Related papers: Coherent spaces, Boolean rings and quantum gates
We introduce coherent-state propagation, a computational framework for simulating bosonic systems. We focus on bosonic circuits composed of displaced linear optics augmented by Kerr nonlinearities, a universal model of bosonic quantum…
We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated…
The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or…
Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only…
Coherent Quantum Phase Slip consists in the coherent transfer of vortices in superfluids. We investigate this phenomenon in two miscible coherently coupled components of a spinor Bose gas confined in a toroidal trap. After imprinting…
Coherent subspaces spanned by a finite number of coherent states are introduced, in a quantum system with Hilbert space that has odd prime dimension $d$. The set of all coherent subspaces is partitioned into equivalence classes, with $d^2$…
We discuss the notion of coherent states from three different perspectives: the seminal approach of Schroedinger, the experimental take of quantum optics, and the theoretical developments in quantum gravity. This comparative study tries to…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
Coherent states for general systems with discrete spectrum, such as the bound states of the hydrogen atom, are discussed. The states in question satisfy: (1) continuity of labeling, (2) resolution of unity, (3) temporal stability, and (4)…
Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position…
We extend the usual definition of coherence, for modules over rings, to partially ordered right modules over a large class of partially ordered rings, called po-rings. In this situation, coherence is equivalent to saying that solution…
We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature. Some examples turn out to be known…
A historical review is given of the emergence of the idea of the quantum logic gate from the theory of reversible Boolean gates. I highlight the quantum XOR or controlled NOT as the fundamental two-bit gate for quantum computation. This…
We apply a dynamical systems approach to concatenation of quantum error correcting codes, extending and generalizing the results of Rahn et al. [1] to both diagonal and nondiagonal channels. Our point of view is global: instead of focusing…
We present a scheme for implementing high-fidelity quantum logic gates using the quantum walk of a few interacting bosons on a one-dimensional lattice. The gate operation is carried out by a single compact lattice described by a…
It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle.…
In the lectures we will be concerned with some aspects of physical implementations of quantum gate operations which are necessary for quantum information processing. We will discuss two possible realizations. One of them is based on qubits…
Quantum dynamics of integrable systems is discussed. Localized wave packets generalizing the conventional coherent states of minimal uncertainty are constructed. The wave packet moves along a certain trajectory and does not change its shape…