Related papers: Observable-geometric phases and quantum computatio…
Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an…
The Hilbert-P\'{o}lya conjecture asserts that the imaginary parts of the nontrivial zeros of the Riemann zeta function (the Riemann zeros) are the eigenvalues of a self-adjoint operator (a quantum mechanical Hamiltonian, in the physical…
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic…
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and…
A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems.…
Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations…
We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases,…
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 the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
In a prevous paper (Phys. Rev. Lett. 96, 150403 (2006)) we have proposed a new way to generate an observable geometric phase on a quantum system by means of a completely incoherent phenomenon. The basic idea was to force the ground state of…
We show how geometric phases may be used to fully describe quantum systems, with or without gravity, by providing knowledge about the geometry and topology of its Hilbert space. We find a direct relation between geometric phases and von…
We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit…
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…
A large-scalable quantum computer model, whose qubits are represented by the subspace subtended by the ground state and the single exciton state on semiconductor quantum dots, is proposed. A universal set of quantum gates in this system may…
Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications, among which geometric quantum computation is a…
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled…
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…
When quantum mechanical qubits as elements of two dimensional complex Hilbert space are generalized to elements of even subalgebra of geometric algebra over three dimensional Euclidian space, geometrically formal complex plane becomes…
Quantum computing in terms of geometric phases, i.e. Berry or Aharonov-Anandan phases, is fault-tolerant to a certain degree. We examine its implementation based on Zeeman coupling with a rotating field and isotropic Heisenberg interaction,…
The second quantized approach to geometric phases is reviewed. The second quantization generally induces a hidden local (time-dependent) gauge symmetry. This gauge symmetry defines the parallel transport and holonomy, and thus it controls…