89 research outputs found
Limit theorem for a time-dependent coined quantum walk on the line
We study time-dependent discrete-time quantum walks on the one-dimensional
lattice. We compute the limit distribution of a two-period quantum walk defined
by two orthogonal matrices. For the symmetric case, the distribution is
determined by one of two matrices. Moreover, limit theorems for two special
cases are presented
Controlled-NOT logic gate for phase qubits based on conditional spectroscopy
A controlled-NOT logic gate based on conditional spectroscopy has been
demonstrated recently for a pair of superconducting flux qubits [Plantenberg et
al., Nature 447, 836 (2007)]. Here we study the fidelity of this type of gate
applied to a phase qubit coupled to a resonator (or a pair of capacitively
coupled phase qubits). Our results show that an intrinsic fidelity of more than
99% is achievable in 45ns.Comment: 5 pages, 5 figures, To appear in Quantum Inf. Pro
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
On the relationship between continuous- and discrete-time quantum walk
Quantum walk is one of the main tools for quantum algorithms. Defined by
analogy to classical random walk, a quantum walk is a time-homogeneous quantum
process on a graph. Both random and quantum walks can be defined either in
continuous or discrete time. But whereas a continuous-time random walk can be
obtained as the limit of a sequence of discrete-time random walks, the two
types of quantum walk appear fundamentally different, owing to the need for
extra degrees of freedom in the discrete-time case.
In this article, I describe a precise correspondence between continuous- and
discrete-time quantum walks on arbitrary graphs. Using this correspondence, I
show that continuous-time quantum walk can be obtained as an appropriate limit
of discrete-time quantum walks. The correspondence also leads to a new
technique for simulating Hamiltonian dynamics, giving efficient simulations
even in cases where the Hamiltonian is not sparse. The complexity of the
simulation is linear in the total evolution time, an improvement over
simulations based on high-order approximations of the Lie product formula. As
applications, I describe a continuous-time quantum walk algorithm for element
distinctness and show how to optimally simulate continuous-time query
algorithms of a certain form in the conventional quantum query model. Finally,
I discuss limitations of the method for simulating Hamiltonians with negative
matrix elements, and present two problems that motivate attempting to
circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian
oracles; v3: published version, with improved analysis of phase estimatio
Quantum walks: a comprehensive review
Quantum walks, the quantum mechanical counterpart of classical random walks,
is an advanced tool for building quantum algorithms that has been recently
shown to constitute a universal model of quantum computation. Quantum walks is
now a solid field of research of quantum computation full of exciting open
problems for physicists, computer scientists, mathematicians and engineers.
In this paper we review theoretical advances on the foundations of both
discrete- and continuous-time quantum walks, together with the role that
randomness plays in quantum walks, the connections between the mathematical
models of coined discrete quantum walks and continuous quantum walks, the
quantumness of quantum walks, a summary of papers published on discrete quantum
walks and entanglement as well as a succinct review of experimental proposals
and realizations of discrete-time quantum walks. Furthermore, we have reviewed
several algorithms based on both discrete- and continuous-time quantum walks as
well as a most important result: the computational universality of both
continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing
Journa
A Bayesian analysis of pentaquark signals from CLAS data
We examine the results of two measurements by the CLAS collaboration, one of
which claimed evidence for a pentaquark, whilst the other found no
such evidence. The unique feature of these two experiments was that they were
performed with the same experimental setup. Using a Bayesian analysis we find
that the results of the two experiments are in fact compatible with each other,
but that the first measurement did not contain sufficient information to
determine unambiguously the existence of a . Further, we suggest a
means by which the existence of a new candidate particle can be tested in a
rigorous manner.Comment: 5 pages, 3 figure
Electron Scattering From High-Momentum Neutrons in Deuterium
We report results from an experiment measuring the semi-inclusive reaction
where the proton is moving at a large angle relative to the
momentum transfer. If we assume that the proton was a spectator to the reaction
taking place on the neutron in deuterium, the initial state of that neutron can
be inferred. This method, known as spectator tagging, can be used to study
electron scattering from high-momentum (off-shell) neutrons in deuterium. The
data were taken with a 5.765 GeV electron beam on a deuterium target in
Jefferson Laboratory's Hall B, using the CLAS detector. A reduced cross section
was extracted for different values of final-state missing mass ,
backward proton momentum and momentum transfer . The data
are compared to a simple PWIA spectator model. A strong enhancement in the data
observed at transverse kinematics is not reproduced by the PWIA model. This
enhancement can likely be associated with the contribution of final state
interactions (FSI) that were not incorporated into the model. A ``bound neutron
structure function'' was extracted as a function of and
the scaling variable at extreme backward kinematics, where effects of
FSI appear to be smaller. For MeV/c, where the neutron is far
off-shell, the model overestimates the value of in the region of
between 0.25 and 0.6. A modification of the bound neutron structure
function is one of possible effects that can cause the observed deviation.Comment: 33 pages RevTeX, 9 figures, to be submitted to Phys. Rev. C. Fixed 1
Referenc
Complete measurement of three-body photodisintegration of 3He for photon energies between 0.35 and 1.55 GeV
The three-body photodisintegration of 3He has been measured with the CLAS
detector at Jefferson Lab, using tagged photons of energies between 0.35 GeV
and 1.55 GeV. The large acceptance of the spectrometer allowed us for the first
time to cover a wide momentum and angular range for the two outgoing protons.
Three kinematic regions dominated by either two- or three-body contributions
have been distinguished and analyzed. The measured cross sections have been
compared with results of a theoretical model, which, in certain kinematic
ranges, have been found to be in reasonable agreement with the data.Comment: 22 pages, 25 eps figures, 2 tables, submitted to PRC. Modifications:
removed 2 figures, improvements on others, a few minor modifications to the
tex
eta-prime photoproduction on the proton for photon energies from 1.527 to 2.227 GeV
Differential cross sections for the reaction gamma p -> eta-prime p have been
measured with the CLAS spectrometer and a tagged photon beam with energies from
1.527 to 2.227 GeV. The results reported here possess much greater accuracy
than previous measurements. Analyses of these data indicate for the first time
the coupling of the etaprime N channel to both the S_11(1535) and P_11(1710)
resonances, known to couple strongly to the eta N channel in photoproduction on
the proton, and the importance of j=3/2 resonances in the process.Comment: 6 pages, 3 figure
Measurement of the Deuteron Structure Function F2 in the Resonance Region and Evaluation of Its Moments
Inclusive electron scattering off the deuteron has been measured to extract
the deuteron structure function F2 with the CEBAF Large Acceptance Spectrometer
(CLAS) at the Thomas Jefferson National Accelerator Facility. The measurement
covers the entire resonance region from the quasi-elastic peak up to the
invariant mass of the final-state hadronic system W~2.7 GeV with four-momentum
transfers Q2 from 0.4 to 6 (GeV/c)^2. These data are complementary to previous
measurements of the proton structure function F2 and cover a similar
two-dimensional region of Q2 and Bjorken variable x. Determination of the
deuteron F2 over a large x interval including the quasi-elastic peak as a
function of Q2, together with the other world data, permit a direct evaluation
of the structure function moments for the first time. By fitting the Q2
evolution of these moments with an OPE-based twist expansion we have obtained a
separation of the leading twist and higher twist terms. The observed Q2
behaviour of the higher twist contribution suggests a partial cancellation of
different higher twists entering into the expansion with opposite signs. This
cancellation, found also in the proton moments, is a manifestation of the
"duality" phenomenon in the F2 structure function
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