2,247 research outputs found
Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes
Among the predictive hidden Markov models that describe a given stochastic
process, the {\epsilon}-machine is strongly minimal in that it minimizes every
R\'enyi-based memory measure. Quantum models can be smaller still. In contrast
with the {\epsilon}-machine's unique role in the classical setting, however,
among the class of processes described by pure-state hidden quantum Markov
models, there are those for which there does not exist any strongly minimal
model. Quantum memory optimization then depends on which memory measure best
matches a given problem circumstance.Comment: 14 pages, 14 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/uemum.ht
Exploration of Reaction Pathways and Chemical Transformation Networks
For the investigation of chemical reaction networks, the identification of
all relevant intermediates and elementary reactions is mandatory. Many
algorithmic approaches exist that perform explorations efficiently and
automatedly. These approaches differ in their application range, the level of
completeness of the exploration, as well as the amount of heuristics and human
intervention required. Here, we describe and compare the different approaches
based on these criteria. Future directions leveraging the strengths of chemical
heuristics, human interaction, and physical rigor are discussed.Comment: 48 pages, 4 figure
Control of quantum phenomena: Past, present, and future
Quantum control is concerned with active manipulation of physical and
chemical processes on the atomic and molecular scale. This work presents a
perspective of progress in the field of control over quantum phenomena, tracing
the evolution of theoretical concepts and experimental methods from early
developments to the most recent advances. The current experimental successes
would be impossible without the development of intense femtosecond laser
sources and pulse shapers. The two most critical theoretical insights were (1)
realizing that ultrafast atomic and molecular dynamics can be controlled via
manipulation of quantum interferences and (2) understanding that optimally
shaped ultrafast laser pulses are the most effective means for producing the
desired quantum interference patterns in the controlled system. Finally, these
theoretical and experimental advances were brought together by the crucial
concept of adaptive feedback control, which is a laboratory procedure employing
measurement-driven, closed-loop optimization to identify the best shapes of
femtosecond laser control pulses for steering quantum dynamics towards the
desired objective. Optimization in adaptive feedback control experiments is
guided by a learning algorithm, with stochastic methods proving to be
especially effective. Adaptive feedback control of quantum phenomena has found
numerous applications in many areas of the physical and chemical sciences, and
this paper reviews the extensive experiments. Other subjects discussed include
quantum optimal control theory, quantum control landscapes, the role of
theoretical control designs in experimental realizations, and real-time quantum
feedback control. The paper concludes with a prospective of open research
directions that are likely to attract significant attention in the future.Comment: Review article, final version (significantly updated), 76 pages,
accepted for publication in New J. Phys. (Focus issue: Quantum control
The instanton method and its numerical implementation in fluid mechanics
A precise characterization of structures occurring in turbulent fluid flows
at high Reynolds numbers is one of the last open problems of classical physics.
In this review we discuss recent developments related to the application of
instanton methods to turbulence. Instantons are saddle point configurations of
the underlying path integrals. They are equivalent to minimizers of the related
Freidlin-Wentzell action and known to be able to characterize rare events in
such systems. While there is an impressive body of work concerning their
analytical description, this review focuses on the question on how to compute
these minimizers numerically. In a short introduction we present the relevant
mathematical and physical background before we discuss the stochastic Burgers
equation in detail. We present algorithms to compute instantons numerically by
an efficient solution of the corresponding Euler-Lagrange equations. A second
focus is the discussion of a recently developed numerical filtering technique
that allows to extract instantons from direct numerical simulations. In the
following we present modifications of the algorithms to make them efficient
when applied to two- or three-dimensional fluid dynamical problems. We
illustrate these ideas using the two-dimensional Burgers equation and the
three-dimensional Navier-Stokes equations
Quantum calcium-ion interactions with EEG
Previous papers have developed a statistical mechanics of neocortical
interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated
Annealing (ASA) has been developed to perform fits to such nonlinear stochastic
systems. An N-dimensional path-integral algorithm for quantum systems,
qPATHINT, has been developed from classical PATHINT. Both fold short-time
propagators (distributions or wave functions) over long times. Previous papers
applied qPATHINT to two systems, in neocortical interactions and financial
options. \textbf{Objective}: In this paper the quantum path-integral for
Calcium ions is used to derive a closed-form analytic solution at arbitrary
time that is used to calculate interactions with classical-physics SMNI
interactions among scales. Using fits of this SMNI model to EEG data, including
these effects, will help determine if this is a reasonable approach.
\textbf{Method}: Methods of mathematical-physics for optimization and for path
integrals in classical and quantum spaces are used for this project. Studies
using supercomputer resources tested various dimensions for their scaling
limits. In this paper the quantum path-integral is used to derive a closed-form
analytic solution at arbitrary time that is used to calculate interactions with
classical-physics SMNI interactions among scales. \textbf{Results}: The
mathematical-physics and computer parts of the study are successful, in that
there is modest improvement of cost/objective functions used to fit EEG data
using these models. \textbf{Conclusion}: This project points to directions for
more detailed calculations using more EEG data and qPATHINT at each time slice
to propagate quantum calcium waves, synchronized with PATHINT propagation of
classical SMNI.Comment: published in Sc
What is the Computational Value of Finite Range Tunneling?
Quantum annealing (QA) has been proposed as a quantum enhanced optimization
heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling
can provide considerable computational advantage. For a crafted problem
designed to have tall and narrow energy barriers separating local minima, the
D-Wave 2X quantum annealer achieves significant runtime advantages relative to
Simulated Annealing (SA). For instances with 945 variables, this results in a
time-to-99%-success-probability that is times faster than SA
running on a single processor core. We also compared physical QA with Quantum
Monte Carlo (QMC), an algorithm that emulates quantum tunneling on classical
processors. We observe a substantial constant overhead against physical QA:
D-Wave 2X again runs up to times faster than an optimized
implementation of QMC on a single core. We note that there exist heuristic
classical algorithms that can solve most instances of Chimera structured
problems in a timescale comparable to the D-Wave 2X. However, we believe that
such solvers will become ineffective for the next generation of annealers
currently being designed. To investigate whether finite range tunneling will
also confer an advantage for problems of practical interest, we conduct
numerical studies on binary optimization problems that cannot yet be
represented on quantum hardware. For random instances of the number
partitioning problem, we find numerically that QMC, as well as other algorithms
designed to simulate QA, scale better than SA. We discuss the implications of
these findings for the design of next generation quantum annealers.Comment: 17 pages, 13 figures. Edited for clarity, in part in response to
comments. Added link to benchmark instance
A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering
Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PD
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