Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers

TL;DR

Layer VQE is a new iterative variational method for combinatorial optimization on noisy quantum computers, demonstrating robustness and efficiency in large-scale simulations compared to existing algorithms.

Contribution

The paper introduces Layer VQE, a scalable iterative approach for quantum optimization that outperforms QAOA in noise resilience and solution quality in simulated noisy environments.

Findings

L-VQE outperforms QAOA in noisy conditions.

L-VQE is more robust to sampling errors.

L-VQE performs well with realistic hardware noise.

Abstract

Combinatorial optimization on near-term quantum devices is a promising path to demonstrating quantum advantage. However, the capabilities of these devices are constrained by high noise or error rates. In this paper, we propose an iterative Layer VQE (L-VQE) approach, inspired by the Variational Quantum Eigensolver (VQE). We present a large-scale numerical study, simulating circuits with up to 40 qubits and 352 parameters, that demonstrates the potential of the proposed approach. We evaluate quantum optimization heuristics on the problem of detecting multiple communities in networks, for which we introduce a novel qubit-frugal formulation. We numerically compare L-VQE with Quantum Approximate Optimization Algorithm (QAOA) and demonstrate that QAOA achieves lower approximation ratios while requiring significantly deeper circuits. We show that L-VQE is more robust to finite sampling errors and has a higher chance of finding the solution as compared with standard VQE approaches. Our simulation results show that L-VQE performs well under realistic hardware noise.