Related papers: Nodal free geometric phases: Concept and applicati…
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…
Quantum manipulation based on geometric phases provides a promising way towards robust quantum gates. However, in the current implementation of nonadiabatic geometric phases, operational and/or random errors tend to destruct the conditions…
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…
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…
An adiabatic cyclic evolution of control parameters of a quantum system ends up with a holonomic operation on the system, determined entirely by the geometry in the parameter space. The operation is given either by a simple phase factor (a…
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…
A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An…
Geometric phase is a promising element to induce high-fidelity and robust quantum operations due to its built-in noise-resilience feature. Unfortunately, its practical applications are usually circumscribed by requiring complex interactions…
The analysis of geometric phases is briefly reviewed by emphasizing various gauge symmetries involved. The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the…
We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…
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…
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting…
A single-loop scenario is proposed to realize nonadiabatic geometric quantum computation. Conventionally, a so-called multi-loop approach is used to remove the dynamical phase accumulated in the operation process for geometric quantum…
Nonadiabatic geometric quantum computation in decoherence-free subspaces has received increasing attention due to the merits of its high-speed implementation and robustness against both control errors and decoherence. However, all the…
We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of…
Geometric phases arise in a number of physical situations and often lead to systematic shifts in frequencies or phases measured in precision experiments. We describe, by working through some simple examples, a method to calculate geometric…
Time-dependent $\mathcal{PT}$-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of…
Geometric phase plays a fundamental role in quantum theory and accounts for wide phenomena ranging from the Aharanov-Bohm effect, the integer and fractional quantum hall effects, and topological phases of matter, including topological…
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…