431 research outputs found
Universality in Quantum Computation
We show that in quantum computation almost every gate that operates on two or
more bits is a universal gate. We discuss various physical considerations
bearing on the proper definition of universality for computational components
such as logic gates.Comment: 11 pages, LaTe
Towards optimization of quantum circuits
Any unitary operation in quantum information processing can be implemented
via a sequence of simpler steps - quantum gates. However, actual implementation
of a quantum gate is always imperfect and takes a finite time. Therefore,
seeking for a short sequence of gates - efficient quantum circuit for a given
operation, is an important task. We contribute to this issue by proposing
optimization of the well-known universal procedure proposed by Barenco et.al
[1]. We also created a computer program which realizes both Barenco's
decomposition and the proposed optimization. Furthermore, our optimization can
be applied to any quantum circuit containing generalized Toffoli gates,
including basic quantum gate circuits.Comment: 10 pages, 11 figures, minor changes+typo
Stabilisation of Quantum Computations by Symmetrisation
We propose a method for the stabilisation of quantum computations (including
quantum state storage). The method is based on the operation of projection into
, the symmetric subspace of the full state space of redundant
copies of the computer. We describe an efficient algorithm and quantum network
effecting --projection and discuss the stabilising effect of the
proposed method in the context of unitary errors generated by hardware
imprecision, and nonunitary errors arising from external environmental
interaction. Finally, limitations of the method are discussed.Comment: 20 pages LaTeX, 2 postscript figure
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
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.
Engineering Functional Quantum Algorithms
Suppose that a quantum circuit with K elementary gates is known for a unitary
matrix U, and assume that U^m is a scalar matrix for some positive integer m.
We show that a function of U can be realized on a quantum computer with at most
O(mK+m^2log m) elementary gates. The functions of U are realized by a generic
quantum circuit, which has a particularly simple structure. Among other
results, we obtain efficient circuits for the fractional Fourier transform.Comment: 4 pages, 2 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
Effective Pure States for Bulk Quantum Computation
In bulk quantum computation one can manipulate a large number of
indistinguishable quantum computers by parallel unitary operations and measure
expectation values of certain observables with limited sensitivity. The initial
state of each computer in the ensemble is known but not pure. Methods for
obtaining effective pure input states by a series of manipulations have been
described by Gershenfeld and Chuang (logical labeling) and Cory et al. (spatial
averaging) for the case of quantum computation with nuclear magnetic resonance.
We give a different technique called temporal averaging. This method is based
on classical randomization, requires no ancilla qubits and can be implemented
in nuclear magnetic resonance without using gradient fields. We introduce
several temporal averaging algorithms suitable for both high temperature and
low temperature bulk quantum computing and analyze the signal to noise behavior
of each.Comment: 24 pages in LaTex, 14 figures, the paper is also avalaible at
http://qso.lanl.gov/qc
Three-Qubit Gate Realization Using Single Quantum Particle
Using virtual spin formalism it is shown that a quantum particle with eight
energy levels can store three qubits. The formalism allows to realize a
universal set of quantum gates. Feasible formalism implementation is suggested
which uses nuclear spin-7/2 as a storage medium and radio frequency pulses as
the gates. One pulse realization of all universal gates has been found,
including three-qubit Toffoli gate.Comment: LaTeX, 6 pages, no figures; Submitted to "Pis'ma v Zh. Eksp. Teor.
Fiz.
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