Related papers: From Symmetric Pattern-Matching to Quantum Control…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by…
When investigating theories at the tiniest conceivable scales in nature, almost all researchers today revert to the quantum language, accepting the verdict from the Copenhagen doctrine that the only way to describe what is going on will…
Quantum lambda calculus has been studied mainly as an idealized programming language -- the evaluation essentially corresponds to a deterministic abstract machine. Very little work has been done to develop a rewriting theory for quantum…
We have proposed in several recent papers a critical view of some parts of quantum mechanics (QM) that is methodologically unusual because it rests on analysing the language of QM by using some elementary but fundamental tools of…
Quantum theory was discovered in an adventurous way, under the urge to solve puzzles-like the spectrum of the blackbody radiation-that haunted the physics community at the beginning of the 20th century. It soon became clear, though, that…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters),…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which…
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…
We extract a novel quantum programming paradigm - superposition of programs - from the design idea of a popular class of quantum algorithms, namely quantum walk-based algorithms. The generality of this paradigm is guaranteed by the…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
This paper serves as a bridge between quantum computing and analogical modeling (a general theory for predicting categories of behavior in varying contexts). Since its formulation in the early 1980s, analogical modeling has been…
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…
In this research, we present a quantum circuit design and implementation for a parallel universal linear bounded automata. This circuit is able to accelerate the inference of algorithmic structures in data for discovering causal generative…
We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including…
The logic which describes quantum robots is not orthodox quantum logic, but a deductive calculus which reproduces the quantum tasks (computational processes, and actions) taking into account quantum superposition and quantum entanglement. A…
The objective of this paper is to present general, mechanically verified, refinement rules for reasoning about recursive programs and while loops in the context of concurrency. Unlike many approaches to concurrency, we do not assume that…