SAT Strikes Back: Parameter and Path Relations in Quantum Toolchains

TL;DR

This paper investigates the transformation paths from k-SAT problems to QUBO in quantum computing toolchains, focusing on optimization, stability, and structure to improve automation and error correction.

Contribution

It introduces a framework for evaluating and predicting transformation paths considering structure, stability, and metrics, advancing automated quantum problem compilation.

Findings

Identifies key factors influencing transformation path quality.

Provides methods to rate and predict transformation stability.

Links current research to quadratisation techniques and their foundations.

Abstract

In the foreseeable future, toolchains for quantum computing should offer automatic means of transforming a high level problem formulation down to a hardware executable form. Thereby, it is crucial to find (multiple) transformation paths that are optimised for (hardware specific) metrics. We zoom into this pictured tree of transformations by focussing on k-SAT instances as input and their transformation to QUBO, while considering structure and characteristic metrics of input, intermediate and output representations. Our results can be used to rate valid paths of transformation in advance -- also in automated (quantum) toolchains. We support the automation aspect by considering stability and therefore predictability of free parameters and transformation paths. Moreover, our findings can be used in the manifesting era of error correction (since considering structure in a high abstraction layer can benefit error correcting codes in layers below). We also show that current research is closely linked to quadratisation techniques and their mathematical foundation.