Classically computing performance bounds on depolarized quantum circuits

TL;DR

This paper introduces a classical numerical method using Lagrangian duality to compute lower bounds on the energy of noisy quantum circuits, helping assess quantum advantage under depolarizing noise.

Contribution

It presents a novel approach to certifiably bound the performance of noisy quantum circuits using Lagrangian duality, which was not previously available.

Findings

The method provides architecture-dependent bounds on quantum circuit performance.

Numerical evidence supports the effectiveness of the approach.

The approach helps evaluate quantum advantage in noisy conditions.

Abstract

Quantum computers and simulators can potentially outperform classical computers in finding ground states of classical and quantum Hamiltonians. However, if this advantage can persist in the presence of noise without error correction remains unclear. In this paper, by exploiting the principle of Lagrangian duality, we develop a numerical method to classically compute a certifiable lower bound on the minimum energy attainable by the output state of a quantum circuit in the presence of depolarizing noise. We provide theoretical and numerical evidence that this approach can provide circuit-architecture dependent bounds on the performance of noisy quantum circuits.