相关论文: Spherical Manifold in Quantum Evolution
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
We show how to represent the state and the evolution of a quantum computer (or any system with an $N$--dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary $N$, is…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Quantum de Sitter geometry is discussed using elementary field operator algebras in Krein space quantization from an observer-independent point of view, {\it i.e.} ambient space formalism. In quantum geometry, the conformal sector of the…
In the geometry of quantum evolutions, a geodesic path is viewed as a path of minimal statistical length connecting two pure quantum states along which the maximal number of statistically distinguishable states is minimum. In this paper, we…
The study of quantum systems evolving from initial states to distinguishable, orthogonal final states is important for information processing applications such as quantum computing and quantum metrology. However, for most unitary evolutions…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
We study the quantum evolution of a two-spin system described by the isotropic Heisenberg Hamiltonian in the external magnetic field. It is shown that this evolution happens on a two-parametric closed manifold. The Fubini-Study metric of…
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
Quantum evolution of a two-spin system with anisotropic Heisenberg Hamiltonian in the magnetic field is considered. We show that this evolution happens on some manifold with geometry depending on the ratio between the interaction couplings…
The fundamental division of the total quantum evolution phase into geometric and dynamical components is a central problem in quantum physics. Here, we prove a remarkably simple and universal law demonstrating that this partitioning is…
We propose a model of time evolution of quantum objects which unites the unitary evolution and the measurement procedures. The model allows to treat the time on equal footing with other dynamical variables.
If universal quantum interaction is really connected with the coset structure of deformations of quantum states then the curvature of projective Hilbert state space should be observable. I discuss some approach to the measurement of…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
We construct a formalism for evolving spherically symmetric black hole initial data sets within a canonical approach to quantum gravity. This problem can be formulated precisely in quantum reduced loop gravity, a framework which has been…
This manuscript gathers and subsumes a long series of works on using QW to simulate transport phenomena. Quantum Walks (QWs) consist of single and isolated quantum systems, evolving in discrete or continuous time steps according to a…
In this paper we establish important relations between Hamiltonian dynamics and Riemannian structures on phase spaces for unitarily evolving finite level quantum systems in mixed states. We show that the energy dispersion (i.e. $1/\hbar$…