1,458 research outputs found
Bounds for mixing time of quantum walks on finite graphs
Several inequalities are proved for the mixing time of discrete-time quantum
walks on finite graphs. The mixing time is defined differently than in
Aharonov, Ambainis, Kempe and Vazirani (2001) and it is found that for
particular examples of walks on a cycle, a hypercube and a complete graph,
quantum walks provide no speed-up in mixing over the classical counterparts. In
addition, non-unitary quantum walks (i.e., walks with decoherence) are
considered and a criterion for their convergence to the unique stationary
distribution is derived.Comment: This is the journal version (except formatting); it is a significant
revision of the previous version, in particular, it contains a new result
about the convergence of quantum walks with decoherence; 16 page
Fast Universal Quantum Computation with Railroad-switch Local Hamiltonians
We present two universal models of quantum computation with a
time-independent, frustration-free Hamiltonian. The first construction uses
3-local (qubit) projectors, and the second one requires only 2-local
qubit-qutrit projectors. We build on Feynman's Hamiltonian computer idea and
use a railroad-switch type clock register. The resources required to simulate a
quantum circuit with L gates in this model are O(L) small-dimensional quantum
systems (qubits or qutrits), a time-independent Hamiltonian composed of O(L)
local, constant norm, projector terms, the possibility to prepare computational
basis product states, a running time O(L log^2 L), and the possibility to
measure a few qubits in the computational basis. Our models also give a
simplified proof of the universality of 3-local Adiabatic Quantum Computation.Comment: Added references to work by de Falco et al., and realized that
Feynman's '85 paper already contained the idea of a switch in i
Few-body spin couplings and their implications for universal quantum computation
Electron spins in semiconductor quantum dots are promising candidates for the
experimental realization of solid-state qubits. We analyze the dynamics of a
system of three qubits arranged in a linear geometry and a system of four
qubits arranged in a square geometry. Calculations are performed for several
quantum dot confining potentials. In the three-qubit case, three-body effects
are identified that have an important quantitative influence upon quantum
computation. In the four-qubit case, the full Hamiltonian is found to include
both three-body and four-body interactions that significantly influence the
dynamics in physically relevant parameter regimes. We consider the implications
of these results for the encoded universality paradigm applied to the
four-electron qubit code; in particular, we consider what is required to
circumvent the four-body effects in an encoded system (four spins per encoded
qubit) by the appropriate tuning of experimental parameters.Comment: 1st version: 33 pages, 25 figures. Described at APS March Meeting in
2004 (P36.010) and 2005 (B17.00009). Most figures made uglier here to reduce
file size. 2nd version: 19 pages, 9 figures. Much mathematical detail chopped
away after hearing from journal referee; a few typos correcte
Universal 2-local Hamiltonian Quantum Computing
We present a Hamiltonian quantum computation scheme universal for quantum
computation (BQP). Our Hamiltonian is a sum of a polynomial number (in the
number of gates L in the quantum circuit) of time-independent, constant-norm,
2-local qubit-qubit interaction terms. Furthermore, each qubit in the system
interacts only with a constant number of other qubits. The computer runs in
three steps - starts in a simple initial product-state, evolves it for time of
order L^2 (up to logarithmic factors) and wraps up with a two-qubit
measurement. Our model differs from the previous universal 2-local Hamiltonian
constructions in that it does not use perturbation gadgets, does not need large
energy penalties in the Hamiltonian and does not need to run slowly to ensure
adiabatic evolution.Comment: recomputed the necessary number of interactions, new geometric
layout, added reference
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Rheological and Mechanical Considerations for Photovoltaic Encapsulants
Photovoltaic (pv) devices are encapsulated in polymeric materials not only for corrosion protection, but also for mechanical support. Even though ethylene-vinyl acetate (EVA) suffers from having both glass and melting phase transitions at temperatures experienced under environmental exposure, its low cost and good optical transmission made EVA the most commonly used material for PV modules. These transitions, however, cause EVA to embrittle at low temperatures (~ -15 deg C) and to be very soft at high temperatures (>40 deg C). From mechanical considerations, one would prefer a material that was relatively unchanged under a wide temperature range. This would produce a more predictable and reliable package. These concerns are likely to become more important as silicon based cells are made thinner
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Accelerated UV Test Methods for Encapsulants of Photovoltaic Modules: Preprint
This paper asserts that materials used for PV encapsulation must be evaluated for their ability to transmit light and to maintain mechanical integrity for extended periods of time under long term UV exposure
Node Sampling using Random Centrifugal Walks
Sampling a network with a given probability distribution has been identified
as a useful operation. In this paper we propose distributed algorithms for
sampling networks, so that nodes are selected by a special node, called the
\emph{source}, with a given probability distribution. All these algorithms are
based on a new class of random walks, that we call Random Centrifugal Walks
(RCW). A RCW is a random walk that starts at the source and always moves away
from it.
Firstly, an algorithm to sample any connected network using RCW is proposed.
The algorithm assumes that each node has a weight, so that the sampling process
must select a node with a probability proportional to its weight. This
algorithm requires a preprocessing phase before the sampling of nodes. In
particular, a minimum diameter spanning tree (MDST) is created in the network,
and then nodes' weights are efficiently aggregated using the tree. The good
news are that the preprocessing is done only once, regardless of the number of
sources and the number of samples taken from the network. After that, every
sample is done with a RCW whose length is bounded by the network diameter.
Secondly, RCW algorithms that do not require preprocessing are proposed for
grids and networks with regular concentric connectivity, for the case when the
probability of selecting a node is a function of its distance to the source.
The key features of the RCW algorithms (unlike previous Markovian approaches)
are that (1) they do not need to warm-up (stabilize), (2) the sampling always
finishes in a number of hops bounded by the network diameter, and (3) it
selects a node with the exact probability distribution
Encoded Universality for Generalized Anisotropic Exchange Hamiltonians
We derive an encoded universality representation for a generalized
anisotropic exchange Hamiltonian that contains cross-product terms in addition
to the usual two-particle exchange terms. The recently developed algebraic
approach is used to show that the minimal universality-generating encodings of
one logical qubit are based on three physical qubits. We show how to generate
both single- and two-qubit operations on the logical qubits, using suitably
timed conjugating operations derived from analysis of the commutator algebra.
The timing of the operations is seen to be crucial in allowing simplification
of the gate sequences for the generalized Hamiltonian to forms similar to that
derived previously for the symmetric (XY) anisotropic exchange Hamiltonian. The
total number of operations needed for a controlled-Z gate up to local
transformations is five. A scalable architecture is proposed.Comment: 11 pages, 4 figure
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Accelerated UV Test Methods for Encapsulants of Photovoltaic Modules
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