EAQGA: A Quantum-Enhanced Genetic Algorithm with Novel Entanglement-Aware Crossovers

TL;DR

EAQGA addresses combinatorial optimization, focusing on portfolio optimization, by integrating quantum circuits into a genetic algorithm and introducing an entanglement-aware crossover. The method identifies correlated bit pairs from the top solutions and encodes them as limited-entanglement quantum states to produce shallow, near-term hardware-compatible circuits. Empirical results on simulators and IBM hardware show EAQGA outperforming a classical GA by up to 33.6% and a quantum-inspired AQGA by up to 37.2% in fitness, validating the approach in practical, utility-scale settings like 100-asset portfolios. The work demonstrates that carefully managed entanglement and circuit depth can harness quantum-inspired mechanisms for real-world optimization without requiring fault-tolerant quantum computing.

Abstract

Genetic algorithms are highly effective optimization techniques for many computationally challenging problems, including combinatorial optimization tasks like portfolio optimization. Quantum computing has also shown potential in addressing these complex challenges. Combining these approaches, quantum genetic algorithms leverage the principles of superposition and entanglement to enhance the performance of classical genetic algorithms. In this work, we propose a novel quantum genetic algorithm introducing an innovative crossover strategy to generate quantum circuits from a binary solution. We incorporate a heuristic method to encode entanglement patterns from parent solutions into circuits for the next generation. Our algorithm advances quantum genetic algorithms by utilizing a limited number of entanglements, enabling efficient exploration of optimal solutions without significantly increasing circuit depth, making it suitable for near-term applications. We test this approach on a portfolio optimization problem using an IBM 127 qubits Eagle processor (ibm_quebec) and simulators. Compared to state-of-the-art algorithms, our results show that the proposed method improves fitness values by 33.6% over classical genetic algorithm and 37.2% over quantum-inspired genetic algorithm, using the same iteration counts and population sizes with real quantum hardware employing 100 qubits. These findings highlight the potential of current quantum computers to address real-world utility-scale combinatorial optimization problems.

Figures (6)

• Figure 1: Diagram of our proposed QGA.
• Figure 2: Entanglement traits in two solutions. We can consider qubits 1 and 2 of both solutions as the $|\psi^n\rangle = \alpha|01\rangle + \beta|10\rangle$ state and qubits 1 and 4 as the$|\psi^p\rangle = \alpha|00\rangle + \beta|11\rangle$ state.
• Figure 3: Two possible circuits to form the entanglement states. Rotation with the angle of $\theta$ controls the amplitude of the states ($\alpha$ and $\beta$)
• Figure 4: Corresponding circuit using the parents from Fig. \ref{['fig:cross2_bits']}.
• Figure 5: Average fitness value of three algorithms using different sizes and populations over all subsets on the simulator.