scholarly journals Quantifying the Unitary Generation of Coherence from Thermal Quantum Systems

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 810 ◽  
Author(s):  
Shimshon Kallush ◽  
Aviv Aroch ◽  
Ronnie Kosloff
Keyword(s):  
External Field ◽  
Quantum Control ◽  
Population Distribution ◽  
Thermal State ◽  
Optimization Procedure ◽  
Global Optimum ◽  
Quantum Systems ◽  
Final Energy ◽  
Optimization Task ◽  
Unitary Transformations

Coherence is associated with transient quantum states; in contrast, equilibrium thermal quantum systems have no coherence. We investigate the quantum control task of generating maximum coherence from an initial thermal state employing an external field. A completely controllable Hamiltonian is assumed allowing the generation of all possible unitary transformations. Optimizing the unitary control to achieve maximum coherence leads to a micro-canonical energy distribution on the diagonal energy representation. We demonstrate such a control scenario starting from a given Hamiltonian applying an external field, reaching the control target. Such an optimization task is found to be trap-less. By constraining the amount of energy invested by the control, maximum coherence leads to a canonical energy population distribution. When the optimization procedure constrains the final energy too tightly, local suboptimal traps are found. The global optimum is obtained when a small Lagrange multiplier is employed to constrain the final energy. Finally, we explore the task of generating coherences restricted to be close to the diagonal of the density matrix in the energy representation.

scholarly journals Quantum Control Landscapes Beyond the Dipole Approximation: Controllability, Singular Controls, and Resources

2021 ◽  
Vol 9 ◽  
Author(s):  
Benjamin Russell ◽  
Re-Bing Wu ◽  
Herschel Rabitz
Keyword(s):  
Quantum Control ◽  
Coupled System ◽  
Dipole Approximation ◽  
Quantum Systems ◽  
Control Field ◽  
Local Optima ◽  
Singular Controls ◽  
Unitary Transformations ◽  
The Relationship ◽  
Control Landscape

We investigate the control landscapes of closed n-level quantum systems beyond the dipole approximation by including a polarizability term in the Hamiltonian. The latter term is quadratic in the control field. Theoretical analysis of singular controls is presented, which are candidates for producing landscape traps. The results for considering the presence of singular controls are compared to their counterparts in the dipole approximation (i.e., without polarizability). A numerical analysis of the existence of traps in control landscapes for generating unitary transformations beyond the dipole approximation is made upon including the polarizability term. An extensive exploration of these control landscapes is achieved by creating many random Hamiltonians which include terms linear and quadratic in a single control field. The discovered singular controls are all found not to be local optima. This result extends a great body of recent work on typical landscapes of quantum systems where the dipole approximation is made. We further investigate the relationship between the magnitude of the polarizability and the fluence of the control resulting from optimization. It is also shown that including a polarizability term in an otherwise uncontrollable dipole coupled system removes traps from the corresponding control landscape by restoring controllability. We numerically assess the effect of a polarizability term on a known example of a particular three-level Λ-system with a second order trap in its control landscape. It is found that the addition of the polarizability removes the trap from the landscape. The general practical control implications of these simulations are discussed.

THE TRAPPED-ION QUBIT: COHERENT CONTROL IN INFINITE-DIMENSIONAL QUANTUM SYSTEMS

2009 ◽  
Vol 24 (32) ◽  
pp. 2565-2578
Author(s):  
C. RANGAN
Keyword(s):  
Quantum Computing ◽  
Quantum System ◽  
Quantum Control ◽  
Coherent Control ◽  
Quantum Information Processing ◽  
Quantum Systems ◽  
Infinite Dimensional ◽  
Trapped Ion ◽  
Rich Variety ◽  
Control Research

Theories of quantum control have, until recently, made the assumption that the Hilbert space of a quantum system can be truncated to finite dimensions. Such truncations, which can be achieved for most quantum systems via bandwidth restrictions, have enabled the development of a rich variety of quantum control and optimal control schemes. Recent studies in quantum information processing have addressed the control of infinite-dimensional quantum systems such as the quantum states of a trapped-ion. Controllability in an infinite-dimensional quantum system is hard to prove with conventional methods, and infinite-dimensional systems provide unique challenges in designing control fields. In this paper, we will discuss the control of a popular system for quantum computing the trapped-ion qubit. This system, modeled by a spin-half particle coupled to a quantized harmonic oscillator, is an example for a surprisingly rich variety of control problems. We will show how this infinite-dimensional quantum system can be examined via the lens of the Finite Controllability Theorem, two-color STIRAP, the generalized Heisenberg system, etc. These results are important from the viewpoint of developing more efficient quantum control protocols, particularly in quantum computing systems. This work shows how one can expand the scope of quantum control research to beyond that of finite-dimensional quantum systems.

scholarly journals Local Spin and Open Quantum Systems: Clarifying Misconceptions, Unifying Approaches

2020 ◽  
Author(s):  
Angel Martín Pendás ◽  
Evelio Francisco
Keyword(s):  
Quantum Control ◽  
Open Systems ◽  
Open Quantum Systems ◽  
Real Space ◽  
Quantum Systems ◽  
Spin Coupling ◽  
Molecular Systems ◽  
Open Quantum ◽  
Local Spin

<p>We now show that Clark and Davidson local spins operators are perfectly defined subsystem operators if a fragment is taken as an <i>open quantum system</i> (OQS). Open systems have become essential in quantum control and quantum computation, but have not received much attention in Chemistry. We have already shown (<i>J. Chem. Theory Comput</i>. <b>2018</b>, <i>15</i>, 1079) how real space OQSs can be defined in molecular systems and how they offer new insights relating quantum mechanical entaglement and chemical bonding. The OQS account of local spin that we offer yields a rigorous, yet easily accessible way to rationalize local spin values. A fragment is found in a mixed state direct sum of sectors characterized by different number of electrons that occur with different probabilities. The local spin is then a weighted sum of otherwise standard <i>S</i>(<i>S</i>+1) values. With OQS glasses, it is obvious that atomic or fragment spins should not vanish. Our approach thus casts doubts on any procedure used to annihilate them, like those used by Mayer and coworkers. OQS local spins allow for a fruitful use of models. One can propose easily sector probabilities for localized, covalent, ionic, zwitterionic, etc. situations, and examine their ideal local spins. We have mapped all 2c-2e cases, and shown how to do that in general multielectron cases. The role of electron correlation is also studied by tuning the Hubbard U/t parameter for H chains. Correlation induced localization changes the spin-coupling patterns even qualitatively, and show how the limiting antiferromagnet arises.</p>

PROBABILITY DENSITY FUNCTION CONTROL OF QUANTUM SYSTEMS

2011 ◽  
Vol 25 (17) ◽  
pp. 2289-2297 ◽  
Author(s):  
YI-FAN XING ◽  
JUN WU
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Quantum Control ◽  
Quantum Systems ◽  
Quantum Model ◽  
Control Engineering ◽  
Control Of Quantum Systems ◽  
Probability Density Function Pdf ◽  
Specific Control

This paper proposes a new method of controlling quantum systems via probability density function (PDF) control. Based on the quantum model from the PDF perspective, two specific control algorithms are proposed for the general case and limited input energy, respectively. Unlike traditional quantum control methods, this method directly controls the probability distribution of the quantum state. It provides an alternative method for quantum control engineering.

Ranked-Based Sensitivity Analysis for Size Optimization of Structures

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Babak Dizangian ◽  
Mohammad Reza Ghasemi
Keyword(s):  
Sensitivity Analysis ◽  
Design Space ◽  
Optimization Technique ◽  
Optimization Procedure ◽  
Global Optimum ◽  
Size Optimization ◽  
Second Phase ◽  
Local Optimum ◽  
Blast Search ◽  
Sliding Technique

This article proposes a novel ranked-based method for size optimization of structures. This method uses violation-based sensitivity analysis and borderline adaptive sliding technique (ViS-BLAST) on the margin of feasible nonfeasible (FNF) design space. ViS-BLAST maybe considered a multiphase optimization technique, where in the first phase, the first arbitrary local optimum is found by few analyses and in the second phase, a sequence of local optimum points is found through jumps and BLASTs until the global optimum is found. In fact, this technique reaches a sensitive margin zone where the global optimum is located, with a small number of analyses, utilizing a space-degradation strategy (SDS). This strategy substantially degrades the high order searching space and then proceeds with the proposed ViS-BLAST search for the optimum design. Its robustness and effectiveness are then defied by some well-known benchmark examples. The ViS-BLAST not only speeds up the optimization procedure but also it ensures nonviolated optimum designs.

Design Optimization of Power Plants by Considering Multiple Partial Load Operation Points

2007 ◽  
Author(s):  
Marc Ju¨des ◽  
George Tsatsaronis
Keyword(s):  
Design Optimization ◽  
Power Plants ◽  
Optimization Procedure ◽  
Optimization Methods ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Optimization Task ◽  
Operation Conditions ◽  
Partial Load ◽  
Conventional Optimization

The design optimization of complex energy conversion systems requires the consideration of typical operation conditions. Due to the complex optimization task, conventional optimization methods normally take into account only one operation point that is, in the majority of cases, the full load case. To guarantee good operation at partial loads additional operation conditions have to be taken into account during the optimization procedure. The optimization task described in this article considers altogether four different operation points of a cogeneration plant. Modelling requirements, such as the equations that describe the partial load behavior of single components, are described as well as the problems that occur, when nonlinear and nonconvex equations are used. For the solution of the resulting non-convex mixed-integer nonlinear programming (MINLP) problem, the solver LaGO is used, which requires that the optimization problem is formulated in GAMS. The results of the conventional optimization approach are compared to the results of the new method. It is shown, that without consideration of different operation points, a flexible operation of the plant may be impossible.

scholarly journals General approach to optimize settings of ship radars repair procedures

2018 ◽  
Vol 234 ◽  
pp. 01008
Author(s):  
Evgeni Guglev ◽  
Chavdar Alexandrov
Keyword(s):  
Global Optimization ◽  
Task Assignment ◽  
Global Optimum ◽  
Scanning Time ◽  
Optimization Task ◽  
Setting Process ◽  
Repair Procedure ◽  
Relevant Group ◽  
Automatic Search ◽  
Electrical Components

A number of possible formal methods for constructing an approach to solve the problem of global optimization of the setting process of ship radars repair procedure are introduced in this paper. The basis of the formalized task assignment is the selection of a sequence of operations related to determining the corresponding values of the electronic (electrical) components of radars, providing the global optimum of the created imitation model of the whole task with the corresponding subtasks. The algorithm of the global optimization task is built in the form of imitation experimental procedures with a multi-alternative optimization model. The multi-plan character (taking into account the different ranges) and the multi-criteria of such an experiment require an automatic search for optimizing the scanning at different ranges. The alternative for inclusion in the relevant group, with good result achieved is set in accordance with expert estimations (for the time of the scanning), Boolean variables (alternative for the inclusion of different ranges) or stochastic variables – by nomograms. The six-steps method (for six different ranges) is presented as a sequence of achieved optimums for the different ranges. The optimal set of functions determined by the task solution method is a solution of a stochastic problem including scanning time, pulse duration and ranges.

Convex Optimized Population Receptive Field (CO-pRF) Mapping

2017 ◽  
Author(s):  
David Slater ◽  
Lester Melie-Garcia ◽  
Stanislaw Adaszewski ◽  
Kendrick Kay ◽  
Antoine Lutti ◽  
...  
Keyword(s):  
Receptive Field ◽  
Human Brain ◽  
Linear Optimization ◽  
Model Fitting ◽  
Optimization Procedure ◽  
Global Optimum ◽  
Parameter Estimates ◽  
Estimation Algorithms ◽  
Sensory Processes

Population receptive field (pRF) mapping represents an invaluable non-invasive tool for the study of sensory organization and plasticity within the human brain. Despite the very appealing result that fMRI derived pRF measures agree well with measurements made from other fields of neuroscience, current techniques often require very computationally expensive non-linear optimization procedures to fit the models to the data which are also vulnerable to bias due local minima issues. In this work we present a general framework for pRF model estimation termed Convex Optimized Population Receptive Field (CO-pRF) mapping and show how the pRF fitting problem can be linearized in order to be solved by extremely fast and efficient algorithms. The framework is general and can be readily applied to a variety of pRF models and measurement schemes. We provide an example of the CO-pRF methodology as applied to a computational neuroimaging approach used to map sensory processes in human visual cortex - the CSS-pRF model. Via simulation and in-vivo fMRI results we demonstrate that the CO-pRF approach achieves robust model fitting even in the presence of noise or reduced data, providing parameter estimates closer to the global optimum across 93% of in-vivo responses as compared to a typical nonlinear optimization procedure. Furthermore the example CO-pRF application substantially reduced model fitting times by a factor of 50. We hope that the availability of such highly accelerated and reliable pRF estimation algorithms will facilitate the spread of pRF techniques to larger imaging cohorts and the future study of neurological disorders and plasticity within the human brain.

Optimization of fuels from waste composition with application of genetic algorithm

2014 ◽  
Vol 32 (5) ◽  
pp. 423-433 ◽  
Author(s):  
Małgorzata Wzorek
Keyword(s):  
Genetic Algorithm ◽  
Sewage Sludge ◽  
Calorific Value ◽  
Optimization Procedure ◽  
Cement Industry ◽  
Meat And Bone Meal ◽  
Bone Meal ◽  
Optimization Task ◽  
Coal Slime

The objective of this article is to elaborate a method to optimize the composition of the fuels from sewage sludge (PBS fuel – fuel based on sewage sludge and coal slime, PBM fuel – fuel based on sewage sludge and meat and bone meal, PBT fuel – fuel based on sewage sludge and sawdust). As a tool for an optimization procedure, the use of a genetic algorithm is proposed. The optimization task involves the maximization of mass fraction of sewage sludge in a fuel developed on the basis of quality-based criteria for the use as an alternative fuel used by the cement industry. The selection criteria of fuels composition concerned such parameters as: calorific value, content of chlorine, sulphur and heavy metals. Mathematical descriptions of fuel compositions and general forms of the genetic algorithm, as well as the obtained optimization results are presented. The results of this study indicate that the proposed genetic algorithm offers an optimization tool, which could be useful in the determination of the composition of fuels that are produced from waste.

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