Related papers: Observable-geometric phases and quantum computatio…
The possibility of realization of quantum gates by means of the non-adiabatic geometric phase is considered. It is shown that the non-adiabatic phase can be used for quantum gates realization as well as the adiabatic one.
The adiabatic theorem states that when the time evolution of the Hamiltonian is "infinitely slow", a system, when started in the ground state, remains in the instantaneous ground state at all times. This, however, does not mean that the…
The existence of Hopf fibrations S^{2N+1}/S^1 = CP^N and S^{4K+3}/S^3 = HP^K allows us to treat the Hilbert space of generic finite-dimensional quantum systems as the total bundle space with respectively $U(1)$ and $SU(2)$ fibers and…
The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation…
In quantum mechanics, geometry has been demonstrated as a useful tool for inferring non-classical behaviors and exotic properties of quantum systems. One standard approach to illustrate the geometry of quantum systems is to project the…
A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define 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…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
We propose a novel proposal for geometric quantum gates using three- or two-level systems, in which a controllable variable, the detuning between the driving frequency and the atomic energy spacing, is introduced to realize geometric…
The experimental realisation of the basic constituents of quantum information processing devices, namely fault-tolerant quantum logic gates, requires conditional quantum dynamics, in which one subsystem undergoes a coherent evolution that…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
Unitary evolution in PT-symmetric quantum mechanics with a time-dependent metric is found to yield a new class of adiabatic processes. As an explicit example, a Berry-like phase associated with a PT-symmetric two-level system is derived and…
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 adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would…
We develop the widest possible generalisation of the well-known connection between quantum mechanical Bargmann invariants and geometric phases. The key notion is that of null phase curves in quantum mechanical ray and Hilbert spaces.…
Nonadiabatic geometric phases are only dependent on the evolution path of a quantum system but independent of the evolution details, and therefore quantum computation based on nonadiabatic geometric phases is robust against control errors.…
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…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…