From quantum to quantum-inspired: the LogQ algorithm as a non-linear continuous relaxation of variables method

TL;DR

This paper presents a classical heuristic inspired by the quantum LogQ algorithm, reformulating it as a non-linear continuous relaxation to eliminate quantum measurement overhead.

Contribution

It introduces a novel classical heuristic based on LogQ, removing the need for Pauli decomposition and measurement, bridging quantum and classical optimization methods.

Findings

LogQ can be reformulated classically, avoiding quantum measurement issues.

The classical heuristic is based on a non-linear continuous relaxation.

This approach exemplifies quantum-inspired classical algorithm development.

Abstract

The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems, which are often encountered in the industry (portfolio optimization, fleet optimization, charging stations, etc.). It was developed within the framework of quantum computing, designed as a pragmatic approach to quantum combinatorial optimization that drastically reduces the number of required qubits and quantum circuit depth. While LogQ has recently been made compliant with gradient-inspired methods, greatly improving parameter optimization efficiency, it still faced hurdles regarding Pauli decomposition and measurement overhead. We here demonstrate that LogQ can be fully reformulated within a classical framework, which effectively eliminates the need for Pauli decomposition and bypasses the measurement challenges altogether. This finally leads to a classical heuristic based on a non-linear continuous relaxation of variables and is, to the best of our knowledge, novel. The LogQ story illustrates how quantum computing can inspire classical algorithms, leading to so-called "quantum-inspired" methods.