Related papers: Geometric Phases and Topological Quantum Computati…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
Cavity-based large scale quantum information processing (QIP) may involve multiple cavities and require performing various quantum logic operations on qubits distributed in different cavities. Geometric-phase-based quantum computing has…
We analyze a scheme for quantum computation where quantum gates can be continuously changed from standard dynamic gates to purely geometric ones. These gates are enacted by controlling a set of parameters that are subject to unwanted…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally,…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths,…
Geometric phase is a key player in many areas of quantum science and technology. In this review article, several foundational aspects of quantum geometric phases and their relations to classical geometric phases are outlined. How the…
In order to achieve universal quantum computation using continuous variables, one needs to jump out of the set of Gaussian operations and have a non-Gaussian element, such as the cubic phase gate. However, such a gate is currently very…
This is a brief overview of quantum holonomies in the context of quantum computation. We choose an adequate set of quantum logic gates, namely, a phase gate, the Hadamard gate, and a conditional-phase gate and show how they can be…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
Quantum gates are the building blocks of quantum circuits, which in turn are the cornerstones of quantum information processing. In this work, we theoretically investigate a single-step implementation of both a universal two- (CNOT) and…
Geometric phases are robust to local noises and the nonadiabatic ones can reduce the evolution time, thus nonadiabatic geometric gates have strong robustness and can approach high fidelity. However, the advantage of geometric phase has not…
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
Recent advancements in the discipline of quantum algorithms have displayed the importance of the geometry of quantum operators. Given this thrust, this paper develops a rigorous geometric framework to analyze how the Riemannian structure of…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…