Verifying quantum programs today requires specialized proof systems built on interactive theorem provers such as Rocq, Lean, Isabelle, or Why3, and even modest quantum algorithms cost substantial human effort to verify. Because quantum programs cannot be effectively checked by runtime testing, formal verification is the only viable path to correctness, making the cost of these bespoke systems the chief barrier to scalable quantum software assurance. We show that verifying a quantum program should be no harder than verifying a classical array program, a paradigm commonly used in parallel programming: the Qafny quantum proof system translates into Hoare logic with array theory completely (every Qafny proof becomes a valid Hoare triple) and soundly (a valid translated triple certifies only true quantum specifications), and we mechanize the completeness direction in Rocq. The embedding determinizes quantum proof obligations and exposes the full machinery of classical automated verifiers (e.g. Dafny and SMT-based separation logic) to quantum code, removing the need for dedicated quantum proof system infrastructure. In particular, the embedding supplies the correctness argument that the existing compilation of Qafny into Dafny lacks.
Verifying quantum programs today requires specialized proof systems built on interactive theorem provers such as Rocq, Lean, Isabelle, or Why3, and even modest quantum algorithms cost substantial human effort to verify. Because quantum programs cannot be effectively checked by runtime testing, formal verification is the only viable path to correctness, making the cost of these bespoke systems the chief barrier to scalable quantum software assurance. We show that verifying a quantum program should be no harder than verifying a classical array program, a paradigm commonly used in parallel programming: the Qafny quantum proof system translates into Hoare logic with array theory completely (every Qafny proof becomes a valid Hoare triple) and soundly (a valid translated triple certifies only true quantum specifications), and we mechanize the completeness direction in Rocq. The embedding determinizes quantum proof obligations and exposes the full machinery of classical automated verifiers (e.g. Dafny and SMT-based separation logic) to quantum code, removing the need for dedicated quantum proof system infrastructure. In particular, the embedding supplies the correctness argument that the existing compilation of Qafny into Dafny lacks.
Because of the probabilistic/nondeterministic behavior of quantum programs, it is highly advisable to verify them formally to ensure that they correctly implement their specifications. Formal verification, however, also traditionally requires significant effort. To address this challenge, we present Qafny, an automated proof system based on the program verifier Dafny and designed for verifying quantum programs. At its core, Qafny uses a type-guided quantum proof system that translates quantum operations to classical array operations modeled within a classical separation logic framework. We prove the soundness and completeness of our proof system and implement a prototype compiler that transforms Qafny programs and specifications into Dafny for automated verification purposes. We then illustrate the utility of Qafny's automated capabilities in efficiently verifying important quantum algorithms, including quantum-walk algorithms, Grover's algorithm, and Shor's algorithm.
Practical quantum programs interleave quantum and classical computation: classical data shape the quantum operations that are performed, and measurement outcomes shape the classical computation that follows. Formal verification of such programs in a proof assistant requires mechanizing a program logic that handles this interplay consistently at every level, from the mathematics of quantum mechanics, through program syntax and semantics, to specifications and proof rules. Such mechanizations, along with the program proofs built on them, typically require substantial manual effort.
We present QEDIA, a framework for verifying quantum programs with classical variables in Lean 4. At its foundation is an open library that formalizes the quantum Hoare logic QHL+ across all these levels and proves the logic sound for both partial and total correctness. We construct the library and the program proofs, under human supervision, using an LLM-based prover agent, whose general-purpose core we extend for quantum program verification. We illustrate QEDIA with verified programs including the quantum Fourier transform, phase estimation, repeat-until-success circuits, and Hamiltonian simulation.
Despite recent development of quantum program verification, it is still in its early stage, where many quantum programs are hard to verify due to their inherent probabilistic nature and parallelism in quantum superposition. We propose Qafny c , a system that compiles quantum program verification into a well-established classical program verifier Dafny, enabling the formal verification of quantum programs. The key insight behind Qafny c is the separation of quantum program verification from its execution, leveraging the strength of classical verifiers to ensure correctness before compiling certified quantum programs into executable circuits. Using Qafny c , we have successfully verified 37 diverse quantum programs by compiling their verification into Dafny. To the best of our knowledge, this is the most extensive formally verified set of quantum programs.
We formalize the theory of quantum Hoare logic (QHL) [TOPLAS 33(6),19], an extension of Hoare logic for reasoning about quantum programs. In particular, we formalize the syntax and semantics of quantum programs in Isabelle/HOL, write down the rules of quantum Hoare logic, and verify the soundness and completeness of the deduction system for partial correctness of quantum programs. As preliminary work, we formalize some necessary mathematical background in linear algebra, and define tensor products of vectors and matrices on quantum variables. As an application, we verify the correctness of Grover’s search algorithm. To our best knowledge, this is the first time a Hoare logic for quantum programs is formalized in an interactive theorem prover, and used to verify the correctness of a nontrivial quantum algorithm.
While recent progress in quantum hardware open the door for significant speedup in certain key areas, quantum algorithms are still hard to implement right, and the validation of such quantum programs is a challenge. Early attempts either suffer from the lack of automation or parametrized reasoning, or target high-level abstract algorithm description languages far from the current de facto consensus of circuit-building quantum programming languages. As a consequence, no significant quantum algorithm implementation has been currently verified in a scale-invariant manner. We propose Qbricks, the first formal verification environment for circuit-building quantum programs, featuring clear separation between code and proof, parametric specifications and proofs, high degree of proof automation and allowing to encode quantum programs in a natural way, i.e. close to textbook style. Qbricks builds on best practice of formal verification for the classical case and tailor them to the quantum case: we bring a new domain-specific circuit-building language for quantum programs, namely Qbricks-DSL, together with a new logical specification language Qbricks-Spec and a dedicated Hoare-style deductive verification rule named Hybrid Quantum Hoare Logic. Especially, we introduce and intensively build upon HOPS, a higher-order extension of the recent path-sum symbolic representation, used for both specification and automation. To illustrate the opportunity of Qbricks, we implement the first verified parametric implementations of several famous and non-trivial quantum algorithms, including the quantum part of Shor integer factoring (Order Finding - Shor-OF), quantum phase estimation (QPE) - a basic building block of many quantum algorithms, and Grover search. These breakthroughs were amply facilitated by the specification and automated deduction principles introduced within Qbricks.
Quantum Hoare Logic (QHL) was introduced in Ying's work to specify and reason about quantum programs. In this paper, we implement a theorem prover for QHL based on Isabelle/HOL. By applying the theorem prover, verifying a quantum program against a specification is transformed equivalently into an order relation between matrices. Due to the limitation of Isabelle/HOL, the calculation of the order relation is solved by calling an outside oracle written in Python. To the best of our knowledge, this is the first theorem prover for quantum programs. To demonstrate its power, the correctness of two well-known quantum algorithms, i.e., Grover Quantum Search and Quantum Phase Estimation (the key step in Shor's quantum algorithm of factoring in polynomial time) are proved using the theorem prover. These are the first mechanized proofs for both of them.