Model checking QCTL plus on quantum Markov chains

Xu, Ming; Fu, Jianling; Mei, Jingyi; Deng, Yuxin

doi:10.1016/j.tcs.2022.01.044

Cited by 7 publications

(2 citation statements)

References 27 publications

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“…One can consider our approach to be an instantiation of classical abstract interpretation [29] that is precise, and our approach to non-equivalence testing as comparing output abstract contexts of two programs. Quantum model checking supports a rich specification language (flavors of temporal logic [38,51,72]). It can be seen as an extension of probabilistic model checking [35,36,38,72,[77][78][79] and is more suitable for verifying high-level protocols due to the limited scalability [10].…”

Section: Related Workmentioning

confidence: 99%

“…Quantum model checking supports a rich specification language (flavors of temporal logic [38,51,72]). It can be seen as an extension of probabilistic model checking [35,36,38,72,[77][78][79] and is more suitable for verifying high-level protocols due to the limited scalability [10]. Techniques based on quantum simulation [39,56,57,60,64,67,68,84,85] allow only one input quantum state and thus have limited analyzing power.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

An Automata-based Framework for Verification and Bug Hunting in Quantum Circuits (Technical Report)

Chen¹,

Chung²,

Lengál³

et al. 2023

Preprint

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We introduce a new paradigm for analysing and finding bugs in quantum circuits. In our approach, the problem is given by a triple { } { } and the question is whether, given a set of quantum states on the input of a circuit , the set of quantum states on the output is equal to (or included in) a set . 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.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

An Automata-based Framework for Verification and Bug Hunting in Quantum Circuits (Technical Report)

Chen¹,

Chung²,

Lengál³

et al. 2023

Preprint

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show abstract

AutoQ: An Automata-Based Quantum Circuit Verifier

Chen

Chung

Lengál

et al. 2023

Lecture Notes in Computer Science

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We present a specification language and a fully automated tool named AutoQ for verifying quantum circuits symbolically. The tool implements the automata-based algorithm from [14] and extends it with the capabilities for symbolic reasoning. The extension allows to specify relational properties, i.e., relationships between states before and after executing a circuit. We present a number of use cases where we used AutoQ to fully automatically verify crucial properties of several quantum circuits, which have, to the best of our knowledge, so far been proved only with human help.

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A Theory of Cartesian Arrays (with Applications in Quantum Circuit Verification)

Chen,

Rümmer,

Tsai

2023

Lecture Notes in Computer Science

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We present a theory of Cartesian arrays, which are multi-dimensional arrays with support for the projection of arrays to sub-arrays, as well as for updating sub-arrays. The resulting logic is an extension of Combinatorial Array Logic (CAL) and is motivated by the analysis of quantum circuits: using projection, we can succinctly encode the semantics of quantum gates as quantifier-free formulas and verify the end-to-end correctness of quantum circuits. Since the logic is expressive enough to represent quantum circuits succinctly, it necessarily has a high complexity; as we show, it suffices to encode the k-color problem of a graph under a succinct circuit representation, an NEXPTIME-complete problem. We present an NEXPTIME decision procedure for the logic and report on preliminary experiments with the analysis of quantum circuits using this decision procedure.

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Model checking QCTL plus on quantum Markov chains

Cited by 7 publications

References 27 publications

An Automata-based Framework for Verification and Bug Hunting in Quantum Circuits (Technical Report)

An Automata-based Framework for Verification and Bug Hunting in Quantum Circuits (Technical Report)

AutoQ: An Automata-Based Quantum Circuit Verifier

A Theory of Cartesian Arrays (with Applications in Quantum Circuit Verification)

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