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

TL;DR

This paper explores the use of evolutionary algorithms to design quantum circuits for stable Boolean gates, cellular automata, and highly entangled states, highlighting the balance between circuit complexity and performance.

Contribution

It introduces a novel application of bio-inspired evolutionary algorithms to optimize quantum circuits for specific tasks, including cellular automata reproduction and entanglement generation.

Findings

Evolutionary algorithms can produce robust quantum implementations of cellular automata.

Optimized circuits can generate highly entangled states for up to five qubits.

Trade-offs exist between circuit complexity and computational cost in design.

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.