Gottesman Types for Quantum Programs

Rand, Robert S.; Sundaram, Aarthi; Singhal, Kartik; Lackey, Brad

doi:10.4204/eptcs.340.14

Cited by 3 publications

(3 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Behavioral Types Another venue for exploration is to incorporate more precise types that can distinguish between qubits in pure classical state vs. those in superposition vs. those in entanglement [JP09] such as those inspired by the various quantum resource theories or the Heisenberg representation of quantum mechanics [RSSL19,RSSL20]. This may help us provide more specific postconditions that quantum programmers expect to hold true of their programs.…”

Section: Discussionmentioning

confidence: 99%

“…Behavioral Types Another avenue for exploration is to incorporate more precise types for qubits that can distinguish between qubits in the pure classical state vs. those in superposition vs. those in entanglement [Jorrand and Perdrix 2009] such as those inspired by the various quantum resource theories or the Heisenberg representation of quantum mechanics [Rand, Sundaram, et al 2019;2020]. For example, in "Gottesman Types for Quantum Programs", Rand, Sundaram, et al [2020] assign types Z and X to single qubits in computational and Hadamard basis states respectively. Then, the Hadamard operator can be assigned the intersection of two arrow types, (X → Z) ∩ (Z → X), as it converts between the computational and Hadamard basis states.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum Hoare Type Theory: Extended Abstract

Singhal

Reppy

2021

Electron. Proc. Theor. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

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

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Quantum Hoare Type Theory: Extended Abstract

Singhal

Reppy

2021

Electron. Proc. Theor. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…QWIRE is built on top of the standard libary of Coq for the theory of real numbers, and builds its own libraries for complex number and matrix theory. Interestingly, the authors of QWIRE report that mathcomp was also considered as external library for early development of QWIRE, but due to the overhead caused by dependent types, the authors use phantom type [Rand et al 2018a] instead. In contrast, the use of mathcomp is more important in our setting, as we aim to support general notions of state.…”

Section: Related Workmentioning

confidence: 99%

CoqQ: Foundational Verification of Quantum Programs

Li¹,

Barthe²,

Strub³

et al. 2022

Preprint

View full text Add to dashboard Cite

CoqQ is a framework for reasoning about quantum programs in the Coq proof assistant. Its main components are: a deeply embedded quantum programming language, in which classic quantum algorithms are easily expressed, and an expressive program logic for proving properties of programs. CoqQ is foundational: the program logic is formally proved sound with respect to a denotational semantics based on state-of-art mathematical libraries (mathcomp and mathcomp analysis). CoqQ is also practical: assertions can use Dirac expressions, which eases concise specifications, and proofs can exploit local and parallel reasoning, which minimizes verification effort. We illustrate the applicability of CoqQ with many examples from the literature.

show abstract

Symbolic Execution for Quantum Error Correction Programs

Fang,

Ying

2024

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

We define QSE, a symbolic execution framework for quantum programs by integrating symbolic variables into quantum states and the outcomes of quantum measurements. The soundness of QSE is established through a theorem that ensures the correctness of symbolic execution within operational semantics. We further introduce symbolic stabilizer states, which symbolize the phases of stabilizer generators, for the efficient analysis of quantum error correction (QEC) programs. Within the QSE framework, we can use symbolic expressions to characterize the possible discrete Pauli errors in QEC, providing a significant improvement over existing methods that rely on sampling with simulators. We implement QSE with the support of symbolic stabilizer states in a prototype tool named QuantumSE.jl. Our experiments on representative QEC codes, including quantum repetition codes, Kitaev's toric codes, and quantum Tanner codes, demonstrate the efficiency of QuantumSE.jl for debugging QEC programs with over 1000 qubits. In addition, by substituting concrete values in symbolic expressions of measurement results, QuantumSE.jl is also equipped with a sampling feature for stabilizer circuits. Despite a longer initialization time than the state-of-the-art stabilizer simulator, Google's Stim, QuantumSE.jl offers a quicker sampling rate in the experiments.

show abstract

Gottesman Types for Quantum Programs

Cited by 3 publications

References 17 publications

Quantum Hoare Type Theory: Extended Abstract

Quantum Hoare Type Theory: Extended Abstract

CoqQ: Foundational Verification of Quantum Programs

Symbolic Execution for Quantum Error Correction Programs

Contact Info

Product

Resources

About