451 research outputs found
Characterization of two-qubit perfect entanglers
Here we consider perfect entanglers from another perspective. It is shown
that there are some {\em special} perfect entanglers which can maximally
entangle a {\em full} product basis. We have explicitly constructed a
one-parameter family of such entanglers together with the proper product basis
that they maximally entangle. This special family of perfect entanglers
contains some well-known operators such as {\textsc{cnot}} and
{\textsc{dcnot}}, but {\em not} {\small{\sqrt{\rm{\textsc{swap}}}}}. In
addition, it is shown that all perfect entanglers with entangling power equal
to the maximal value, 2/9, are also special perfect entanglers. It is proved
that the one-parameter family is the only possible set of special perfect
entanglers. Also we provide an analytic way to implement any arbitrary
two-qubit gate, given a proper special perfect entangler supplemented with
single-qubit gates. Such these gates are shown to provide a minimum universal
gate construction in that just two of them are necessary and sufficient in
implementation of a generic two-qubit gate.Comment: 6 pages, 1 eps figur
A Note on Linear Optics Gates by Post-Selection
Recently it was realized that linear optics and photo-detectors with feedback
can be used for theoretically efficient quantum information processing. The
first of three steps toward efficient linear optics quantum computation (eLOQC)
was to design a simple non-deterministic gate, which upon post-selection based
on a measurement result implements a non-linear phase shift on one mode. Here a
computational strategy is given for finding non-deterministic gates for bosonic
qubits with helper photons. A more efficient conditional sign flip gate is
obtained.Comment: 14 pages. Minor changes for clarit
Programmable quantum gate arrays
We show how to construct quantum gate arrays that can be programmed to
perform different unitary operations on a data register, depending on the input
to some program register. It is shown that a universal quantum gate array - a
gate array which can be programmed to perform any unitary operation - exists
only if one allows the gate array to operate in a probabilistic fashion. The
universal quantum gate array we construct requires an exponentially smaller
number of gates than a classical universal gate array.Comment: 3 pages, REVTEX. Submitted to Phys. Rev. Let
Optimal dense coding with mixed state entanglement
I investigate dense coding with a general mixed state on the Hilbert space
shared between a sender and receiver. The following result
is proved. When the sender prepares the signal states by mutually orthogonal
unitary transformations with equal {\it a priori} probabilities, the capacity
of dense coding is maximized. It is also proved that the optimal capacity of
dense coding satisfies , where is the relative entropy of entanglement of
the shared entangled state.Comment: Revised. To appear in J. Phys. A: Math. Gen. (Special Issue: Quantum
Information and Computation). LaTeX2e (iopart.cls), 8 pages, no figure
Distribution of interference in random quantum algorithms
We study the amount of interference in random quantum algorithms using a
recently derived quantitative measure of interference. To this end we introduce
two random circuit ensembles composed of random sequences of quantum gates from
a universal set, mimicking quantum algorithms in the quantum circuit
representation. We show numerically that these ensembles converge to the
well--known circular unitary ensemble (CUE) for general complex quantum
algorithms, and to the Haar orthogonal ensemble (HOE) for real quantum
algorithms. We provide exact analytical formulas for the average and typical
interference in the circular ensembles, and show that for sufficiently large
numbers of qubits a random quantum algorithm uses with probability close to one
an amount of interference approximately equal to the dimension of the Hilbert
space. As a by-product, we offer a new way of efficiently constructing random
operators from the Haar measures of CUE or HOE in a high dimensional Hilbert
space using universal sets of quantum gates.Comment: 14 pages revtex, 11 eps figure
Approximate Quantum Fourier Transform and Decoherence
We discuss the advantages of using the approximate quantum Fourier transform
(AQFT) in algorithms which involve periodicity estimations. We analyse quantum
networks performing AQFT in the presence of decoherence and show that extensive
approximations can be made before the accuracy of AQFT (as compared with
regular quantum Fourier transform) is compromised. We show that for some
computations an approximation may imply a better performance.Comment: 14 pages, 10 fig. (8 *.eps files). More information on
http://eve.physics.ox.ac.uk/QChome.html
http://www.physics.helsinki.fi/~kasuomin
http://www.physics.helsinki.fi/~kira/group.htm
Explicit Form of the Evolution Operator of Tavis-Cummings Model : Three and Four Atoms Cases
In this letter the explicit form of evolution operator of the Tavis-Cummings
model with three and four atoms is given. This is an important progress in
quantum optics or mathematical physics.Comment: Latex file, 10 pages. We combined quant-ph/0404034(the three atoms
case) and quant-ph/0406184(the four atoms case) into an article. to appear in
International Journal of Geometric Methods in Modern Physic
Analytical technique for simplification of the encoder-decoder circuit for a perfect five-qubit error correction
Simpler encoding and decoding networks are necessary for more reliable
quantum error correcting codes (QECCs). The simplification of the
encoder-decoder circuit for a perfect five-qubit QECC can be derived
analytically if the QECC is converted from its equivalent one-way entanglement
purification protocol (1-EPP). In this work, the analytical method to simplify
the encoder-decoder circuit is introduced and a circuit that is as simple as
the existent simplest circuits is presented as an example. The encoder-decoder
circuit presented here involves nine single- and two-qubit unitary operations,
only six of which are controlled-NOT (CNOT) gates
Quantum Physics and Computers
Recent theoretical results confirm that quantum theory provides the
possibility of new ways of performing efficient calculations. The most striking
example is the factoring problem. It has recently been shown that computers
that exploit quantum features could factor large composite integers. This task
is believed to be out of reach of classical computers as soon as the number of
digits in the number to factor exceeds a certain limit. The additional power of
quantum computers comes from the possibility of employing a superposition of
states, of following many distinct computation paths and of producing a final
output that depends on the interference of all of them. This ``quantum
parallelism'' outstrips by far any parallelism that can be thought of in
classical computation and is responsible for the ``exponential'' speed-up of
computation.
This is a non-technical (or at least not too technical) introduction to the
field of quantum computation. It does not cover very recent topics, such as
error-correction.Comment: 27 pages, LaTeX, 8 PostScript figures embedded. A bug in one of the
postscript files has been fixed. Reprints available from the author. The
files are also available from
http://eve.physics.ox.ac.uk/Articles/QC.Articles.htm
Efficient Scheme for Initializing a Quantum Register with an Arbitrary Superposed State
Preparation of a quantum register is an important step in quantum computation
and quantum information processing. It is straightforward to build a simple
quantum state such as |i_1 i_2 ... i_n\ket with being either 0 or 1,
but is a non-trivial task to construct an {\it arbitrary} superposed quantum
state. In this Paper, we present a scheme that can most generally initialize a
quantum register with an arbitrary superposition of basis states.
Implementation of this scheme requires standard 1- and 2-bit gate
operations, {\it without introducing additional quantum bits}. Application of
the scheme in some special cases is discussed.Comment: 4 pages, 4 figures, accepted by Phys. Rev.
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