Related papers: Quantum Hoare Logic with Ghost Variables
A quantum codeword is a redundant representation of a logical qubit by means of several physical qubits. It is constructed in such a way that if one of the physical qubits is perturbed, for example if it gets entangled with an unknown…
Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to…
It is proved that in non-relativistic quantum mechanics (without spin) the transition probability may be described in terms of particle paths, every path having a (positive) probability. This leads to a stochastic hidden variables theory…
Quantum mechanical weak values of projection operators have been used to answer which-way questions, e.g. to trace which arms in a multiple Mach-Zehnder setup a particle may have traversed from a given initial to a prescribed final state. I…
The application of a random modulation of a system parameter usually increases decoherence effects. Here we show how, employing an appropriate stochastic modulation, it is instead possible to preserve the quantum coherence of a system.
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational…
Reasoning about program correctness has been a central topic in static analysis for many years, with Hoare logic (HL) playing an important role. The key notions in HL are partial and total correctness. Both require that program executions…
This paper introduces quantum multiparty protocols which allow the use of temporary assumptions. We prove that secure quantum multiparty computations are possible if and only if classical multi party computations work. But these strict…
Nonlinear modifications of quantum theory are considered potential candidates for the theory of quantum gravity, with the intuitive argument that since Einstein field equations are nonlinear, quantum gravity should be nonlinear as well.…
Previously, gradual verification has been developed using overapproximating logics such as Hoare logic. We show that the static verification component of gradual verification is also connected to underapproximating logics like incorrectness…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily…
Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…
The hidden-variables premise is shown to be equivalent to the existence of generic filters for algebras of commuting propositions and for certain more general propositional systems. The significance of this equivalence is interpreted in…
This paper presents a proof system for reasoning about execution time bounds for a core imperative programming language. Proof systems are defined for three different scenarios: approximations of the worst-case execution time, exact time…
We propose a new quantum numerical scheme to control the dynamics of a quantum walker in a two dimensional space-time grid. More specifically, we show how, introducing a quantum memory for each of the spatial grid, this result can be…
Relational Hoare logics extend the applicability of modular, deductive verification to encompass important 2-run properties including dependency requirements such as confidentiality and program relations such as equivalence or similarity…
Logic programming languages present clear advantages in terms of declarativeness and conciseness. However, the ideas of logic programming have been met with resistance in other programming communities, and have not generally been adopted by…
We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice…