A Comparative Study On Solving Optimization Problems With Exponentially Fewer Qubits

TL;DR

This paper evaluates a VQE-based quantum optimization algorithm that uses exponentially fewer qubits than QAOA, addressing numerical stability and optimizing classical procedures for better performance.

Contribution

It introduces a VQE-based approach with fewer qubits, proposes a classical optimization method to improve stability and efficiency, and compares optimizers on specific combinatorial problems.

Findings

The VQE-based algorithm requires exponentially fewer qubits than QAOA.

The proposed classical optimization improves convergence and stability.

Classical optimizers vary in performance depending on the problem.

Abstract

Variational Quantum optimization algorithms, such as the Variational Quantum Eigensolver (VQE) or the Quantum Approximate Optimization Algorithm (QAOA), are among the most studied quantum algorithms. In our work, we evaluate and improve an algorithm based on VQE, which uses exponentially fewer qubits compared to the QAOA. We highlight the numerical instabilities generated by encoding the problem into the variational ansatz and propose a classical optimization procedure to find the ground-state of the ansatz in less iterations with a better or similar objective. Furthermore, we compare classical optimizers for this variational ansatz on quadratic unconstrained binary optimization and graph partitioning problems.