Related papers: Holonomy in Quantum Information Geometry
The holonomic approach to controlling (nitrogen-vacancy) NV-center qubits provides an elegant way of theoretically devising universal quantum gates that operate on qubits via calculable microwave pulses. There is, however, a lack of…
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…
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…
Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are…
We present a review of theories of states of quantum matter without quasiparticle excitations. Solvable examples of such states are provided through a holographic duality with gravitational theories in an emergent spatial dimension. We…
Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus…
Non-Abelian geometric phases can be generated and detected in certain superconducting nanocircuits. Here we consider an example where the holonomies are related to the adiabatic charge dynamics of the Josephson network. We demonstrate that…
The finite-curvature phase diagram of IHQCD, a bottom-up holographic model for large $N_c$ non-supersymmetric YM$_4$, is investigated. This holographic theory belongs to a class of Einstein-Dilaton theories that exhibit no scaling in the…
The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous…
We investigate a class of cyclic evolutions for %the cyclic evolution of driven two-level quantum systems (effective spin-1/2) with a particular focus on the geometric characteristics of the driving and their specific imprints on the…
We consider arbitrary mixed state in unitary evolution and provide a comprehensive description of corresponding geometric phase in which two different points of view prevailing currently can be unified. Introducing an ancillary system and…
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. $1/\hbar$…
This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques…
All the geometric phases, adiabatic and non-adiabatic, are formulated in a unified manner in the second quantized path integral formulation. The exact hidden local symmetry inherent in the Schr\"{o}dinger equation defines the holonomy. All…
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…
The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…
Geometric phases have been shown to be feasible in implementing quantum gates to perform quantum information processing. For all the realistic applications, the environmental influence on the geometric phase and decoherence such as memory…
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…
Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal…