相关论文: Quantum Weakest Preconditions
We apply the notion of quantum predicate proposed by D'Hondt and Panangaden to analyze a purely quantum language fragment which describes the quantum part of a future quantum computer in Knill's architecture. The denotational semantics,…
In a recent letter [Information Processing Letters~104 (2007) 152-158], it has shown some sufficient conditions for commutativity of quantum weakest preconditions. This paper provides some alternative and simple characterizations for the…
Quantum computers promise significant speedups in solving problems intractable for conventional computers but, despite recent progress, remain limited in scaling and availability. Therefore, quantum software and hardware development heavily…
Conditioning is a key feature in probabilistic programming to enable modeling the influence of data (also known as observations) to the probability distribution described by such programs. Determining the posterior distribution is also…
We present a novel \emph{weakest pre calculus} for \emph{reasoning about quantitative hyperproperties} over \emph{nondeterministic and probabilistic} programs. Whereas existing calculi allow reasoning about the expected value that a…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
Weakest preconditions are a useful notion for program verification as they reduce a problem of program verification to a problem of constraint solving. Category-theoretic generalisations of weakest preconditions have been studied to capture…
In this article we investigate the relationships between the classical notions of weakest precondition and weakest liberal precondition, and provide several results, namely that in general, weakest liberal precondition is neither stronger…
In the paper "Does the weak trace show the past of a quantum particle?" [arXiv:2109.14060v2], it is argued that null weak values of the spatial projectors are inadequate to infer the presence of a quantum particle at an intermediate time…
We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a necessary resource for all schemes of…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…
A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speedup and, in particular, for fault-tolerant quantum computation. We establish a remarkable connection…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
Auto-active program verification rests on the ability to effectively the translation from annotated programs into verification conditions that are then discharged by automated theorem provers in the background. Characteristic such tools,…
Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and…
We present a weakest-precondition-style calculus for reasoning about the expected values (pre-expectations) of \emph{mixed-sign unbounded} random variables after execution of a probabilistic program. The semantics of a while-loop is…
Refinement calculus provides a structured framework for the progressive and modular development of programs, ensuring their correctness throughout the refinement process. This paper introduces a refinement calculus tailored for quantum…
We present a novel strongest-postcondition-style calculus for quantitative reasoning about non-deterministic programs with loops. Whereas existing quantitative weakest pre allows reasoning about the value of a quantity after a program…
We introduce a notion of contextuality for transformations in sequential contexts, distinct from the Bell-Kochen-Specker and Spekkens notions of contextuality. Within a transformation-based model for quantum computation we show that strong…
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no…