[Paper Review] Evolving Quantum Circuits

Daniel Tandeitnik, Thiago Guerreiro|arXiv (Cornell University)|Oct 11, 2022

Quantum Computing Algorithms and Architecture86 references4 citations

TL;DR

This paper proposes using genetic algorithms (GAs) to evolve quantum circuits, specifically stabilizer quantum error correction codes, by navigating complex Hilbert space via fitness landscapes. The method successfully evolves known codes like the 5-qubit perfect code, Shor’s 9-qubit code, and the 7-qubit color code from random initial circuits, demonstrating that evolution outperforms random search and offers a scalable, hardware-aware approach for NISQ-era quantum circuit design.

ABSTRACT

We develop genetic algorithms for searching quantum circuits, in particular stabilizer quantum error correction codes. Quantum codes equivalent to notable examples such as the 5-qubit perfect code, Shor's code, and the 7-qubit color code are evolved out of initially random quantum circuits. We anticipate evolution as a promising tool in the NISQ era, with applications such as the search for novel topological ordered states, quantum compiling, and hardware optimization.

Motivation & Objective

• To investigate whether artificial selection via genetic algorithms can effectively search for complex quantum circuits, particularly stabilizer quantum error correction codes.
• To overcome the limitations of random search in high-dimensional Hilbert space by leveraging evolutionary optimization.
• To demonstrate that GAs can evolve known, high-performing quantum codes from random initial populations.
• To explore the application of fitness functions incorporating hardware-specific constraints for tailored circuit design.

Proposed method

• Genetic algorithms are applied to evolve quantum circuits by iteratively selecting, mutating, and recombining populations of random stabilizer circuits based on a fitness function.
• The fitness function is designed to reward circuits that exhibit desired quantum error correction properties, such as logical qubit protection and high distance.
• Mutations are applied to single-qubit Clifford gates and two-qubit CNOT gates, preserving the stabilizer formalism and ensuring efficient classical simulation.
• The fitness function incorporates entanglement structure via mutual information between subsystems, quantifying error-correcting capacity.
• Hardware-specific constraints are encoded in the fitness function using complexity geometry metrics that penalize non-native gate operations based on device topology.
• The method is tested on known codes like the 5-qubit perfect code and 7-qubit color code, with successful recovery of equivalent circuits.

Experimental results

Research questions

• RQ1 Can genetic algorithms efficiently navigate the vast Hilbert space of quantum circuits to discover known quantum error correction codes?
• RQ2 How does evolutionary search compare to random search in identifying low-depth, stabilizer-based quantum circuits with high error-correcting capability?
• RQ3 Can fitness functions based on entanglement structure and topological features guide the evolution of topological quantum codes such as the 7-qubit color code?
• RQ4 To what extent can hardware-specific constraints be encoded in the fitness function to generate optimized circuits for real NISQ devices?
• RQ5 Can this evolutionary approach discover novel quantum codes beyond known textbook examples?

Key findings

• The genetic algorithm successfully evolved the 5-qubit perfect code from a random initial population, demonstrating that evolution can surpass random search in complex Hilbert spaces.
• The method reliably recovered Shor’s 9-qubit code and the 7-qubit color code, confirming its effectiveness for well-known stabilizer codes.
• Evolved circuits exhibited low depth and high logical protection, indicating suitability for noisy intermediate-scale quantum (NISQ) devices.
• Fitness functions based on mutual information between subsystems effectively guided the search toward codes with high error-correcting distance.
• Hardware-aware fitness functions incorporating device topology and gate complexity metrics enabled the generation of circuits tailored to specific quantum hardware, such as IBM’s quantum processors.
• The approach demonstrated that evolutionary computation can discover complex quantum circuits with minimal human intuition, suggesting potential for automated discovery of novel quantum algorithms and codes.