5 research outputs found
A Deductive Verification Framework for Circuit-building Quantum Programs
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
A Theorem Prover for Quantum Hoare Logic and Its Applications
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