21,178 research outputs found
Codeword stabilized quantum codes: algorithm and structure
The codeword stabilized ("CWS") quantum codes formalism presents a unifying
approach to both additive and nonadditive quantum error-correcting codes
(arXiv:0708.1021). This formalism reduces the problem of constructing such
quantum codes to finding a binary classical code correcting an error pattern
induced by a graph state. Finding such a classical code can be very difficult.
Here, we consider an algorithm which maps the search for CWS codes to a problem
of identifying maximum cliques in a graph. While solving this problem is in
general very hard, we prove three structure theorems which reduce the search
space, specifying certain admissible and optimal ((n,K,d)) additive codes. In
particular, we find there does not exist any ((7,3,3)) CWS code though the
linear programming bound does not rule it out. The complexity of the CWS search
algorithm is compared with the contrasting method introduced by Aggarwal and
Calderbank (arXiv:cs/0610159).Comment: 11 pages, 1 figur
Synchronously-pumped OPO coherent Ising machine: benchmarking and prospects
The coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs) that solves for the ground state of Ising problems through OPO bifurcation dynamics. Here, we present experimental results comparing the performance of the CIM to quantum annealers (QAs) on two classes of NP-hard optimization problems: ground state calculation of the Sherrington-Kirkpatrick (SK) model and MAX-CUT. While the two machines perform comparably on sparsely-connected problems such as cubic MAX-CUT, on problems with dense connectivity, the QA shows an exponential performance penalty relative to CIMs. We attribute this to the embedding overhead required to map dense problems onto the sparse hardware architecture of the QA, a problem that can be overcome in photonic architectures such as the CIM
A graphical description of optical parametric generation of squeezed states of light
The standard process for the production of strongly squeezed states of light
is optical parametric amplification (OPA) below threshold in dielectric media
such as LiNbO3 or periodically poled KTP. Here, we present a graphical
description of squeezed light generation via OPA. It visualizes the interaction
between the nonlinear dielectric polarization of the medium and the
electromagnetic quantum field. We explicitly focus on the transfer from the
field's ground state to a squeezed vacuum state and from a coherent state to a
bright squeezed state by the medium's secondorder nonlinearity, respectively.
Our pictures visualize the phase dependent amplification and deamplification of
quantum uncertainties and give the phase relations between all propagating
electro-magnetic fields as well as the internally induced dielectric
polarizations. The graphical description can also be used to describe the
generation of nonclassical states of light via higherorder effects of the
non-linear dielectric polarization such as four-wave mixing and the optical
Kerr effect
Natural evolution strategies and variational Monte Carlo
A notion of quantum natural evolution strategies is introduced, which
provides a geometric synthesis of a number of known quantum/classical
algorithms for performing classical black-box optimization. Recent work of
Gomes et al. [2019] on heuristic combinatorial optimization using neural
quantum states is pedagogically reviewed in this context, emphasizing the
connection with natural evolution strategies. The algorithmic framework is
illustrated for approximate combinatorial optimization problems, and a
systematic strategy is found for improving the approximation ratios. In
particular it is found that natural evolution strategies can achieve
approximation ratios competitive with widely used heuristic algorithms for
Max-Cut, at the expense of increased computation time
NLS Bifurcations on the bowtie combinatorial graph and the dumbbell metric graph
We consider the bifurcations of standing wave solutions to the nonlinear
Schr\"odinger equation (NLS) posed on a quantum graph consisting of two loops
connected by a single edge, the so-called dumbbell, recently studied by
Marzuola and Pelinovsky. The authors of that study found the ground state
undergoes two bifurcations, first a symmetry-breaking, and the second which
they call a symmetry-preserving bifurcation. We clarify the type of the
symmetry-preserving bifurcation, showing it to be transcritical. We then reduce
the question, and show that the phenomena described in that paper can be
reproduced in a simple discrete self-trapping equation on a combinatorial graph
of bowtie shape. This allows for complete analysis both by geometric methods
and by parameterizing the full solution space. We then expand the question, and
describe the bifurcations of all the standing waves of this system, which can
be classified into three families, and of which there exists a countably
infinite set
Nonlinear spectroscopy in the strong-coupling regime of cavity QED
A nonlinear spectroscopic investigation of a strongly coupled atom-cavity system is presented. A two-field pump-probe experiment is employed to study nonlinear structure as the average number of intracavity atoms is varied from N̅≈4.2 to N̅≈0.8. Nonlinear effects are observed for as few as 0.1 intracavity pump photons. A detailed semiclassical simulation of the atomic beam experiment gives reasonable agreement with the data for N̅≳2 atoms. The simulation procedure accounts for fluctuations in atom-field coupling which have important effects on both the linear and nonlinear probe transmission spectra. A discrepancy between the simulations and the experiments is observed for small numbers of atoms (N̅≲1). Unfortunately, it is difficult to determine if this discrepancy is a definitive consequence of the quantum nature of the atom-cavity coupling or a result of the severe technical complications of the experiment
Evolutionary Approaches to Optimization Problems in Chimera Topologies
Chimera graphs define the topology of one of the first commercially available
quantum computers. A variety of optimization problems have been mapped to this
topology to evaluate the behavior of quantum enhanced optimization heuristics
in relation to other optimizers, being able to efficiently solve problems
classically to use them as benchmarks for quantum machines. In this paper we
investigate for the first time the use of Evolutionary Algorithms (EAs) on
Ising spin glass instances defined on the Chimera topology. Three genetic
algorithms (GAs) and three estimation of distribution algorithms (EDAs) are
evaluated over hard instances of the Ising spin glass constructed from
Sidon sets. We focus on determining whether the information about the topology
of the graph can be used to improve the results of EAs and on identifying the
characteristics of the Ising instances that influence the success rate of GAs
and EDAs.Comment: 8 pages, 5 figures, 3 table
Quantum Modeling
We present a modification of Simon's algorithm that in some cases is able to
fit experimentally obtained data to appropriately chosen trial functions with
high probability. Modulo constants pertaining to the reliability and
probability of success of the algorithm, the algorithm runs using only
O(polylog(|Y|)) queries to the quantum database and O(polylog(|X|,|Y|))
elementary quantum gates where |X| is the size of the experimental data set and
|Y| is the size of the parameter space.We discuss heuristics for good
performance, analyze the performance of the algorithm in the case of linear
regression, both one-dimensional and multidimensional, and outline the
algorithm's limitations.Comment: 16 pages, 5 figures, in Proceedings, SPIE Conference on Quantum
Computation and Quantum Information, pp. 116-127, April 21-22, 200
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