How quantum and evolutionary algorithms can help each other: two examples

2024-08-01

arXiv.org

AI Summary

This study addresses two key challenges in quantum circuit design: (1) robustly implementing stochastic cellular automata governed by prescribed rules, and (2) efficiently generating highly entangled quantum states. We propose the first framework that deeply integrates evolutionary algorithms with quantum circuit optimization—employing genetic algorithms, quantum-gate-sequence encoding, and multi-scale mutation-rate control, with the Mayer–Wallach measure serving as the fitness function to systematically explore the trade-off between circuit complexity and entanglement performance. On 5-qubit systems, our approach successfully evolves quantum circuits achieving high entanglement, demonstrating its efficacy in identifying high-performance quantum architectures under resource constraints. This work establishes the first evolvable paradigm for quantum entanglement optimization, offering a novel pathway for hardware-aware quantum compilation and quantum state engineering in resource-limited settings.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Designing quantum circuits for stable Boolean gates and cellular automata rules
• Optimizing circuits to generate highly entangled quantum states efficiently
• Balancing circuit complexity and performance trade-offs in quantum computing

Innovation

• Evolutionary algorithms optimize quantum circuit designs
• Balancing mutation rates for exploration and exploitation
• Mayer-Wallach entanglement measure defines fitness function