Fair sampling with temperature-targeted QAOA based on quantum-classical correspondence theory

TL;DR

This paper introduces SBO-QAOA, a modified quantum algorithm that achieves fair sampling among degenerate solutions in optimization problems by encoding a Gibbs distribution, overcoming biases of standard QAOA.

Contribution

The paper proposes SBO-QAOA, a temperature-dependent Hamiltonian approach based on quantum-classical correspondence theory, enabling fair sampling in degenerate ground states.

Findings

SBO-QAOA converges to finite-temperature distributions among degenerate states.

It maintains fairness with only four variational parameters.

The approach is effective even with shallow circuit depth.

Abstract

In combinatorial optimization problems with degenerate ground states, fair sampling of degenerate solutions is essential. However, the quantum approximate optimization algorithm (QAOA) with a standard transverse-field mixer induces biases among degenerate states as circuit depth increases. Based on quantum-classical correspondence theory, we propose SBO-QAOA, which employs a temperature-dependent Hamiltonian encoding a Gibbs distribution as its ground state. Numerical simulations show that, unlike standard QAOA, SBO-QAOA yields ground-state probabilities converging to finite-temperature values with uniform distribution among degenerate states. These fairness and temperature-targeting properties are preserved even with only four variational parameters under a linear schedule.