相关论文: Algebraic Reasoning of Quantum Programs via Non-id…
(1) Let 1\leq k\leq \omega. Call an atom structure \alpha weakly k neat representable, the term algebra is in \RCA_n\cap \Nr_n\CA_{n+k}, but the complex algebra is not representable. Call an atom structure neat if there is an atomic algebra…
Hoare logic provides a syntax-oriented method to reason about program correctness and has been proven effective in the verification of classical and probabilistic programs. Existing proposals for quantum Hoare logic either lack completeness…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
We exhibit a uniform method for obtaining (wellfounded and non-wellfounded) cut-free sequent-style proof systems that are sound and complete for various classes of action algebras, i.e., Kleene algebras enriched with meets and residuals.…
We propose Weighted Guarded Kleene Algebra with Tests (wGKAT), an uninterpreted weighted programming language equipped with branching, conditionals, and loops. We provide an operational semantics for wGKAT using a variant of weighted…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
We initiate the study of parallel quantum programming by defining the operational and denotational semantics of parallel quantum programs. The technical contributions of this paper include: (1) find a series of useful proof rules for…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Synchronous Kleene algebra (SKA), an extension of Kleene algebra (KA), was proposed by Prisacariu as a tool for reasoning about programs that may execute synchronously, i.e., in lock-step. We provide a countermodel witnessing that the…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
Guarded Kleene Algebra with Tests (GKAT) provides a sound and complete framework to reason about trace equivalence between simple imperative programs. However, there are still several notable limitations. First, GKAT is completely agnostic…
Concurrent Kleene Algebra (CKA) was introduced by Hoare, Moeller, Struth and Wehrman in 2009 as a framework to reason about concurrent programs. We prove that the axioms for CKA with bounded parallelism are complete for the semantics…
Kozen and Tiuryn have introduced the substructural logic $\mathsf{S}$ for reasoning about correctness of while programs (ACM TOCL, 2003). The logic $\mathsf{S}$ distinguishes between tests and partial correctness assertions, representing…
In this paper, we investigate the fundamental laws of quantum programming. We extend a comprehensive set of Hoare et al.'s basic laws of classical programming to the quantum setting. These laws characterise the algebraic properties of…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously-developed denotational semantics of QML. The completeness…
We propose a quantum programming paradigm where all data are familiar classical data, and the only non-classical element is a random number generator that can return results with negative probability. Currently, the vast majority of quantum…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
Quantum Machine Learning (QML) hasn't yet demonstrated extensively and clearly its advantages compared to the classical machine learning approach. So far, there are only specific cases where some quantum-inspired techniques have achieved…