880 research outputs found
Plasma Magnetohydrodynamics and Energy Conversion
Contains reports on three research projects.National Science Foundation under Grant G-9330U. S. Air Force (Aeronautical Systems Division) under Contract AF33(616)-7624 with the Aeronautical Accessories Laboratory, Wright-Patterson Air Force Base, Ohi
Eigenlevel statistics of the quantum adiabatic algorithm
We study the eigenlevel spectrum of quantum adiabatic algorithm for
3-satisfiability problem, focusing on single-solution instances. The properties
of the ground state and the associated gap, crucial for determining the running
time of the algorithm, are found to be far from the predictions of random
matrix theory. The distribution of gaps between the ground and the first
excited state shows an abundance of small gaps. Eigenstates from the central
part of the spectrum are, on the other hand, well described by random matrix
theory.Comment: 8 pages, 10 ps figure
Quantum Computation with Diatomic Bits in Optical Lattices
We propose a scheme for scalable and universal quantum computation using
diatomic bits with conditional dipole-dipole interaction, trapped within an
optical lattice. The qubit states are encoded by the scattering state and the
bound heteronuclear molecular state of two ultracold atoms per site. The
conditional dipole-dipole interaction appears between neighboring bits when
they both occupy the molecular state. The realization of a universal set of
quantum logic gates, which is composed of single-bit operations and a two-bit
controlled-NOT gate, is presented. The readout method is also discussed.Comment: 5 pages, 1 eps figure, accepted for publication in Phys. Rev.
Discrete-time quantum walks on one-dimensional lattices
In this paper, we study discrete-time quantum walks on one-dimensional
lattices. We find that the coherent dynamics depends on the initial states and
coin parameters. For infinite size of lattice, we derive an explicit expression
for the return probability, which shows scaling behavior
and does not depends on the initial states of the walk. In the long-time limit,
the probability distribution shows various patterns, depending on the initial
states, coin parameters and the lattice size. The average mixing time
closes to the limiting probability in linear (size of the
lattice) for large values of thresholds . Finally, we introduce
another kind of quantum walk on infinite or even-numbered size of lattices, and
show that the walk is equivalent to the traditional quantum walk with
symmetrical initial state and coin parameter.Comment: 17 pages research not
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
Fractional recurrence in discrete-time quantum walk
Quantum recurrence theorem holds for quantum systems with discrete energy
eigenvalues and fails to hold in general for systems with continuous energy. We
show that during quantum walk process dominated by interference of amplitude
corresponding to different paths fail to satisfy the complete quantum
recurrence theorem. Due to the revival of the fractional wave packet, a
fractional recurrence characterized using quantum P\'olya number can be seen.Comment: 10 pages, 11 figure : Accepted to appear in Central European Journal
of Physic
Valence bond solid formalism for d-level one-way quantum computation
The d-level or qudit one-way quantum computer (d1WQC) is described using the
valence bond solid formalism and the generalised Pauli group. This formalism
provides a transparent means of deriving measurement patterns for the
implementation of quantum gates in the computational model. We introduce a new
universal set of qudit gates and use it to give a constructive proof of the
universality of d1WQC. We characterise the set of gates that can be performed
in one parallel time step in this model.Comment: 26 pages, 9 figures. Published in Journal of Physics A: Mathematical
and Genera
Exact sampling from non-attractive distributions using summary states
Propp and Wilson's method of coupling from the past allows one to efficiently
generate exact samples from attractive statistical distributions (e.g., the
ferromagnetic Ising model). This method may be generalized to non-attractive
distributions by the use of summary states, as first described by Huber. Using
this method, we present exact samples from a frustrated antiferromagnetic
triangular Ising model and the antiferromagnetic q=3 Potts model. We discuss
the advantages and limitations of the method of summary states for practical
sampling, paying particular attention to the slowing down of the algorithm at
low temperature. In particular, we show that such a slowing down can occur in
the absence of a physical phase transition.Comment: 5 pages, 6 EPS figures, REVTeX; additional information at
http://wol.ra.phy.cam.ac.uk/mackay/exac
Quantum Reading Capacity
The readout of a classical memory can be modelled as a problem of quantum
channel discrimination, where a decoder retrieves information by distinguishing
the different quantum channels encoded in each cell of the memory [S.
Pirandola, Phys. Rev. Lett. 106, 090504 (2011)]. In the case of optical
memories, such as CDs and DVDs, this discrimination involves lossy bosonic
channels and can be remarkably boosted by the use of nonclassical light
(quantum reading). Here we generalize these concepts by extending the model of
memory from single-cell to multi-cell encoding. In general, information is
stored in a block of cells by using a channel-codeword, i.e., a sequence of
channels chosen according to a classical code. Correspondingly, the readout of
data is realized by a process of "parallel" channel discrimination, where the
entire block of cells is probed simultaneously and decoded via an optimal
collective measurement. In the limit of an infinite block we define the quantum
reading capacity of the memory, quantifying the maximum number of readable bits
per cell. This notion of capacity is nontrivial when we suitably constrain the
physical resources of the decoder. For optical memories (encoding bosonic
channels), such a constraint is energetic and corresponds to fixing the mean
total number of photons per cell. In this case, we are able to prove a
separation between the quantum reading capacity and the maximum information
rate achievable by classical transmitters, i.e., arbitrary classical mixtures
of coherent states. In fact, we can easily construct nonclassical transmitters
that are able to outperform any classical transmitter, thus showing that the
advantages of quantum reading persist in the optimal multi-cell scenario.Comment: REVTeX. 16 pages. 11 figure
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