A loop Quantum Approximate Optimization Algorithm with Hamiltonian updating

TL;DR

This paper introduces loop-QAOA, a noise-resilient quantum algorithm that iteratively updates the problem Hamiltonian using shallow circuit outputs to improve solutions on NISQ devices.

Contribution

The paper proposes a novel loop-QAOA that updates the problem Hamiltonian based on shallow circuit outputs, enhancing noise resilience and solution quality.

Findings

Loop-QAOA outperforms traditional QAOA under noise conditions.

Performance improves with more loops, demonstrating iterative enhancement.

Shallow circuits reduce noise impact while maintaining quantum advantage.

Abstract

Designing noisy-resilience quantum algorithms is indispensable for practical applications on Noisy Intermediate-Scale Quantum~(NISQ) devices. Here we propose a quantum approximate optimization algorithm~(QAOA) with a very shallow circuit, called loop-QAOA, to avoid issues of noises at intermediate depths, while still can be able to exploit the power of quantum computing. The key point is to use outputs of shallow-circuit QAOA as a bias to update the problem Hamiltonian that encodes the solution as the ground state. By iterating a loop between updating the problem Hamiltonian and optimizing the parameterized quantum circuit, the loop-QAOA can gradually transform the problem Hamiltonian to one easy for solving. We demonstrate the loop-QAOA on Max-Cut problems both with and without noises. Compared with the conventional QAOA whose performance will decrease due to noises, the performance of the loop-QAOA can still get better with an increase in the number of loops. The insight of exploiting outputs from shallow circuits as bias may be applied for other quantum algorithms.