Quantum Hoare Type Theory: Extended Abstract

Abstract

As quantum computers become real, it is high time we come up with effective techniques that help programmers write correct quantum programs. In classical computing, formal verification and sound static type systems prevent several classes of bugs from being introduced. There is a need for similar techniques in the quantum regime. Inspired by Hoare Type Theory [NMB08] in the classical paradigm, we propose Quantum Hoare Types by extending the Quantum IO Monad [AG09] by indexing it with pre-and postconditions that serve as program specifications. In this paper, we introduce Quantum Hoare Type Theory (QHTT), present its syntax and typing rules, and demonstrate its effectiveness with the help of examples.QHTT has the potential to be a unified system for programming, specifying, and reasoning about quantum programs. This is a work in progress. 1

Formal Methods for Quantum Algorithms

“…However, to be able to go further and characterize functional correctness with respect to specification, or validate the number of gates of a circuit, or catch subtle bugs involving concatenation of inverted circuits, one needs to move away from the simple linear type systems of quantum lambdacalculi and shift towards sophisticated dependent types, such as the extension ProtoQuipper-D [77] of ProtoQuipper, or the approach of QWIRE. The gain in expressiveness is then at the expense of automation [177,148].…”

“…Quantum Hoare type theory [177] is inspired by classical Hoare type theory and extends the Quantum IO Monad [3] by indexing it with pre-and postconditions that serve as program specifications, which has the potential to be a unified system for programming, specifying, and reasoning about quantum programs.…”

Q# as a Quantum Algorithmic Language

“…Finally, Staton remarks upon a variant of his theory [54, §6.2] that applies to the QRAM model, where instead of working with qubits, we work with references to qubits. This is the approach taken in projects like the Quantum IO Monad [2], Quantum Hoare Type Theory [50,51], and, to our advantage, Q#. 2 Here we reproduce Staton's theory of a "quantum local store" [54, §6.2, p. 11] for reference; we will 1 Perhaps a better name for functors would be 'combinators' from the functional programming community to avoid confusion with other accepted meanings of the term 'functor.'…”

Formal Methods for Quantum Programs: A Survey

“…Quantum Hoare type theory [152] is inspired by classical Hoare type theory and extends the Quantum IO Monad [3] by indexing it with pre-and post-conditions that serve as program specifications, which has the potential to be a unified system for programming, specifying, and reasoning about quantum programs.…”