Vol.7
No.3
March 1, 2007
Research Articles:
How to build a 300 bit, 1 Gigaoperation
quantum computer
(pp171183) PDF
A.M. Steane
Experimental methods for laser control of trapped ions
have reached sufficient maturity that it is possible to set out in
detail a design for a large quantum computer based on such methods,
without any major omissions or uncertainties. The main features of such
a design are given, with a view to identifying areas for study. The
machine is based on 13000 ions moved via 20$\mu$m vacuum channels around
a chip containing 160000 electrodes and associated classical control
circuits; 1000 laser beam pairs are used to manipulate the hyperfine
states of the ions and drive fluorescence for readout. The computer
could run a quantum algorithm requiring $10^9$ logical operations on 300
logical qubits, with a physical gate rate of 1 MHz and a logical gate
rate of 8 kHz, using methods for quantum gates that have already been
experimentally implemented. Routes for faster operation are discussed.
Cluster state quantum computation for manylevel systems
(pp184208) PDF
W. Hall
The cluster state model for quantum computation [Phys.
Rev. Lett. \textbf{86}, 5188] outlines a scheme that allows one to use
measurement on a large set of entangled quantum systems in what is known
as a cluster state to undertake quantum computations. The model itself
and many works dedicated to it involve using entangled qubits. In this
paper we consider the issue of using entangled qudits instead. We
present a complete framework for cluster state quantum computation using
qudits, which not only contains the features of the original qubit model
but also contains the new idea of adaptive computation: via a change in
the classical computation that helps to correct the errors that are
inherent in the model, the implemented quantum computation can be
changed. This feature arises through the extra degrees of freedom that
appear when using qudits. Finally, for prime dimensions, we give a very
explicit description of the model, making use of mutually unbiased
bases.
Convex hulls of varieties and entanglement measures based on the roof
construction
(pp209227) PDF
T.J. Osborne
In this paper we study the problem of calculating the
convex hull of certain affine algebraic varieties. As we explain, the
motivation for considering this problem is that certain purestate
measures of quantum entanglement, which we call \emph{polynomial
entanglement measures}, can be represented as affine algebraic
varieties. We consider the evaluation of certain mixedstate extensions
of these polynomial entanglement measures, namely \emph{convex and
concave roofs}. We show that the evaluation of a roofbased mixedstate
extension is equivalent to calculating a hyperplane which is multiply
tangent to the variety in a number of places equal to the number of
terms in an optimal decomposition for the measure. In this way we
provide an \emph{implicit} representation of optimal decompositions for
mixedstate entanglement measures based on the roof construction.
Universal quantum circuit for nqubit quantum gate: a programmable
quantum gate
(pp228242) PDF
P.B.M. Sousa and R.V. Ramos
Quantum computation has attracted much attention, among
other things, due to its potentialities to solve classical NP problems
in polynomial time. For this reason, there has been a growing interest
to build a quantum computer. One of the basic steps is to implement the
quantum circuit able to realize a given unitary operation. This task has
been solved using decomposition of unitary matrices in simpler ones till
reach quantum circuits having only singlequbits and CNOTs gates.
Usually the goal is to find the minimal quantum circuit able to solve a
given problem. In this paper we go in a different direction. We propose
a general quantum circuit able to implement any specific quantum circuit
by just setting correctly the parameters. In other words, we propose a
programmable quantum circuit. This opens the possibility to construct a
real quantum computer where several different quantum operations can be
realized in the same hardware. The configuration is proposed and its
optical implementation is discussed.
Optimal fingerprinting strategies with onesided error
(pp243264) PDF
A.J. Scott, J. Walgate, and B.C.
Sanders
Fingerprinting enables two parties to infer whether the
messages they hold are the same or different when the cost of
communication is high: each message is associated with a smaller
fingerprint and comparisons between messages are made in terms of their
fingerprints alone. In the simultaneous message passing model, it is
known that fingerprints composed of quantum information can be made
exponentially smaller than those composed of classical information. For
small message lengths, we present constructions of optimal classical
fingerprinting strategies with onesided error, in both the oneway and
simultaneous message passing models, and provide bounds on the
worstcase error probability with the help of extremal set theory. The
performance of these protocols is then compared to that for quantum
fingerprinting strategies constructed from spherical codes, equiangular
tight frames and mutually unbiased bases.
Quantum Gaussian channels with additive correlated classical noise
(pp265272) PDF
G. Ruggeri and S. Mancini
We provide a model to study memory effects in quantum
Gaussian channels with additive classical noise over an arbitrary number
of uses. The correlation among different uses is introduced by
contiguous twomode interactions. Numerical results for few modes are
presented. They confirm the possibility to enhance the classical
information rate with the aid of entangled inputs, and show a likely
asymptotic behavior that should lead to the full capacity of the
channel.
Continuousdiscrete entanglement: an example with nonrelativistic
particles (pp273280) PDF
N.L.
Harshman
This article discusses entanglement between two
subsystems, one with discrete degrees of freedom and the other with
continuous degrees of freedom. The overlap integral between continuous
variable wave functions emerges as an important parameter to
characterize this kind entanglement. ``Beamlike'' entanglement and
``shapelike'' entanglement are contrasted. One example of this kind of
entanglement is between between the spin degrees of freedom and the
momentum degrees of freedom for a nonrelativistic particle. This
intraparticle entanglement is Galilean invariant.
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