558 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

### 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

### 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
$\cal SYM$, the symmetric subspace of the full state space of $R$ redundant
copies of the computer. We describe an efficient algorithm and quantum network
effecting $\cal SYM$--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

### Optimal dense coding with mixed state entanglement

I investigate dense coding with a general mixed state on the Hilbert space
$C^{d}\otimes C^{d}$ 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 $\chi ^{*}$ satisfies $E_{R}(\rho)\leq \chi ^{*}\leq E_{R}(\rho
)+\log_{2}d$, where $E_{R}(\rho)$ 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

### 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

- …