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Symbolic Regression with Evolutionary Quantum Annealing

Jincheng Zhang

Published Aug 28, 2026• 0 citations
Publisher

Abstract

Symbolic regression is a technique used to discover mathematical equations from data. Despite its potential, traditional symbolic regression methods often struggle to find complex and accurate expressions, particularly when dealing with high-dimensional datasets or intricate relationships. This work proposes a novel approach combining evolutionary algorithms with quantum annealing to address these limitations. The core idea is to leverage the strengths of both techniques: the evolutionary algorithm's ability to explore the solution space effectively and the quantum annealer's capability to efficiently find low-energy states, representing potential mathematical expressions. We utilize the quantum annealer to optimize the search space, guiding the evolutionary algorithm towards promising solutions. Our approach demonstrates improved performance in discovering complex equations compared to standard symbolic regression techniques. The key equation for measuring the fitness of a candidate equation is: *f(x) = a1xn1 + a2xn2 + ... + akxnk* Where *x* is the independent variable, *ai* are the coefficients, and *ni* are the exponents. The fitness function, *F(e)*, is defined as the sum of squared errors between the predicted values of the equation and the observed data: *F(e) = Σi=1N (yi - f(xi))2* Where *yi* represents the i-th observed data point and *xi* the corresponding independent variable. The annealing process is governed by the Hamiltonian: *H(σ) = Σi σi2 + J Σi σi σj cos(θij)* Where σi represents the qubit state, *J* is the coupling strength, and θij are the angles between the qubit states. The evolutionary algorithm employs a selection, crossover, and mutation process to refine the solutions generated by the quantum annealer.

DOI
10.5281/zenodo.22138739

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This paper presents a novel approach to symbolic regression that integrates evolutionary algorithms with quantum annealing. Existing symbolic regression methods often face challenges in efficiently exploring the high-dimensional solution space, particularly when dealing with complex mathematical relationships. Our proposed framework leverages the strengths of both quantum computing and evolutionary optimization. Quantum annealing is employed to identify promising regions within the solution space, guided by the inherent probabilistic nature of quantum systems. Subsequently, evolutionary algorithms are utilized to refine and optimize these candidate expressions, ensuring a robust and accurate representation of the underlying data. The combination of these techniques aims to overcome the limitations of traditional symbolic regression, potentially leading to the discovery of more accurate and efficient mathematical models. The core claim is that this synergistic approach significantly enhances the exploration capabilities of symbolic regression.
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Symbolic regression is a powerful technique for uncovering hidden mathematical relationships within data. However, its computational complexity grows dramatically with dataset size and the desired expression complexity. This work proposes a novel approach combining symbolic regression with evolutionary algorithms executed on a quantum computer. The core idea is to exploit the inherent parallelism of quantum computation to accelerate the exploration of the vast solution space, while leveraging an evolutionary algorithm to refine and optimize the generated symbolic expressions. We hypothesize that this hybrid approach will significantly outperform traditional symbolic regression methods, particularly for challenging datasets. The system is designed to iteratively generate symbolic expressions through quantum computation and then refine them using an evolutionary strategy. This process aims to find an expression that best represents the data while maintaining a desired level of complexity and accuracy. The effectiveness of this approach is evaluated theoretically and through simulation, demonstrating its potential for tackling complex symbolic regression problems.
This paper explores the application of quantum annealing to the field of symbolic regression, a technique for automatically discovering mathematical equations from data. The core idea is to frame the symbolic regression problem as a quadratic unconstrained binary optimization (QUBO) problem, which can then be solved using the quantum annealing algorithm. This approach aims to identify previously unknown mathematical relationships that accurately represent a given dataset. The paper details the methodology, including the mapping process, the QUBO formulation, and the utilization of the quantum annealing solver. We demonstrate, through theoretical analysis and conceptual design, the potential for quantum annealing to outperform classical methods in certain scenarios, particularly when dealing with complex datasets and high-dimensional search spaces. The resulting equations are presented as a set of symbolic expressions, enabling both quantitative analysis and further investigation. The ultimate goal is to provide a framework for automated equation discovery, potentially leading to advancements in various scientific and engineering domains.
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