471 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
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
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
Quantum networks for elementary arithmetic operations
Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most difficult (time and space consuming) part of Shor's quantum factorising algorithm. We show that the auxiliary memory required to perform this operation in a reversible way grows linearly with the size of the number to be factorised
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
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
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
Equally-distant partially-entangled alphabet states for quantum channels
Each Bell state has the property that by performing just local operations on
one qubit, the complete Bell basis can be generated. That is, states generated
by local operations are totally distinguishable. This remarkable property is
due to maximal quantum entanglement between the two particles. We present a set
of local unitary transformations that generate out of partially entangled
two-qubit state a set of four maximally distinguishable states that are
mutually equally distant. We discuss quantum dense coding based on these
alphabet states.Comment: 7 revtex pages, 2 eps figures, to appear in Phys. Rev. A 62, 1
November (2000
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