Related papers: A Categorical Model for Classical and Quantum Bloc…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial…
Some problems of the quantum error-correcting codes theory can be reduced to the investigation of the higher-rank numerical ranges of the operators related to the error operators. We constructively verify a conjecture on the structure of…
We consider a programming language that can manipulate both classical and quantum information. Our language is type-safe and designed for variational quantum programming, which is a hybrid classical-quantum computational paradigm. The…
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 computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study of their quantum counterparts. These quantum graphical…
The emergence of quantum computing proposes a revolutionary paradigm that can radically transform numerous scientific and industrial application domains. The ability of quantum computers to scale computations implies better performance and…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…
This work introduces and characterizes quantum sequential circuits (QSCs) as a hardware-oriented paradigm for quantum computing, built upon a novel foundational element termed the quantum transistor. Unlike conventional qubit-based…
Stochastic matrices and positive maps in matrix algebras proved to be very important tools for analysing classical and quantum systems. In particular they represent a natural set of transformations for classical and quantum states,…
Underlying any theory of physics is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with physical phenomena, but they also constitute our fundamental assumptions about reality. Many of the…
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…
In this paper, we investigate the classicality and quantumness of a quantum ensemble. We define a quantity called classicality to characterize how classical a quantum ensemble is. An ensemble of commuting states that can be manipulated…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
Coecke and Heunen described completely positive maps in dagger monoidal categories and the {\sf CP}-infinity construction on these categories in order to construct a category of arbitrary dimensional quantum processes. This article…