Optimizing Quantum Circuits with Evolutionary Algorithms for Stable Boolean Gates, Elementary Cellular Automata, and Highly Entangled Quantum States
Shailendra Bhandari, Stefano Nichele, Sergiy Denysov and Pedro G. Lind
We investigate the potential of bio-inspired evolutionary algorithms (EAs) for designing quantum circuits with specific goals, focusing on two particular tasks. The first task involves using these algorithms 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 sampling 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 Meyer-Wallach (MW) 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.
Keywords: Quantum computing, Quantum circuits, quantum gates, entanglement, evolutionary algorithms