Advances in Quantum Genetic Algorithms

TL;DR

This survey surveys three decades of Quantum Genetic Algorithms (QGAs), clarifying how quantum representations of populations and gate-based implementations address core GA steps—initialization, fitness computation, selection, crossover, and mutation. It distinguishes architectures from general hybrid QGAs to Reduced QGAs and fully quantum/un supervised schemes, identifying selection via Grover-like amplitude amplification as a primary source of speedups when properly matched to problem structure. The Thomson problem and molecular eigensolving serve as central physical benchmarks, illustrating energy-based fitness and Hamiltonian-ground-state objectives encoded through density matrices or Ising-like representations. The paper also catalogs diverse applications across engineering and science, highlights performance tradeoffs between speed and fidelity, and outlines future directions such as unsupervised QGAs and generalized physical-encoding schemes to broaden quantum advantages in real-world optimization problems.

Abstract

Quantum Genetic Algorithms (QGAs) are an emerging field of multivariate quantum optimization that emulate Darwinian evolution and natural selection, with vast applications in chemistry and engineering. The appropriate application of fitness functions and fitness selection are the problem-encoding step and the slowest step in designing QGAs for specific physical applications. In this paper, we provide a comprehensive review of these crucial steps. Our survey maps cases of quantum advantage, classifies and illustrates QGAs and their subroutines, and discusses the two main physical problems tackled by QGAs: potential energy minimization of particles on a sphere, and molecular eigensolving. We conclude that the encoding used by the Thomson problem is a decisive step toward the use of QGAs in a variety of physical applications, while Grover's search as a selection step in Reduced QGAs is the main driver of quantum speedup.

Figures (8)

• Figure 1: Venn diagram illustrates QGA as overlap of three different areas: Artificial Life, Optimization and Quantum Computing.
• Figure 2: Timeline of QGA research from foundations of quantum computing to recent applications. References from top to bottom and left to right: (red boxes) narayanan1996quantumbuvzek1996quantumgrover1997quantumjones1998implementation, (yellow boxes) talbi2004newjang2004face, (white boxes) udrescu2006implementingmalossini2008quantumrylander2001quantumalvarez2014biomimetic, (purple boxes) ardelean2022graphibarrondo2022quantumamal2022quantumballinas2023hybrid, (green box) ibarrondo2023quantum.
• Figure 3: Quantum advantage of speedup versus fidelity (diagonal Hamiltonian and $\mathrm{H}_2$ Hamiltonian eigensolving problems) or accuracy (Knapsack Problem), adapted from ballinas2023hybrid and ibarrondo2022quantum, as compared with classical GAs. (a) Ellipses are Gaussian fittings after outlier removal. (b) Zoom-in of double advantage regions of the elliptical clusters. (c) Box plots including outliers. In the Knapsack Problem, six models of QGA were studied, and the populations had 10, 15 and 20 individuals. In the other two problems, four QGA models were studied, and the populations were all of four individuals.
• Figure 4: Venn diagram illustrating the conjectured relationships between classical complexity classes P, NP, and the quantum class BQP.
• Figure 5: The Bloch sphere, a geometric representation of a single qubit state $|\psi\rangle$ defined by the polar angle $\theta$ and azimuthal angle $\phi$.