Quadratic Continuous Quantum Optimization

TL;DR

This paper introduces QCQO, a novel quantum annealing algorithm that approximates continuous quadratic optimization problems by iteratively solving QUBO instances, enabling quantum hardware to tackle a broader range of continuous tasks.

Contribution

QCQO is the first method to implicitly represent continuous variables in quantum annealing, allowing flexible control over binary variables and demonstrating convergence and effectiveness on regression tasks.

Findings

QCQO achieves accurate solutions with fewer qubits.

The method converges under certain conditions.

Performance decreases on noisy hardware.

Abstract

Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that approximates solutions to unconstrained quadratic programs via a sequence of QUBO instances. Rather than encoding real variables as binary vectors, QCQO implicitly represents them using continuous QUBO weights and iteratively refines the solution by summing sampled vectors. This allows flexible control over the number of binary variables and adapts well to hardware constraints. We prove convergence properties, introduce a step size adaptation scheme, and validate the method on linear regression. Experiments with simulated and real quantum annealers show that QCQO achieves accurate results with fewer qubits, though convergence slows on noisy hardware. Our approach enables quantum annealing to address a wider class of continuous problems.