71 research outputs found
Perfect initialization of a quantum computer of neutral atoms in an optical lattice of large lattice constant
We propose a scheme for the initialization of a quantum computer based on
neutral atoms trapped in an optical lattice with large lattice constant. Our
focus is the development of a compacting scheme to prepare a perfect optical
lattice of simple orthorhombic structure with unit occupancy. Compacting is
accomplished by sequential application of two types of operations: a flip
operator that changes the internal state of the atoms, and a shift operator
that moves them along the lattice principal axis. We propose physical
mechanisms for realization of these operations and we study the effects of
motional heating of the atoms. We carry out an analysis of the complexity of
the compacting scheme and show that it scales linearly with the number of
lattice sites per row of the lattice, thus showing good scaling behavior with
the size of the quantum computer.Comment: 18 page
Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach
In this paper, we study the -forest problem in the model of resource
augmentation. In the -forest problem, given an edge-weighted graph ,
a parameter , and a set of demand pairs , the
objective is to construct a minimum-cost subgraph that connects at least
demands. The problem is hard to approximate---the best-known approximation
ratio is . Furthermore, -forest is as hard to
approximate as the notoriously-hard densest -subgraph problem.
While the -forest problem is hard to approximate in the worst-case, we
show that with the use of resource augmentation, we can efficiently approximate
it up to a constant factor.
First, we restate the problem in terms of the number of demands that are {\em
not} connected. In particular, the objective of the -forest problem can be
viewed as to remove at most demands and find a minimum-cost subgraph that
connects the remaining demands. We use this perspective of the problem to
explain the performance of our algorithm (in terms of the augmentation) in a
more intuitive way.
Specifically, we present a polynomial-time algorithm for the -forest
problem that, for every , removes at most demands and has
cost no more than times the cost of an optimal algorithm
that removes at most demands
Recurrence of biased quantum walks on a line
The Polya number of a classical random walk on a regular lattice is known to
depend solely on the dimension of the lattice. For one and two dimensions it
equals one, meaning unit probability to return to the origin. This result is
extremely sensitive to the directional symmetry, any deviation from the equal
probability to travel in each direction results in a change of the character of
the walk from recurrent to transient. Applying our definition of the Polya
number to quantum walks on a line we show that the recurrence character of
quantum walks is more stable against bias. We determine the range of parameters
for which biased quantum walks remain recurrent. We find that there exist
genuine biased quantum walks which are recurrent.Comment: Journal reference added, minor corrections in the tex
The effect of large-decoherence on mixing-time in Continuous-time quantum walks on long-range interacting cycles
In this paper, we consider decoherence in continuous-time quantum walks on
long-range interacting cycles (LRICs), which are the extensions of the cycle
graphs. For this purpose, we use Gurvitz's model and assume that every node is
monitored by the corresponding point contact induced the decoherence process.
Then, we focus on large rates of decoherence and calculate the probability
distribution analytically and obtain the lower and upper bounds of the mixing
time. Our results prove that the mixing time is proportional to the rate of
decoherence and the inverse of the distance parameter (\emph{m}) squared.
This shows that the mixing time decreases with increasing the range of
interaction. Also, what we obtain for \emph{m}=0 is in agreement with
Fedichkin, Solenov and Tamon's results \cite{FST} for cycle, and see that the
mixing time of CTQWs on cycle improves with adding interacting edges.Comment: 16 Pages, 2 Figure
Evanescence in Coined Quantum Walks
In this paper we complete the analysis begun by two of the authors in a
previous work on the discrete quantum walk on the line [J. Phys. A 36:8775-8795
(2003) quant-ph/0303105 ]. We obtain uniformly convergent asymptotics for the
"exponential decay'' regions at the leading edges of the main peaks in the
Schr{\"o}dinger (or wave-mechanics) picture. This calculation required us to
generalise the method of stationary phase and we describe this extension in
some detail, including self-contained proofs of all the technical lemmas
required. We also rigorously establish the exact Feynman equivalence between
the path-integral and wave-mechanics representations for this system using some
techniques from the theory of special functions. Taken together with the
previous work, we can now prove every theorem by both routes.Comment: 32 pages AMS LaTeX, 5 figures in .eps format. Rewritten in response
to referee comments, including some additional references. v3: typos fixed in
equations (131), (133) and (134). v5: published versio
On the Quantum Computational Complexity of the Ising Spin Glass Partition Function and of Knot Invariants
It is shown that the canonical problem of classical statistical
thermodynamics, the computation of the partition function, is in the case of
+/-J Ising spin glasses a particular instance of certain simple sums known as
quadratically signed weight enumerators (QWGTs). On the other hand it is known
that quantum computing is polynomially equivalent to classical probabilistic
computing with an oracle for estimating QWGTs. This suggests a connection
between the partition function estimation problem for spin glasses and quantum
computation. This connection extends to knots and graph theory via the
equivalence of the Kauffman polynomial and the partition function for the Potts
model.Comment: 8 pages, incl. 2 figures. v2: Substantially rewritte
Locality for quantum systems on graphs depends on the number field
Adapting a definition of Aaronson and Ambainis [Theory Comput. 1 (2005),
47--79], we call a quantum dynamics on a digraph "saturated Z-local" if the
nonzero transition amplitudes specifying the unitary evolution are in exact
correspondence with the directed edges (including loops) of the digraph. This
idea appears recurrently in a variety of contexts including angular momentum,
quantum chaos, and combinatorial matrix theory. Complete characterization of
the digraph properties that allow such a process to exist is a long-standing
open question that can also be formulated in terms of minimum rank problems. We
prove that saturated Z-local dynamics involving complex amplitudes occur on a
proper superset of the digraphs that allow restriction to the real numbers or,
even further, the rationals. Consequently, among these fields, complex numbers
guarantee the largest possible choice of topologies supporting a discrete
quantum evolution. A similar construction separates complex numbers from the
skew field of quaternions. The result proposes a concrete ground for
distinguishing between complex and quaternionic quantum mechanics.Comment: 9 page
Quantum key distribution based on orthogonal states allows secure quantum bit commitment
For more than a decade, it was believed that unconditionally secure quantum
bit commitment (QBC) is impossible. But basing on a previously proposed quantum
key distribution scheme using orthogonal states, here we build a QBC protocol
in which the density matrices of the quantum states encoding the commitment do
not satisfy a crucial condition on which the no-go proofs of QBC are based.
Thus the no-go proofs could be evaded. Our protocol is fault-tolerant and very
feasible with currently available technology. It reopens the venue for other
"post-cold-war" multi-party cryptographic protocols, e.g., quantum bit string
commitment and quantum strong coin tossing with an arbitrarily small bias. This
result also has a strong influence on the Clifton-Bub-Halvorson theorem which
suggests that quantum theory could be characterized in terms of
information-theoretic constraints.Comment: Published version plus an appendix showing how to defeat the
counterfactual attack, more references [76,77,90,118-120] cited, and other
minor change
General immunity and superadditivity of two-way Gaussian quantum cryptography
We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achieved by exploiting the random on/off switching of the two-way quantum communication. This allows the parties to choose the appropriate communication instances to prepare the key, accordingly to the tomography of the quantum channel. The random opening and closing of the circuit represents, in fact, an additional degree of freedom allowing the parties to convert, a posteriori, the two-mode correlations of the eavesdropping into noise. The eavesdropper is assumed to have no access to the on/off switching and, indeed, cannot adapt her attack. We explicitly prove that this mechanism enhances the security performance, no matter if the eavesdropper performs collective or coherent attacks
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