106 research outputs found
Full-revivals in 2-D Quantum Walks
Recurrence of a random walk is described by the Polya number. For quantum
walks, recurrence is understood as the return of the walker to the origin,
rather than the full-revival of its quantum state. Localization for two
dimensional quantum walks is known to exist in the sense of non-vanishing
probability distribution in the asymptotic limit. We show on the example of the
2-D Grover walk that one can exploit the effect of localization to construct
stationary solutions. Moreover, we find full-revivals of a quantum state with a
period of two steps. We prove that there cannot be longer cycles for a
four-state quantum walk. Stationary states and revivals result from
interference which has no counterpart in classical random walks
Optimizing the discrete time quantum walk using a SU(2) coin
We present a generalized version of the discrete time quantum walk, using the
SU(2) operation as the quantum coin. By varying the coin parameters, the
quantum walk can be optimized for maximum variance subject to the functional
form and the probability distribution in the position
space can be biased. We also discuss the variation in measurement entropy with
the variation of the parameters in the SU(2) coin. Exploiting this we show how
quantum walk can be optimized for improving mixing time in an -cycle and for
quantum walk search.Comment: 6 pages, 6 figure
Decoherence can be useful in quantum walks
We present a study of the effects of decoherence in the operation of a
discrete quantum walk on a line, cycle and hypercube. We find high sensitivity
to decoherence, increasing with the number of steps in the walk, as the
particle is becoming more delocalised with each step. However, the effect of a
small amount of decoherence is to enhance the properties of the quantum walk
that are desirable for the development of quantum algorithms. Specifically, we
observe a highly uniform distribution on the line, a very fast mixing time on
the cycle, and more reliable hitting times across the hypercube.Comment: (Imperial College London) 6 (+epsilon) pages, 6 embedded eps figures,
RevTex4. v2 minor changes to correct typos and refs, submitted version. v3
expanded into article format, extra figure, updated refs, Note on "glued
trees" adde
Discrete antiferromagnetic spin-wave excitations in the giant ferric wheel Fe18
The low-temperature elementary spin excitations in the AFM molecular wheel
Fe18 were studied experimentally by inelastic neutron scattering and
theoretically by modern numerical methods, such as dynamical density matrix
renormalization group or quantum Monte Carlo techniques, and analytical
spin-wave theory calculations. Fe18 involves eighteen spin-5/2 Fe(III) ions
with a Hilbert space dimension of 10^14, constituting a physical system that is
situated in a region between microscopic and macroscopic. The combined
experimental and theoretical approach allowed us to characterize and discuss
the magnetic properties of Fe18 in great detail. It is demonstrated that
physical concepts such as the rotational-band or L&E-band concepts developed
for smaller rings are still applicable. In particular, the higher-lying
low-temperature elementary spin excitations in Fe18 or AFM wheels in general
are of discrete antiferromagnetic spin-wave character.Comment: 16 pages, 10 figure
Quantum diffusion on a cyclic one dimensional lattice
The quantum diffusion of a particle in an initially localized state on a
cyclic lattice with N sites is studied. Diffusion and reconstruction time are
calculated. Strong differences are found for even or odd number of sites and
the limit N->infinit is studied. The predictions of the model could be tested
with micro - and nanotechnology devices.Comment: 17 pages, 5 figure
State permutations from manipulation of near level-crossings
We discuss some systematic methods for implementing state manipulations in
systems formally similar to chains of a few spins with nearest-neighbor
interactions, arranged such that there are strong and weak scales of coupling
links. States are permuted by means of bias potentials applied to a few
selected sites. This generic structure is then related to an atoms-in-a-cavity
model that has been proposed in the literature as a way of achieving a
decoherence free subspace. A new method using adiabatically varying laser
detuning to implement a CNOT gate in this model is proposed.Comment: 6 pages, 5 figures. Substantial revision and extension of the
introduction and the atoms-in-a-cavity section
Continuous deformations of the Grover walk preserving localization
The three-state Grover walk on a line exhibits the localization effect
characterized by a non-vanishing probability of the particle to stay at the
origin. We present two continuous deformations of the Grover walk which
preserve its localization nature. The resulting quantum walks differ in the
rate at which they spread through the lattice. The velocities of the left and
right-traveling probability peaks are given by the maximum of the group
velocity. We find the explicit form of peak velocities in dependence on the
coin parameter. Our results show that localization of the quantum walk is not a
singular property of an isolated coin operator but can be found for entire
families of coins
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