Polynomial Reduction Methods and their Impact on QAOA Circuits

TL;DR

This paper explores how polynomial reduction methods and higher-order formulations can optimize quantum approximate optimization algorithms (QAOA) by improving abstraction layers and tailoring quantum circuits for better performance.

Contribution

It introduces a method to transform higher-order problem formulations into QUBO form, enabling better trade-offs and optimization of quantum circuit performance.

Findings

Higher-order formulations improve expressivity in quantum optimization.

Automatic transformations into QUBO can prioritize non-functional properties.

The approach enables satisfying different trade-offs in quantum circuit design.

Abstract

Abstraction layers are of paramount importance in software architecture, as they shield the higher-level formulation of payload computations from lower-level details. Since quantum computing (QC) introduces many such details that are often unaccustomed to computer scientists, an obvious desideratum is to devise appropriate abstraction layers for QC. For discrete optimisation, one such abstraction is to cast problems in quadratic unconstrained binary optimisation (QUBO) form, which is amenable to a variety of quantum approaches. However, different mathematically equivalent forms can lead to different behaviour on quantum hardware, ranging from ease of mapping onto qubits to performance scalability. In this work, we show how using higher-order problem formulations (that provide better expressivity in modelling optimisation tasks than plain QUBO formulations) and their automatic transformation into QUBO form can be used to leverage such differences to prioritise between different desired non-functional properties for quantum optimisation. Our quantitative study shows that the approach allows us to satisfy different trade-offs, and suggests various possibilities for the future construction of general-purpose abstractions and automatic generation of useful quantum circuits from high-level problem descriptions.