相关论文: An unsharp logic from quantum computation
We consider an example of a quantum algorithm from the point of view of the de Broglie-Bohm formulation of quantum mechanics. For concreteness we look at two particular implementations: one using spin-1/2 particles as described by a simple…
A major goal in quantum computing is to build a fault-tolerant quantum computer. One approach involves quantum low-density parity-check (qLDPC) codes that support transversal non-Clifford gates. In this work, we provide a large family of…
Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
We naturally obtain the NOT and CNOT logic gates, which are key pieces of quantum computing algorithms, in the framework of the non-Abelian Chern-Simons-Higgs theory in two spatial dimensions. For that, we consider the anyonic quantum…
Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism…
Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts…
The question of finding a lower bound on the number of Toffoli gates in a classical reversible circuit is addressed. A method based on quantum information concepts is proposed. The method involves solely concepts from quantum information -…
Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a…
We try to design a quantum neural network with qubits instead of classical neurons with deterministic states, and also with quantum operators replacing teh classical action potentials. With our choice of gates interconnecting teh neural…
Quantum computers are expected to be able to solve mathematical problems that cannot be solved using conventional computers. Many of these problems are of practical importance, especially in the areas of cryptography and secure…
An implementation method of a gate in a quantum computer is studied in terms of a finite number of steps evolving in time according to a finite number of basic Hamiltonians, which are controlled by on-off switches. As a working example, the…
A new paradigm of quantum computing, namely, soft quantum computing, is proposed for nonclassical computation using real world quantum systems with naturally occurring environment-induced decoherence and dissipation. As a specific example…
The simplest decomposition of a Toffoli gate acting on three qubits requires {\em five} 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to six. We show that the number of…
A liaison between quantum logics and non-commutative differential geometry is outlined: a class of quantum logics are proved to possess the structure of discrete differential manifolds. We show that the set of proper elements of an…
Finite group extensions offer a natural language to quantum computing. In a nutshell, one roughly describes the action of a quantum computer as consisting of two finite groups of gates: error gates from the general Pauli group P and…
We present two new constructions for the Toffoli gate which substantially reduce resource costs in fault-tolerant quantum computing. The first contribution is a Toffoli gate requiring Clifford operations plus only four $T =…
The term quantum neural computing indicates a unity in the functioning of the brain. It assumes that the neural structures perform classical processing and that the virtual particles associated with the dynamical states of the structures…
We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma et al., in a way that might potentially allow for the topologically protected construction of a…
We discuss quantum non-locality and contextuality, emphasising logical and structural aspects. We also show how the same mathematical structures arise in various areas of classical computation.