Optimizing quantum circuits with evolutionary algorithms for stable Boolean gates, elementary cellular automata, and highly entangled quantum states

TL;DR

The study demonstrates how evolutionary algorithms can actively design quantum circuits for two aims: recreating quantum cellular automata rules and engineering highly entangled multi-qubit states. It employs KL-divergence as a fitness for CA-rule replication and Mayer–Wallach entanglement (with von Neumann entropy as a supplementary metric) to drive entangling-circuit design, evaluating circuits on 3–5 qubits with 3–15 gates. The results show that carefully tuned mutation rates (around 10–20%) yield circuits that accurately reproduce CA dynamics and produce near-maximally entangled states (MW scores approaching 1) for small qubit counts, albeit with a noticeable trade-off between circuit depth and entanglement in deeper circuits. The work highlights scalability challenges and suggests pathways, including hybrid optimization and hardware-in-the-loop approaches, to extend these methods to larger quantum systems and practical applications, with the QUEVO framework made available for reproducibility.

Abstract

We investigate the potential of bio-inspired evolutionary algorithms for designing quantum circuits with specific goals, focusing on two particular tasks. The first one is motivated by the ideas of Artificial Life that are used to reproduce stochastic cellular automata with given rules. We test the robustness of quantum implementations of the cellular automata for different numbers of quantum gates The second task deals with the sampling of quantum circuits that generate highly entangled quantum states, which constitute an important resource for quantum computing. In particular, an evolutionary algorithm is employed to optimize circuits with respect to a fitness function defined with the Mayer-Wallach entanglement measure. We demonstrate that, by balancing the mutation rate between exploration and exploitation, we can find entangling quantum circuits for up to five qubits. We also discuss the trade-off between the number of gates in quantum circuits and the computational costs of finding the gate arrangements leading to a strongly entangled state. Our findings provide additional insight into the trade-off between the complexity of a circuit and its performance, which is an important factor in the design of quantum circuits.

Figures (8)

• Figure 1: a) The fitness scores as a function of the number of generations, for different number of gates. b) The number of gates vs. the best fitness scores. The fitness scores of each gate for the box plots are the best fitness scores per run, and the fitness scores for the lower two plots are the average fitness scores of 50 runs.
• Figure 2: a) The fitness scores as a function of the number of generations, for different mutation rates. b) Mutation rates vs. the best fitness scores. The fitness scores of each gate are the average fitness scores of 50 runs.
• Figure 3: a) Fitness scores for different sets of probabilities against the number of generations for the KL-fitness function. b) Best fitness scores per run for $D_{KL}$ fitness function for different sets of probabilities. The fitness scores of each gate are the average fitness scores of 50 runs.
• Figure 4: a) Comparison of the best fitness scores across all 50 runs over 500 generations for different CA rules. b) Visualization of the optimal quantum circuit: Achieving a fitness score of 0.294 using the $D_{KL}$ fitness function for Critical Stochastic Cellular Automaton. The circuit, composed of 15 gates with a 10% mutation probability, represents the most exceptional outcome within the study, underscoring the success of our approach in circuit optimization.
• Figure 5: a) Evolutionary optimization of three-qubit quantum circuits with three gates using the MW entanglement measure brennen2003observable as the fitness function. b) Plots show mean and best fitness across generations for different mutation rates: 5%, including a third-order polynomial fit to the mean fitness. c) Best fitness comparison with varying mutation rates and gate numbers. d) Fitness outcomes for different gate numbers at a constant 10% mutation probability, averaged over 50 runs with standard error bars. An example circuit achieves a high fitness score of 0.999 with only three gates and 10% mutation probability.