Quantum Hardware-Efficient Selection of Auxiliary Variables for QUBO Formulations

TL;DR

This paper introduces a hardware-efficient method for selecting auxiliary variables in QUBO formulations tailored for quantum architectures with limited connectivity, significantly reducing circuit depth for QAOA.

Contribution

It proposes a novel auxiliary variable selection approach that constructs interaction graphs compatible with quantum hardware constraints, improving circuit efficiency.

Findings

Reduces circuit depth by nearly 40% compared to conventional methods.

Constructs interaction graphs with regular structure and limited degree.

Implementation available at https://github.com/munich-quantum-toolkit/problemsolver.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) requires considered optimization problems to be translated into a compatible format. A popular transformation step in this pipeline involves the quadratization of higher-order binary optimization problems, translating them into Quadratic Unconstrained Binary Optimization (QUBO) formulations through the introduction of auxiliary variables. Conventional algorithms for the selection of auxiliary variables often aim to minimize the total number of required variables without taking the constraints of the underlying quantum computer-in particular, the connectivity of its qubits-into consideration. This quickly results in interaction graphs that are incompatible with the target device, resulting in a substantial compilation overhead even with highly optimized compilers. To address this issue, this work presents a novel approach for the selection of auxiliary variables tailored for architectures with limited connectivity. By specifically constructing an interaction graph with a regular structure and a limited maximal degree of vertices, we find a way to construct QAOA circuits that can be mapped efficiently to a variety of architectures. We show that, compared to circuits constructed from a QUBO formulation using conventional auxiliary selection methods, the proposed approach reduces the circuit depth by almost 40%. An implementation of all proposed methods is publicly available at https://github.com/munich-quantum-toolkit/problemsolver.