Parameterized Verification of Quantum Circuits

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Abstract
We present the first fully automatic framework for verifying relational properties of parameterized quantum programs , i.e., a program that, given an input size, generates a corresponding quantum circuit. We focus on verifying input-output correctness as well as equivalence. At the core of our approach is a new automata model, synchronized weighted tree automata (SWTAs), which compactly and precisely captures the infinite families of quantum states produced by parameterized programs. We introduce a class of transducers to model quantum gate semantics and develop composition algorithms for constructing transducers of parameterized circuits. Verification is reduced to functional inclusion or equivalence checking between SWTAs, for which we provide decision procedures. Our implementation demonstrates both the expressiveness and practical efficiency of the framework by verifying a diverse set of representative parameterized quantum programs with verification times ranging from milliseconds to seconds
Funding Information
  • Grantová Agentura České Republiky (25-18318S)
  • Grantová Agentura České Republiky (25-17934S)
  • Fakulta Informačních Technologií, Vysoké Učení Technické v Brně (FIT-S-23-8151)
  • National Science and Technology Council (NSTC 114-2221-E-027-044 -MY2)
  • National Science and Technology Council (NSTC 114-2119-M-001-002-)
  • Air Force Office of Scientific Research (FA2386-23-1-4107)
  • Academia Sinica (AS-IV-114-M07)
  • Brno City Municipality (Brno Ph.D. Talent)