7,487 research outputs found
Quantum algorithm for the Boolean hidden shift problem
The hidden shift problem is a natural place to look for new separations
between classical and quantum models of computation. One advantage of this
problem is its flexibility, since it can be defined for a whole range of
functions and a whole range of underlying groups. In a way, this distinguishes
it from the hidden subgroup problem where more stringent requirements about the
existence of a periodic subgroup have to be made. And yet, the hidden shift
problem proves to be rich enough to capture interesting features of problems of
algebraic, geometric, and combinatorial flavor. We present a quantum algorithm
to identify the hidden shift for any Boolean function. Using Fourier analysis
for Boolean functions we relate the time and query complexity of the algorithm
to an intrinsic property of the function, namely its minimum influence. We show
that for randomly chosen functions the time complexity of the algorithm is
polynomial. Based on this we show an average case exponential separation
between classical and quantum time complexity. A perhaps interesting aspect of
this work is that, while the extremal case of the Boolean hidden shift problem
over so-called bent functions can be reduced to a hidden subgroup problem over
an abelian group, the more general case studied here does not seem to allow
such a reduction.Comment: 10 pages, 1 figur
Adiabatic quantum computation and quantum phase transitions
We analyze the ground state entanglement in a quantum adiabatic evolution
algorithm designed to solve the NP-complete Exact Cover problem. The entropy of
entanglement seems to obey linear and universal scaling at the point where the
mass gap becomes small, suggesting that the system passes near a quantum phase
transition. Such a large scaling of entanglement suggests that the effective
connectivity of the system diverges as the number of qubits goes to infinity
and that this algorithm cannot be efficiently simulated by classical means. On
the other hand, entanglement in Grover's algorithm is bounded by a constant.Comment: 5 pages, 4 figures, accepted for publication in PR
Classical and Quantum Annealing in the Median of Three Satisfiability
We determine the classical and quantum complexities of a specific ensemble of
three-satisfiability problems with a unique satisfying assignment for up to
N=100 and N=80 variables, respectively. In the classical limit we employ
generalized ensemble techniques and measure the time that a Markovian Monte
Carlo process spends in searching classical ground states. In the quantum limit
we determine the maximum finite correlation length along a quantum adiabatic
trajectory determined by the linear sweep of the adiabatic control parameter in
the Hamiltonian composed of the problem Hamiltonian and the constant transverse
field Hamiltonian. In the median of our ensemble both complexities diverge
exponentially with the number of variables. Hence, standard, conventional
adiabatic quantum computation fails to reduce the computational complexity to
polynomial. Moreover, the growth-rate constant in the quantum limit is 3.8
times as large as the one in the classical limit, making classical fluctuations
more beneficial than quantum fluctuations in ground-state searches
Universality of Entanglement and Quantum Computation Complexity
We study the universality of scaling of entanglement in Shor's factoring
algorithm and in adiabatic quantum algorithms across a quantum phase transition
for both the NP-complete Exact Cover problem as well as the Grover's problem.
The analytic result for Shor's algorithm shows a linear scaling of the entropy
in terms of the number of qubits, therefore difficulting the possibility of an
efficient classical simulation protocol. A similar result is obtained
numerically for the quantum adiabatic evolution Exact Cover algorithm, which
also shows universality of the quantum phase transition the system evolves
nearby. On the other hand, entanglement in Grover's adiabatic algorithm remains
a bounded quantity even at the critical point. A classification of scaling of
entanglement appears as a natural grading of the computational complexity of
simulating quantum phase transitions.Comment: 30 pages, 17 figures, accepted for publication in PR
The relation between Hardy's non-locality and violation of Bell inequality
We give a analytic quantitative relation between Hardy's non-locality and
Bell operator. We find that Hardy's non-locality is a sufficient condition for
violation of Bell inequality, the upper bound of Hardy's non-locality allowed
by information causality just correspond to Tsirelson bound of Bell inequality,
and the upper bound of Hardy's non-locality allowed by the principle of
no-signaling just correspond to the algebraic maximum of Bell operator. Then we
study the Cabello's argument of Hardy's non-locality (a generalization of
Hardy's argument) and find a similar relation between it and violation of Bell
inequality. Finally, we give a simple derivation of the bound of Hardy's
non-locality under the constraint of information causality with the aid of
above derived relation between Hardy's non-locality and Bell operator, this
bound is the main result of a recent work of Ahanj \emph{et al.} [Phys. Rev. A
{\bf81}, 032103(2010)].Comment: 4 pages, no figure, minor chang
Strong nonlocality: A trade-off between states and measurements
Measurements on entangled quantum states can produce outcomes that are
nonlocally correlated. But according to Tsirelson's theorem, there is a
quantitative limit on quantum nonlocality. It is interesting to explore what
would happen if Tsirelson's bound were violated. To this end, we consider a
model that allows arbitrary nonlocal correlations, colloquially referred to as
"box world". We show that while box world allows more highly entangled states
than quantum theory, measurements in box world are rather limited. As a
consequence there is no entanglement swapping, teleportation or dense coding.Comment: 11 pages, 2 figures, very minor change
On the adiabatic condition and the quantum hitting time of Markov chains
We present an adiabatic quantum algorithm for the abstract problem of
searching marked vertices in a graph, or spatial search. Given a random walk
(or Markov chain) on a graph with a set of unknown marked vertices, one can
define a related absorbing walk where outgoing transitions from marked
vertices are replaced by self-loops. We build a Hamiltonian from the
interpolated Markov chain and use it in an adiabatic quantum
algorithm to drive an initial superposition over all vertices to a
superposition over marked vertices. The adiabatic condition implies that for
any reversible Markov chain and any set of marked vertices, the running time of
the adiabatic algorithm is given by the square root of the classical hitting
time. This algorithm therefore demonstrates a novel connection between the
adiabatic condition and the classical notion of hitting time of a random walk.
It also significantly extends the scope of previous quantum algorithms for this
problem, which could only obtain a full quadratic speed-up for state-transitive
reversible Markov chains with a unique marked vertex.Comment: 22 page
Grid tool integration within the eMinerals Project
In this article we describe the eMinerals mini grid, which is now running in production mode. Thisis an integration of both compute and data components, the former build upon Condor, PBS and thefunctionality of Globus v2, and the latter being based on the combined use of the Storage ResourceBroker and the CCLRC data portal. We describe how we have integrated the middleware components,and the different facilities provided to the users for submitting jobs within such an environment. We willalso describe additional functionality we found it necessary to provide ourselves
Statistical Mechanics of the Quantum K-Satisfiability problem
We study the quantum version of the random -Satisfiability problem in the
presence of the external magnetic field applied in the transverse
direction. We derive the replica-symmetric free energy functional within static
approximation and the saddle-point equation for the order parameter: the
distribution of functions of magnetizations. The order parameter is
interpreted as the histogram of probability distributions of individual
magnetizations. In the limit of zero temperature and small transverse fields,
to leading order in magnetizations become relevant in
addition to purely classical values of . Self-consistency
equations for the order parameter are solved numerically using Quasi Monte
Carlo method for K=3. It is shown that for an arbitrarily small
quantum fluctuations destroy the phase transition present in the classical
limit , replacing it with a smooth crossover transition. The
implications of this result with respect to the expected performance of quantum
optimization algorithms via adiabatic evolution are discussed. The
replica-symmetric solution of the classical random -Satisfiability problem
is briefly revisited. It is shown that the phase transition at T=0 predicted by
the replica-symmetric theory is of continuous type with atypical critical
exponents.Comment: 35 pages, 23 figures; changed abstract, improved discussion in the
introduction, added references, corrected typo
Mg/Ti multilayers: structural, optical and hydrogen absorption properties
Mg-Ti alloys have uncommon optical and hydrogen absorbing properties,
originating from a "spinodal-like" microstructure with a small degree of
chemical short-range order in the atoms distribution. In the present study we
artificially engineer short-range order by depositing Pd-capped Mg/Ti
multilayers with different periodicities and characterize them both
structurally and optically. Notwithstanding the large lattice parameter
mismatch between Mg and Ti, the as-deposited metallic multilayers show good
structural coherence. Upon exposure to H2 gas a two-step hydrogenation process
occurs, with the Ti layers forming the hydride before Mg. From in-situ
measurements of the bilayer thickness L at different hydrogen pressures, we
observe large out-of-plane expansions of the Mg and Ti layers upon
hydrogenation, indicating strong plastic deformations in the films and a
consequent shortening of the coherence length. Upon unloading at room
temperature in air, hydrogen atoms remain trapped in the Ti layers due to
kinetic constraints. Such loading/unloading sequence can be explained in terms
of the different thermodynamic properties of hydrogen in Mg and Ti, as shown by
diffusion calculations on a model multilayered systems. Absorption isotherms
measured by hydrogenography can be interpreted as a result of the elastic
clamping arising from strongly bonded Mg/Pd and broken Mg/Ti interfaces
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