674,553 research outputs found
On Aspects and Implications of the New Covariant 4D, N = 1 Green-Schwarz Sigma-model Action
Utilizing (2,0) superfields, we write a supersymmetry-squared action and
partially relate it to the new formulation of the Green-Schwarz action given by
Berkovits and Siegel. Recent results derived from this new formulation are
discussed within the context of some prior proposals in the literature. Among
these, we note that 4D, N = 1 beta-FFC superspace geometry with a composite
connection for R-symmetry has now been confirmed as the only presently known
limit of 4D, N = 1 heterotic string theory that is derivable in a completely
rigorous manner.Comment: 15 pages, LaTe
Optimal two-qubit quantum circuits using exchange interactions
The Heisenberg exchange interaction is a natural method to implement
non-local (i.e., multi-qubit) quantum gates in quantum information processing.
We consider quantum circuits comprising of gates, which are
realized through the exchange interaction, and single-qubit gates. A universal
two-qubit quantum circuit is constructed from only three gates
and six single-qubit gates. We further show that three gates
are not only sufficient, but necessary. Since six single-qubit gates are known
to be necessary, our universal two-qubit circuit is optimal in terms of the
number of {\em both} and single-qubit gates.Comment: 4 page
Elementary gates for quantum computation
We show that a set of gates that consists of all one-bit quantum gates (U(2))
and the two-bit exclusive-or gate (that maps Boolean values to ) is universal in the sense that all unitary operations on
arbitrarily many bits (U()) can be expressed as compositions of these
gates. We investigate the number of the above gates required to implement other
gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2)
transformation to one input bit if and only if the logical AND of all remaining
input bits is satisfied. These gates play a central role in many proposed
constructions of quantum computational networks. We derive upper and lower
bounds on the exact number of elementary gates required to build up a variety
of two-and three-bit quantum gates, the asymptotic number required for -bit
Deutsch-Toffoli gates, and make some observations about the number required for
arbitrary -bit unitary operations.Comment: 31 pages, plain latex, no separate figures, submitted to Phys. Rev.
A. Related information on http://vesta.physics.ucla.edu:7777
Deterministic construction of arbitrary states with quadratically increasing number of two-qubit gates
We propose a quantum circuit composed of gates and four single-qubit
gates to generate a state of three qubits. This circuit was then enhanced
by integrating two-qubit gates to create a state of four and five qubits.
After a couple of enhancements, we show that an arbitrary state can be
generated depending only on the degree of enhancement. The generalized formula
for the number of two-qubit gates required is given, showing that an -qubit
-state generation can be achieved with quadratically increasing number of
two-qubit gates. Also, the practical feasibility is discussed regarding photon
sources and various applications of gates
Mathematical Estimation of Logical Masking Capability of Majority/Minority Gates Used in Nanoelectronic Circuits
In nanoelectronic circuit synthesis, the majority gate and the inverter form
the basic combinational logic primitives. This paper deduces the mathematical
formulae to estimate the logical masking capability of majority gates, which
are used extensively in nanoelectronic digital circuit synthesis. The
mathematical formulae derived to evaluate the logical masking capability of
majority gates holds well for minority gates, and a comparison with the logical
masking capability of conventional gates such as NOT, AND/NAND, OR/NOR, and
XOR/XNOR is provided. It is inferred from this research work that the logical
masking capability of majority/minority gates is similar to that of XOR/XNOR
gates, and with an increase of fan-in the logical masking capability of
majority/minority gates also increases
Robust Logic Gates and Realistic Quantum Computation
The composite rotation approach has been used to develop a range of robust
quantum logic gates, including single qubit gates and two qubit gates, which
are resistant to systematic errors in their implementation. Single qubit gates
based on the BB1 family of composite rotations have been experimentally
demonstrated in a variety of systems, but little study has been made of their
application in extended computations, and there has been no experimental study
of the corresponding robust two qubit gates to date. Here we describe an
application of robust gates to Nuclear Magnetic Resonance (NMR) studies of
approximate quantum counting. We find that the BB1 family of robust gates is
indeed useful, but that the related NB1, PB1, B4 and P4 families of tailored
logic gates are less useful than initially expected.Comment: 6 pages RevTex4 including 5 figures (3 low quality to save space).
Revised at request of referee and incorporting minor corrections and updates.
Now in press at Phys Rev
- …