Quantum Approximate Optimization Algorithm with Adaptive Bias Fields

TL;DR

This paper introduces an adaptive bias field modification to the QAOA, which uses measurement feedback to improve optimization efficiency, significantly reducing runtime for MaxCut problems without extra quantum resources.

Contribution

The paper proposes a novel adaptive bias field approach for QAOA that enhances performance by updating operators based on measurement feedback, improving scalability and efficiency.

Findings

Reduces QAOA runtime substantially for MaxCut problems.

Performance improvement increases with problem size.

Requires no additional quantum gates or measurements.

Abstract

The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wavefunction into one which encodes a solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which two unitary operators are alternately applied to the qubits. In this paper, the QAOA is modified by updating the operators themselves to include local fields, using information from the measured wavefunction at the end of one iteration step to improve the operators at later steps. It is shown by numerical simulation on MaxCut problems that, for a fixed accuracy, this procedure decreases the runtime of QAOA very substantially. This improvement appears to increase with the problem size. Our method requires essentially the same number of quantum gates per optimization step as the standard QAOA, and no additional measurements. This modified algorithm enhances the prospects for quantum advantage for certain optimization problems.