Related papers: Relational Proofs for Quantum Programs
It is argued that a fuzzy version of 4-truth-valued paraconsistent logic (with truth values corresponding to True, False, Both and Neither) can be approximately isomorphically mapped into the complex-number algebra of quantum probabilities.…
A temporal logic is presented for reasoning about the correctness of timed concurrent constraint programs. The logic is based on modalities which allow one to specify what a process produces as a reaction to what its environment inputs.…
Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of…
It is well known that quantum technology allows for an unprecedented level of data and software protection for quantum computers as well as for quantum-assisted classical computers. To exploit these properties, probabilistic one-time…
Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…
The identification of causal relations is a cornerstone of the scientific method. Traditional approaches to this task are based on classical statistics. However, such classical approaches do not apply in the quantum domain, where a broader…
Quantum algorithms and protocols are often presented as quantum circuits for a better understanding. We give a list of equivalence rules which can help in the analysis and design of quantum circuits. As example applications we study quantum…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
Quantum computing has emerged as a promising field with the potential to revolutionize various domains by harnessing the principles of quantum mechanics. As quantum hardware and algorithms continue to advance, developing high-quality…
A first-order logic with quantum variables is needed as an assertion language for specifying and reasoning about various properties (e.g. correctness) of quantum programs. Surprisingly, such a logic is missing in the literature, and the…
We aim to reason about the correctness of behaviour-preserving transformations of Erlang programs. Behaviour preservation is characterised by semantic equivalence. Based upon our existing formal semantics for Core Erlang, we investigate…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood…
Quantum processes describe concurrent communicating systems that may involve quantum information. We propose a notion of open bisimulation for quantum processes and show that it provides both a sound and complete proof methodology for a…
In order for quantum communications systems to become widely used, it will probably be necessary to develop quantum repeaters that can extend the range of quantum key distribution systems and correct for errors in the transmission of…
We consider the problems of statically refuting equivalence and similarity of output distributions defined by a pair of probabilistic programs. Equivalence and similarity are two fundamental relational properties of probabilistic programs…
The Curry-Howard correspondence is about a relationship between types and programs on the one hand and propositions and proofs on the other. The implications for programming language design and program verification is an active field of…
Quantum computation has made considerable progress in the last decade with multiple emerging technologies providing proof-of-principle experimental demonstrations of such calculations. However, these experimental demonstrations of quantum…
This paper develops verification methodology for quantum programs, and the contribution of the paper is two-fold: 1. Sharir, Pnueli and Hart [SIAM J. Comput. 13(1984)292-314] presented a general method for proving properties of…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…