Quadratic Continuous Quantum Optimization Achieves Accurate Regression with Fewer Resources

Continuous optimisation, a crucial task in fields like machine learning and data analysis, presents a significant challenge for many quantum algorithms. Sascha Mücke, Thore Gerlach, and Nico Piatkowski, from TU Dortmund University, University of Bonn, and Fraunhofer IAIS respectively, address this limitation with their development of Quadratic Continuous Optimisation, or QCQO. This new algorithm overcomes the difficulties existing quantum methods have with continuous problems by approximating solutions to complex equations through a series of more manageable, discrete steps. QCQO cleverly uses continuous values within a quantum framework, allowing it to tackle a broader range of real-world problems with potentially fewer quantum components and offering a pathway towards more practical applications of quantum computing in data science and beyond.

This new algorithm overcomes the difficulties existing quantum methods have with continuous problems by approximating solutions to complex equations through a series of more manageable, discrete steps. QCQO cleverly uses continuous values within a quantum framework, allowing it to tackle a broader range of real-world problems with potentially fewer quantum components and offering a pathway towards more practical applications of quantum computing in data science and beyond.,.

Continuous QUBO for Quadratic Program Optimisation

Scientists developed Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm designed to approximate solutions to unconstrained quadratic programs using a sequence of Quadratic Unconstrained Binary Optimization (QUBO) instances. This breakthrough addresses a key limitation of traditional QUBO approaches, which struggle with continuous optimization tasks like regression due to their inherently discrete nature. The team engineered a method that implicitly represents real variables using continuous QUBO weights, iteratively refining solutions by summing sampled vectors, providing flexible control over the number of binary variables employed. This innovative approach allows the algorithm to adapt effectively to the constraints of available quantum annealing hardware, expanding the range of solvable problems.,.

Continuous Quadratic Optimization via Flexible QUBOs

Scientists have developed Quadratic Continuous Optimization (QCQO), a novel anytime algorithm that effectively approximates solutions to unconstrained quadratic programs using a sequence of Quadratic Unconstrained Binary Optimization (QUBO) instances. This breakthrough addresses a key limitation of traditional QUBO approaches, which struggle with continuous optimization tasks like regression due to their inherently discrete nature. The team’s method implicitly represents real variables using continuous QUBO weights, iteratively refining solutions by summing sampled vectors, and offering flexible control over the number of binary variables employed. Experiments demonstrate that QCQO achieves accurate results while requiring fewer qubits than conventional methods for encoding continuous variables, a significant advantage for current quantum annealing hardware. The research establishes convergence properties for the algorithm and introduces a step size adaptation scheme to enhance performance, validated initially through linear regression tasks. Tests on both simulated and real quantum annealers reveal that QCQO successfully minimizes the energy function, achieving precise solutions even with the inherent noise present in quantum systems.,.

Continuous Optimisation via Quantum Annealing

This research presents a novel algorithm, Quadratic Continuous Quantum Optimization (QCQO), which effectively addresses continuous optimization problems, a challenge for traditional quantum annealers that excel at solving discrete problems. The team successfully bridges this gap by approximating solutions to complex quadratic programs through a series of more manageable Quadratic Unconstrained Binary Optimization (QUBO) problems, leveraging the strengths of existing quantum annealing hardware. QCQO uniquely represents variables using continuous weights, allowing for flexible adaptation to the limitations of available quantum bits and improving the potential for scalable solutions. The method’s efficacy has been demonstrated through successful application to linear regression tasks, both in simulation and on a real quantum annealer.

Importantly, the researchers developed an adaptive step size scheme that significantly enhances both the speed and accuracy of the algorithm’s convergence. While experiments on quantum hardware revealed reduced solution quality and slower convergence compared to simulations, the team confirmed the algorithm’s functionality on a physical device, opening avenues for tackling a broader range of continuous problems including those found in areas like finance, signal processing, and combinatorial optimization. The authors acknowledge that the current step size adaptation is largely based on empirical observation and that the sampling method for a key matrix could potentially be refined, suggesting directions for future investigation. Further research will also explore the algorithm’s performance on problems with more complex, non-convex loss functions.,.