Related papers: When geometric phases turn topological

Quantum circuits consisting of random unitary gates and subject to local measurements have been shown to undergo a phase transition, tuned by the rate of measurement, from a state with volume-law entanglement to an area-law state. From a…

Topological phases are characterised by a topological invariant that remains unchanged by deformations in the Hamiltonian. Materials exhibiting topological phases include topological insulators, superconductors exhibiting strong spin-orbit…

Geometric phases are robust to local noises and the nonadiabatic ones can reduce the evolution time, thus nonadiabatic geometric gates have strong robustness and can approach high fidelity. However, the advantage of geometric phase has not…

There is mounting theoretical evidence that black hole horizons induce decoherence on a quantum system, say a particle, put in a superposition of locations, with the decoherence functional, evaluated after closure of the superposition,…

The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle can be demonstrated in various ways that do not necessarily provide a geometry-independent description. For example, the position probability…

We map the geometric quantum potential on the nonlinear sigma model and use homotopy to estimate the lower bound of the geometric quantum potential. We investigate a catenoid (wormhole section), a two dimensional bilayer geometry smoothly…

Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…

The level crossing problem and associated geometric terms are neatly formulated by using the second quantization technique both in the operator and path integral formulations. The analysis of geometric phases is then reduced to the familiar…

The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…

We study the influence of geometry of quantum systems underlying space of states on its quantum many-body dynamics. We observe an interplay between dynamical and topological ingredients of quantum non-equilibrium dynamics revealed by the…

Ground states of spin lattices can serve as a resource for measurement-based quantum computation. Ideally, the ability to perform quantum gates via measurements on such states would be insensitive to small variations in the Hamiltonian.…

We consider the STIRAP process in a three-level atom. Viewed as a closed system, no geometric phase is acquired. But in the presence of spontaneous emission and/or collisional relaxation we show numerically that a non-vanishing, purely…

We find the geometric phase of a two-level system undergoing pure dephasing via interaction with an arbitrary environment, taking into account the effect of the initial system-environment correlations. We use our formalism to calculate the…

A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles…

We consider topological protection mechanisms in dissipative quantum systems in the presence of quenched disorder, with the intent to prolong coherence times of qubits. The physical setting is a network of qubits and dissipative cavities…

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…

The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…

We consider whether quantum coherence in the form of mutual entanglement between a pair of qubits is susceptible to decay that may be more rapid than the decay of the coherence of either qubit individually. An instance of potential…

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…

Geometric phases, which accompany the evolution of a quantum system and depend only on its trajectory in state space, are commonly studied in two-level systems. Here, however, we study the adiabatic geometric phase in a weakly anharmonic…