421 research outputs found
The Lanczos algorithm with selective orthogonalization
A new stable and efficient implementation of the Lanczos algorithm is presented. The algorithm is a powerful method for finding a few eigenvalues and eigenvectors at one or both ends of the spectrum of a symmetric matrix A. The algorithm is particularly effective if A is large and sparse in that the only way in which A enters the calculation is through a subroutine which computes Av for any vector v. Thus the user is free to take advantage of any sparsity structure in A and A need not even be represented as a matrix et al
A Processor Core Model for Quantum Computing
We describe an architecture based on a processing 'core' where multiple
qubits interact perpetually, and a separate 'store' where qubits exist in
isolation. Computation consists of single qubit operations, swaps between the
store and the core, and free evolution of the core. This enables computation
using physical systems where the entangling interactions are 'always on'.
Alternatively, for switchable systems our model constitutes a prescription for
optimizing many-qubit gates. We discuss implementations of the quantum Fourier
transform, Hamiltonian simulation, and quantum error correction.Comment: 5 pages, 2 figures; improved some arguments as suggested by a refere
Perfect State Transfer, Effective Gates and Entanglement Generation in Engineered Bosonic and Fermionic Networks
We show how to achieve perfect quantum state transfer and construct effective
two-qubit gates between distant sites in engineered bosonic and fermionic
networks. The Hamiltonian for the system can be determined by choosing an
eigenvalue spectrum satisfying a certain condition, which is shown to be both
sufficient and necessary in mirror-symmetrical networks. The natures of the
effective two-qubit gates depend on the exchange symmetry for fermions and
bosons. For fermionic networks, the gates are entangling (and thus universal
for quantum computation). For bosonic networks, though the gates are not
entangling, they allow two-way simultaneous communications. Protocols of
entanglement generation in both bosonic and fermionic engineered networks are
discussed.Comment: RevTeX4, 6 pages, 1 figure; replaced with a more general example and
clarified the sufficient and necessary condition for perfect state transfe
Parallel Self-Consistent-Field Calculations via Chebyshev-Filtered Subspace Acceleration
Solving the Kohn-Sham eigenvalue problem constitutes the most computationally
expensive part in self-consistent density functional theory (DFT) calculations.
In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace
iteration method, which avoids computing explicit eigenvectors except at the
first SCF iteration. The method may be viewed as an approach to solve the
original nonlinear Kohn-Sham equation by a nonlinear subspace iteration
technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue
problem. It reaches self-consistency within a similar number of SCF iterations
as eigensolver-based approaches. However, replacing the standard
diagonalization at each SCF iteration by a Chebyshev subspace filtering step
results in a significant speedup over methods based on standard
diagonalization. Here, we discuss an approach for implementing this method in
multi-processor, parallel environment. Numerical results are presented to show
that the method enables to perform a class of highly challenging DFT
calculations that were not feasible before
A short note on the presence of spurious states in finite basis approximations
The genesis of spurious solutions in finite basis approximations to operators
which possess a continuum and a point spectrum is discussed and a simple
solution for identifying these solutions is suggested
Negative Impurity Magnetic Susceptibility and Heat Capacity in a Kondo Model with Narrow Peaks in the Local Density of Electron States
Temperature dependencies of the impurity magnetic susceptibility, entropy,
and heat capacity have been obtained by the method of numerical renormalization
group and exact diagonalization for the Kondo model with peaks in the electron
density of states near the Fermi energy (in particular, with logarithmic Van
Hove singularities). It is shown that these quantities can be {\it negative}. A
new effect has been predicted (which, in principle, can be observed
experimentally), namely, the decrease in the magnetic susceptibility and heat
capacity of a nonmagnetic sample upon the addition of magnetic impurities into
it
Stability of two-dimensional spatial solitons in nonlocal nonlinear media
We discuss existence and stability of two-dimensional solitons in media with
spatially nonlocal nonlinear response. We show that such systems, which include
thermal nonlinearity and dipolar Bose Einstein condensates, may support a
variety of stationary localized structures - including rotating spatial
solitons. We also demonstrate that the stability of these structures critically
depends on the spatial profile of the nonlocal response function.Comment: 8 pages, 9 figure
Hitting Time of Quantum Walks with Perturbation
The hitting time is the required minimum time for a Markov chain-based walk
(classical or quantum) to reach a target state in the state space. We
investigate the effect of the perturbation on the hitting time of a quantum
walk. We obtain an upper bound for the perturbed quantum walk hitting time by
applying Szegedy's work and the perturbation bounds with Weyl's perturbation
theorem on classical matrix. Based on the definition of quantum hitting time
given in MNRS algorithm, we further compute the delayed perturbed hitting time
(DPHT) and delayed perturbed quantum hitting time (DPQHT). We show that the
upper bound for DPQHT is actually greater than the difference between the
square root of the upper bound for a perturbed random walk and the square root
of the lower bound for a random walk.Comment: 9 page
A Convergent Method for Calculating the Properties of Many Interacting Electrons
A method is presented for calculating binding energies and other properties
of extended interacting systems using the projected density of transitions
(PDoT) which is the probability distribution for transitions of different
energies induced by a given localized operator, the operator on which the
transitions are projected. It is shown that the transition contributing to the
PDoT at each energy is the one which disturbs the system least, and so, by
projecting on appropriate operators, the binding energies of equilibrium
electronic states and the energies of their elementary excitations can be
calculated. The PDoT may be expanded as a continued fraction by the recursion
method, and as in other cases the continued fraction converges exponentially
with the number of arithmetic operations, independent of the size of the
system, in contrast to other numerical methods for which the number of
operations increases with system size to maintain a given accuracy. These
properties are illustrated with a calculation of the binding energies and
zone-boundary spin- wave energies for an infinite spin-1/2 Heisenberg chain,
which is compared with analytic results for this system and extrapolations from
finite rings of spins.Comment: 30 pages, 4 figures, corrected pd
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