10,651 research outputs found
Spatial quantum search in a triangular network
The spatial search problem consists in minimizing the number of steps
required to find a given site in a network, under the restriction that only
oracle queries or translations to neighboring sites are allowed. We propose a
quantum algorithm for the spatial search problem on a triangular lattice with N
sites and torus-like boundary conditions. The proposed algortithm is a special
case of the general framework for abstract search proposed by Ambainis, Kempe
and Rivosh [AKR05] (AKR) and Tulsi [Tulsi08], applied to a triangular network.
The AKR-Tulsi formalism was employed to show that the time complexity of the
quantum search on the triangular lattice is O(sqrt(N logN)).Comment: 10 pages, 4 Postscript figures, uses sbc-template.sty, appeared in
Annals of WECIQ 2010, III Workshop of Quantum Computation and Quantum
Informatio
Spatial search in a honeycomb network
The spatial search problem consists in minimizing the number of steps
required to find a given site in a network, under the restriction that only
oracle queries or translations to neighboring sites are allowed. In this paper,
a quantum algorithm for the spatial search problem on a honeycomb lattice with
sites and torus-like boundary conditions. The search algorithm is based on
a modified quantum walk on a hexagonal lattice and the general framework
proposed by Ambainis, Kempe and Rivosh is used to show that the time complexity
of this quantum search algorithm is .Comment: 10 pages, 2 figures; Minor typos corrected, one Reference added.
accepted in Math. Structures in Computer Science, special volume on Quantum
Computin
Triangular nanobeam photonic cavities in single crystal diamond
Diamond photonics provides an attractive architecture to explore room
temperature cavity quantum electrodynamics and to realize scalable multi-qubit
computing. Here we review the present state of diamond photonic technology. The
design, fabrication and characterization of a novel triangular cross section
nanobeam cavity produced in a single crystal diamond is demonstrated. The
present cavity design, based on a triangular cross section allows vertical
confinement and better signal collection efficiency than that of slab-based
nanocavities, and eliminates the need for a pre-existing membrane. The nanobeam
is fabricated by Focused-Ion-Beam (FIB) patterning. The cavity is characterized
by a confocal photoluminescence. The modes display quality factors of Q ~220
and are deviated in wavelength by only ~1.7nm from the NV- color center zero
phonon line (ZPL). The measured results are found in good agreement with 3D
Finite-Difference-Time-Domain (FDTD) calculations. A more advanced cavity
design with Q=22,000 is modeled, showing the potential for high-Q
implementations using the triangular cavity design. The prospects of this
concept and its application to spin non-demolition measurement and quantum
computing are discussed.Comment: 18 pages,7 figure
Phase transitions of geometrically frustrated mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices
Phase transitions of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on
several decorated planar lattices consisting of interconnected diamonds are
investigated within the framework of the generalized decoration-iteration
transformation. The main attention is paid to the systematic study of the
finite-temperature phase diagrams in dependence on the lattice topology. The
critical behaviour of the hybrid quantum-classical Ising-Heisenberg model is
compared with the relevant behaviour of its semi-classical Ising analogue. It
is shown that both models on diamond-like decorated planar lattices exhibit a
striking critical behaviour including reentrant phase transitions. The higher
the lattice coordination number is, the more pronounced reentrance may be
detected.Comment: 11 pages, 5 figure
Spin-orbital quantum liquid on the honeycomb lattice
In addition to low-energy spin fluctuations, which distinguish them from band
insulators, Mott insulators often possess orbital degrees of freedom when
crystal-field levels are partially filled. While in most situations spins and
orbitals develop long-range order, the possibility for the ground state to be a
quantum liquid opens new perspectives. In this paper, we provide clear evidence
that the SU(4) symmetric Kugel-Khomskii model on the honeycomb lattice is a
quantum spin-orbital liquid. The absence of any form of symmetry breaking -
lattice or SU(N) - is supported by a combination of semiclassical and numerical
approaches: flavor-wave theory, tensor network algorithm, and exact
diagonalizations. In addition, all properties revealed by these methods are
very accurately accounted for by a projected variational wave-function based on
the \pi-flux state of fermions on the honeycomb lattice at 1/4-filling. In that
state, correlations are algebraic because of the presence of a Dirac point at
the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the
honeycomb lattice is an algebraic quantum spin-orbital liquid. This model
provides a good starting point to understand the recently discovered
spin-orbital liquid behavior of Ba_3CuSb_2O_9. The present results also suggest
to choose optical lattices with honeycomb geometry in the search for quantum
liquids in ultra-cold four-color fermionic atoms.Comment: 10 pages, 7 figure
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