1,542 research outputs found
Efficient Algorithms for Universal Quantum Simulation
A universal quantum simulator would enable efficient simulation of quantum
dynamics by implementing quantum-simulation algorithms on a quantum computer.
Specifically the quantum simulator would efficiently generate qubit-string
states that closely approximate physical states obtained from a broad class of
dynamical evolutions. I provide an overview of theoretical research into
universal quantum simulators and the strategies for minimizing computational
space and time costs. Applications to simulating many-body quantum simulation
and solving linear equations are discussed
Superoscillations and tunneling times
It is proposed that superoscillations play an important role in the
interferences which give rise to superluminal effects. To exemplify that, we
consider a toy model which allows for a wave packet to travel, in zero time and
negligible distortion a distance arbitrarily larger than the width of the wave
packet. The peak is shown to result from a superoscillatory superposition at
the tail. Similar reasoning applies to the dwell time.Comment: 12 page
Temporal Talbot effect in interference of matter waves from arrays of Bose-Einstein condensates and transition to Fraunhofer diffraction
We consider interference patterns produced by coherent arrays of
Bose-Einstein condensates during their one-dimensional expansion. Several
characteristic pattern structures are distinguished depending on value of the
evolution time. Transformation of Talbot ``collapse-revival'' behavior to
Fraunhofer interference fringes is studied in detail.Comment: 11 pages, 4 figures; misprints correcte
Adiabatic following criterion, estimation of the nonadiabatic excitation fraction and quantum jumps
An accurate theory describing adiabatic following of the dark, nonabsorbing
state in the three-level system is developed. An analytical solution for the
wave function of the particle experiencing Raman excitation is found as an
expansion in terms of the time varying nonadiabatic perturbation parameter. The
solution can be presented as a sum of adiabatic and nonadiabatic parts. Both
are estimated quantitatively. It is shown that the limiting value to which the
amplitude of the nonadiabatic part tends is equal to the Fourier component of
the nonadiabatic perturbation parameter taken at the Rabi frequency of the
Raman excitation. The time scale of the variation of both parts is found. While
the adiabatic part of the solution varies slowly and follows the change of the
nonadiabatic perturbation parameter, the nonadiabatic part appears almost
instantly, revealing a jumpwise transition between the dark and bright states.
This jump happens when the nonadiabatic perturbation parameter takes its
maximum value.Comment: 33 pages, 8 figures, submitted to PRA on 28 Oct. 200
On the relationship between continuous- and discrete-time quantum walk
Quantum walk is one of the main tools for quantum algorithms. Defined by
analogy to classical random walk, a quantum walk is a time-homogeneous quantum
process on a graph. Both random and quantum walks can be defined either in
continuous or discrete time. But whereas a continuous-time random walk can be
obtained as the limit of a sequence of discrete-time random walks, the two
types of quantum walk appear fundamentally different, owing to the need for
extra degrees of freedom in the discrete-time case.
In this article, I describe a precise correspondence between continuous- and
discrete-time quantum walks on arbitrary graphs. Using this correspondence, I
show that continuous-time quantum walk can be obtained as an appropriate limit
of discrete-time quantum walks. The correspondence also leads to a new
technique for simulating Hamiltonian dynamics, giving efficient simulations
even in cases where the Hamiltonian is not sparse. The complexity of the
simulation is linear in the total evolution time, an improvement over
simulations based on high-order approximations of the Lie product formula. As
applications, I describe a continuous-time quantum walk algorithm for element
distinctness and show how to optimally simulate continuous-time query
algorithms of a certain form in the conventional quantum query model. Finally,
I discuss limitations of the method for simulating Hamiltonians with negative
matrix elements, and present two problems that motivate attempting to
circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian
oracles; v3: published version, with improved analysis of phase estimatio
Coherent oscillations and incoherent tunnelling in one - dimensional asymmetric double - well potential
For a model 1d asymmetric double-well potential we calculated so-called
survival probability (i.e. the probability for a particle initially localised
in one well to remain there). We use a semiclassical (WKB) solution of
Schroedinger equation. It is shown that behaviour essentially depends on
transition probability, and on dimensionless parameter which is a ratio of
characteristic frequencies for low energy non-linear in-well oscillations and
inter wells tunnelling. For the potential describing a finite motion
(double-well) one has always a regular behaviour. For the small value of the
parameter there is well defined resonance pairs of levels and the survival
probability has coherent oscillations related to resonance splitting. However
for the large value of the parameter no oscillations at all for the survival
probability, and there is almost an exponential decay with the characteristic
time determined by Fermi golden rule. In this case one may not restrict oneself
to only resonance pair levels. The number of perturbed by tunnelling levels
grows proportionally to the value of this parameter (by other words instead of
isolated pairs there appear the resonance regions containing the sets of
strongly coupled levels). In the region of intermediate values of the parameter
one has a crossover between both limiting cases, namely the exponential decay
with subsequent long period recurrent behaviour.Comment: 19 pages, 7 figures, Revtex, revised version. Accepted to Phys. Rev.
Toll-like receptor 2 contributes to antibacterial defence against pneumolysin-deficient pneumococci
Toll-like receptors (TLRs) are pattern recognition receptors that recognize conserved molecular patterns expressed by pathogens. Pneumolysin, an intracellular toxin found in all Streptococcus pneumoniae clinical isolates, is an important virulence factor of the pneumococcus that is recognized by TLR4. Although TLR2 is considered the most important receptor for Gram-positive bacteria, our laboratory previously could not demonstrate a decisive role for TLR2 in host defence against pneumonia caused by a serotype 3 S. pneumoniae. Here we tested the hypothesis that in the absence of TLR2, S. pneumoniae can still be sensed by the immune system through an interaction between pneumolysin and TLR4. C57BL/6 wild-type (WT) and TLR2 knockout (KO) mice were intranasally infected with either WT S. pneumoniae D39 (serotype 2) or the isogenic pneumolysin-deficient S. pneumoniae strain D39 PLN. TLR2 did not contribute to antibacterial defence against WT S. pneumoniae D39. In contrast, pneumolysin-deficient S. pneumoniae only grew in lungs of TLR2 KO mice. TLR2 KO mice displayed a strongly reduced early inflammatory response in their lungs during pneumonia caused by both pneumolysin-producing and pneumolysin-deficient pneumococci. These data suggest that pneumolysin-induced TLR4 signalling can compensate for TLR2 deficiency during respiratory tract infection with S. pneumoniae
Zeta Function Zeros, Powers of Primes, and Quantum Chaos
We present a numerical study of Riemann's formula for the oscillating part of
the density of the primes and their powers. The formula is comprised of an
infinite series of oscillatory terms, one for each zero of the zeta function on
the critical line and was derived by Riemann in his paper on primes assuming
the Riemann hypothesis. We show that high resolution spectral lines can be
generated by the truncated series at all powers of primes and demonstrate
explicitly that the relative line intensities are correct. We then derive a
Gaussian sum rule for Riemann's formula. This is used to analyze the numerical
convergence of the truncated series. The connections to quantum chaos and
semiclassical physics are discussed
Entangling power and operator entanglement in qudit systems
We establish the entangling power of a unitary operator on a general
finite-dimensional bipartite quantum system with and without ancillas, and give
relations between the entangling power based on the von Neumann entropy and the
entangling power based on the linear entropy. Significantly, we demonstrate
that the entangling power of a general controlled unitary operator acting on
two equal-dimensional qudits is proportional to the corresponding operator
entanglement if linear entropy is adopted as the quantity representing the
degree of entanglement. We discuss the entangling power and operator
entanglement of three representative quantum gates on qudits: the SUM, double
SUM, and SWAP gates.Comment: 8 pages, 1 figure. Version 3: Figure was improved and the MS was a
bit shortene
- …