An Automata-Based Framework for Verification and Bug Hunting in Quantum Circuits

An Automata-Based Framework for Verification and Bug Hunting in Quantum Circuits

WoS Article

We introduce a new paradigm for analysing and finding bugs in quantum circuits. In our approach, the problem is given by a triple {P} C {Q} and the question is whether, given a set of quantum states P on the input of a circuit C, the set of quantum states on the output is equal to (or included in) a set Q. While this is not suitable to specify, e.g., functional correctness of a quantum circuit, it is sufficient to detect many bugs in quantum circuits. We propose a technique based on tree automata to compactly represent sets of quantum states and develop transformers to implement the semantics of quantum gates over this representation. Our technique computes with an algebraic representation of quantum states, avoiding the inaccuracy of working with floating-point numbers. We implemented the proposed approach in a prototype tool and evaluated its performance against various benchmarks from the literature. The evaluation shows that our approach is quite scalable, e.g., we managed to verify a large circuit with 40 qubits and 141,527 gates, or catch bugs injected into a circuit with 320 qubits and 1,758 gates, where all tools we compared with failed. In addition, our work establishes a connection between quantum program verification and automata, opening new possibilities to exploit the richness of automata theory and automata-based verification in the world of quantum computing.

We introduce a new paradigm for analysing and finding bugs in quantum circuits. In our approach, the problem is given by a triple {P} C {Q} and the question is whether, given a set of quantum states P on the input of a circuit C, the set of quantum states on the output is equal to (or included in) a set Q. While this is not suitable to specify, e.g., functional correctness of a quantum circuit, it is sufficient to detect many bugs in quantum circuits. We propose a technique based on tree automata to compactly represent sets of quantum states and develop transformers to implement the semantics of quantum gates over this representation. Our technique computes with an algebraic representation of quantum states, avoiding the inaccuracy of working with floating-point numbers. We implemented the proposed approach in a prototype tool and evaluated its performance against various benchmarks from the literature. The evaluation shows that our approach is quite scalable, e.g., we managed to verify a large circuit with 40 qubits and 141,527 gates, or catch bugs injected into a circuit with 320 qubits and 1,758 gates, where all tools we compared with failed. In addition, our work establishes a connection between quantum program verification and automata, opening new possibilities to exploit the richness of automata theory and automata-based verification in the world of quantum computing.

quantum circuit, verification, tree automata, bug hunting

quantum circuit, verification, tree automata, bug hunting

LENGÁL, O.; CHEN, Y.; TSAI, W.; LIN, J.; CHUNG, K.; YEN, D.

2024

17.06.2023

Proceedings of PLDI'23

2475-1421

Proceedings of the ACM on Programming Languages-PACMPL

7

6

United States of America

1218

1243

26

http://dx.doi.org/10.1145/3591270