An Automated Deductive Verification Framework for Circuit-building Quantum Programs

Abstract

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. In this paper we propose Qbricks, a formal verification environment for circuit-building quantum programs, featuring both parametric specifications and a high degree of proof automation. We propose a logical framework based on first-order logic, and develop the main tool we rely upon for achieving the automation of proofs of quantum specification: PPS, a parametric extension of the recently developed path sum semantics. To back-up our claims, we implement and verify parametric versions of several famous and non-trivial quantum algorithms, including the quantum parts of Shor’s integer factoring, quantum phase estimation (QPE) and Grover’s search.

Symbolic Reasoning About Quantum Circuits in Coq

“…In contrast, we can also deal with mixed states in the form of density matrices. Chareton et al [24] proposed a verification framework QBRICKS embedded in the Why3 deductive verification tool 8 ○ . It specifies quantum circuits by a variant of the path-sum representation [25] called parametrized path-sums and can describe circuits in a functional language efficiently.…”

Formal Methods for Quantum Programs: A Survey

“…In a lower-level verification approach view, instead of inputting quantum operations as primitive functions, one builds quantum circuit implementations of these operations, by adequately combining quantum gates. Such a framework [78,135,29] lies on a circuit description language such as QUIPPER or QWIRE. Then, an adequate semantics characterization for the built circuits enables to reason about the quantum data received as inputs and delivered as outputs.…”

“…• another possibility is to reduce the expressivity of the language, so as to prevent any possible violation of no-cloning. In SQIR [78] or QBRICKS [29], quantum data registers are addressed to via integer indexes, but the data they hold only concern the semantics of the language and the specification language. Hence, the respecting conditions for the no cloning theorem are reduced to simple indexing rules for quantum circuits.…”

“…QBRICKS [29] is a recently proposed circuit description language together with a deductive verification framework. It enables an automated proof support for program specifications, reducing the required human effort for the development of verified programs.…”

“…A path-sum P is said to correctly interpret a given circuit C (written (C p)) if and only if C has width n = pps width(P) and for any bit vector x of length n, Mat(C) • | x = Ps(P, | x ). The relation ( ) enjoys nice composition properties along QBRICKS-DSL circuit constructors (see [29] ).…”