623 research outputs found
Quantum Metropolis Sampling
The original motivation to build a quantum computer came from Feynman who
envisaged a machine capable of simulating generic quantum mechanical systems, a
task that is believed to be intractable for classical computers. Such a machine
would have a wide range of applications in the simulation of many-body quantum
physics, including condensed matter physics, chemistry, and high energy
physics. Part of Feynman's challenge was met by Lloyd who showed how to
approximately decompose the time-evolution operator of interacting quantum
particles into a short sequence of elementary gates, suitable for operation on
a quantum computer. However, this left open the problem of how to simulate the
equilibrium and static properties of quantum systems. This requires the
preparation of ground and Gibbs states on a quantum computer. For classical
systems, this problem is solved by the ubiquitous Metropolis algorithm, a
method that basically acquired a monopoly for the simulation of interacting
particles. Here, we demonstrate how to implement a quantum version of the
Metropolis algorithm on a quantum computer. This algorithm permits to sample
directly from the eigenstates of the Hamiltonian and thus evades the sign
problem present in classical simulations. A small scale implementation of this
algorithm can already be achieved with today's technologyComment: revised versio
Preparing projected entangled pair states on a quantum computer
We present a quantum algorithm to prepare injective PEPS on a quantum
computer, a class of open tensor networks representing quantum states. The
run-time of our algorithm scales polynomially with the inverse of the minimum
condition number of the PEPS projectors and, essentially, with the inverse of
the spectral gap of the PEPS' parent Hamiltonian.Comment: 5 pages, 1 figure. To be published in Physical Review Letters.
Removed heuristics, refined run-time boun
Nonnegative solutions of algebraic Riccati equations
AbstractNonnegative Hermitian solutions of various types of continuous and discrete algebraic Riccati equations are studied. The Hamiltonian is considered with respect to two different indefinite scalar products. For the set of nonnegative solutions the order structure and the topology of the set and the stability of solutions is treated. For general Hermitian solutions a method to compute the inertia is given. Although most attention is payed to the classical types arising from LQ optimal control theory, the case where the quadratic term has an indefinite coefficient is studied as well
Resonantly enhanced pair production in a simple diatomic model
A new mechanism for the production of electron-positron pairs from the
interaction of a laser field and a fully stripped diatomic molecule in the
tunneling regime is presented. When the laser field is turned off, the Dirac
operator has resonances in both the positive and the negative energy continua
while bound states are in the mass gap. When this system is immersed in a
strong laser field, the resonances move in the complex energy plane: the
negative energy resonances are pushed to higher energies while the bound states
are Stark shifted. It is argued here that there is a pair production
enhancement at the crossing of resonances by looking at a simple 1-D model: the
nuclei are modeled simply by Dirac delta potential wells while the laser field
is assumed to be static and of finite spatial extent. The average rate for the
number of electron-positron pairs produced is evaluated and the results are
compared to the single nucleus and to the free cases. It is shown that
positrons are produced by the Resonantly Enhanced Pair Production (REPP)
mechanism, which is analogous to the resonantly enhanced ionization of
molecular physics. This phenomenon could be used to increase the number of
pairs produced at low field strength, allowing the study of the Dirac vacuum.Comment: 11 pages, 4 figure
Supervised learning with quantum enhanced feature spaces
Machine learning and quantum computing are two technologies each with the
potential for altering how computation is performed to address previously
untenable problems. Kernel methods for machine learning are ubiquitous for
pattern recognition, with support vector machines (SVMs) being the most
well-known method for classification problems. However, there are limitations
to the successful solution to such problems when the feature space becomes
large, and the kernel functions become computationally expensive to estimate. A
core element to computational speed-ups afforded by quantum algorithms is the
exploitation of an exponentially large quantum state space through controllable
entanglement and interference. Here, we propose and experimentally implement
two novel methods on a superconducting processor. Both methods represent the
feature space of a classification problem by a quantum state, taking advantage
of the large dimensionality of quantum Hilbert space to obtain an enhanced
solution. One method, the quantum variational classifier builds on [1,2] and
operates through using a variational quantum circuit to classify a training set
in direct analogy to conventional SVMs. In the second, a quantum kernel
estimator, we estimate the kernel function and optimize the classifier
directly. The two methods present a new class of tools for exploring the
applications of noisy intermediate scale quantum computers [3] to machine
learning.Comment: Fixed typos, added figures and discussion about quantum error
mitigatio
Dressed test particles, oscillation centres and pseudo-orbits
A general semi-analytical method for accurate and efficient numerical
calculation of the dielectrically screened ("dressed") potential around a
non-relativistic test particle moving in an isotropic, collisionless,
unmagnetised plasma is presented. The method requires no approximations and is
illustrated using results calculated for two cases taken from the MSc thesis of
the first author: test particles with velocities above and below the ion sound
speed in plasmas with Maxwellian ions and warm electrons. The idea that the
fluctuation spectrum of a plasma can be described as a superposition of the
fields around \emph{non-interacting} dressed test particles is an expression of
the quasiparticle concept, which has also been expressed in the development of
the oscillation-centre and pseudo-orbit formalisms.Comment: 14 pages to Plasma Physics and Controlled Fusion for publication with
a cluster of papers associated with workshop Stability and Nonlinear Dynamics
of Plasmas, October 31, 2009 Atlanta, GA on occasion of the 65th birthday of
R.L. Dewar. Version 2: Reference [27] added in Sec. 5. Version 3: Revised in
response to referee
Entropic uncertainty measures for large dimensional hydrogenic systems
The entropic moments of the probability density of a quantum system in position and momentum spaces describe not only some fundamental and/or experimentally accessible quantities of the system but also the entropic uncertainty measures of R\xc3\xa9nyi type, which allow one to find the most relevant mathematical formalizations of the position-momentum Heisenberg\'s uncertainty principle, the entropic uncertainty relations. It is known that the solution of difficult three-dimensional problems can be very well approximated by a series development in 1/D in similar systems with a nonstandard dimensionality D; moreover, several physical quantities of numerous atomic and molecular systems have been numerically shown to have values in the large- D limit comparable to the corresponding ones provided by the three-dimensional numerical self-consistent field methods. The D-dimensional hydrogenic atom is the main prototype of the physics of multidimensional many-electron systems. In this work, we rigorously determine the leading term of the R\xc3\xa9nyi entropies of the Ddimensional hydrogenic atom at the limit of large D. As a byproduct, we show that our results saturate the known position-momentum R\xc3\xa9nyi-entropy-based uncertainty relations
Sequential Strong Measurements and Heat Vision
We study scenarios where a finite set of non-demolition von-Neumann
measurements are available. We note that, in some situations, repeated
application of such measurements allows estimating an infinite number of
parameters of the initial quantum state, and illustrate the point with a
physical example. We then move on to study how the system under observation is
perturbed after several rounds of projective measurements. While in the finite
dimensional case the effect of this perturbation always saturates, there are
some instances of infinite dimensional systems where such a perturbation is
accumulative, and the act of retrieving information about the system increases
its energy indefinitely (i.e., we have `Heat Vision'). We analyze this effect
and discuss a specific physical system with two dichotomic von-Neumann
measurements where Heat Vision is expected to show.Comment: See the Appendix for weird examples of heat visio
Landau-Zener-St\"uckelberg interferometry in pair production from counterpropagating lasers
The rate of electron-positron pair production in linearly polarized
counter-propagating lasers is evaluated from a recently discovered solution of
the time-dependent Dirac equation. The latter is solved in momentum space where
it is formally equivalent to the Schr\"odinger equation describing a strongly
driven two-level system. The solution is found from a simple transformation of
the Dirac equation and is given in compact form in terms of the
doubly-confluent Heun's function. By using the analogy with the two-level
system, it is shown that for high-intensity lasers, pair production occurs
through periodic non-adiabatic transitions when the adiabatic energy gap is
minimal. These transitions give rise to an intricate interference pattern in
the pair spectrum, reminiscent of the Landau-Zener-St\"uckelberg phenomenon in
molecular physics: the accumulated phase result in constructive or destructive
interference. The adiabatic-impulse model is used to study this phenomenon and
shows an excellent agreement with the exact result.Comment: 22 pages, 7 figure
Power Utility Maximization in Discrete-Time and Continuous-Time Exponential Levy Models
Consider power utility maximization of terminal wealth in a 1-dimensional
continuous-time exponential Levy model with finite time horizon. We discretize
the model by restricting portfolio adjustments to an equidistant discrete time
grid. Under minimal assumptions we prove convergence of the optimal
discrete-time strategies to the continuous-time counterpart. In addition, we
provide and compare qualitative properties of the discrete-time and
continuous-time optimizers.Comment: 18 pages, to appear in Mathematical Methods of Operations Research.
The final publication is available at springerlink.co
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