground state of a certain Hamiltonian. Recent works have provided global convergence guarantees for VQEs under suitable local surjectivity and smoothness hypotheses, but little has been done in characterizing convergence of these algorithms when the underlying quantum circuit is affected by noise. In this work, we characterize the effect of different coherent and incoherent noise processes on the optimal parameters and the optimal cost of the VQE, and we study their influence on the convergence guarantees of the algorithm. Our work provides novel theoretical insight into the behavior of parameterized quantum circuits. Furthermore, we accompany our results with numerical simulations implemented via Pennylane.