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.

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.

On the relationship between quantum control landscape structure and optimization complexity

2008 ◽  
Vol 128 (15) ◽  
pp. 154117 ◽  
Author(s):  
Katharine Moore ◽  
Michael Hsieh ◽  
Herschel Rabitz
Keyword(s):  
Landscape Structure ◽  
Quantum Control ◽  
The Relationship ◽  
Control Landscape

Determination of Underwater Plate Dynamics Using Laser Beams

1974 ◽  
Vol 96 (3) ◽  
pp. 722-728
Author(s):  
Rudolph E. Croteau ◽  
Herman E. Sheets
Keyword(s):  
Near Field ◽  
Surface Displacement ◽  
Coupled System ◽  
Green Laser ◽  
Testing Facility ◽  
Acoustic Testing ◽  
Propeller Blades ◽  
The Relationship ◽  
Made In

Underwater plate vibration and its associated noise are of interest for the analysis of ship structures, propeller blades, and other areas of underwater acoustics. In order to analyze the relationship between a plate vibrating underwater and the acoustic pressure in the near-field, optical interferometric holography, using a blue-green laser beam, was used to determine surface displacement for the vibrating plate, which was excited through a fluid-coupled system. Acoustic measurements of the same source were made in a water tower concurrently with the holography and later at a precision acoustic testing facility. This method permits prediction of underwater plate modal frequencies and shapes with high accuracy.

scholarly journals Experimental exploration over a quantum control landscape through nuclear magnetic resonance

2014 ◽  
Vol 89 (3) ◽  
Author(s):  
Qiuyang Sun ◽  
István Pelczer ◽  
Gregory Riviello ◽  
Re-Bing Wu ◽  
Herschel Rabitz
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Quantum Control ◽  
Control Landscape ◽  
Nuclear Magnetic

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>

scholarly journals Generalized approximate boundary synchronization for a coupled system of wave equations

2020 ◽  
Author(s):  
Yanyan Wang
Keyword(s):  
Wave Equations ◽  
Dirichlet Boundary ◽  
Coupled System ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Exact Boundary ◽  
Boundary Controls ◽  
The Relationship ◽  
Exact Boundary Synchronization ◽  
Dirichlet Boundary Controls

In this paper, we consider the generalized approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls. We analyse the relationship between the generalized approximate boundary synchronization and the generalized exact boundary synchronization, give a sufficient condition to realize the generalized approximate boundary synchronization and a necessary condition in terms of Kalman’s matrix, and show the meaning of the number of total controls. Besides, by the generalized synchronization decomposition, we define the generalized approximately synchronizable state, and obtain its properties and a sufficient condition for it to be independent of applied boundary controls.

Exploring the transition-probability-control landscape of open quantum systems: Application to a two-level case

2013 ◽  
Vol 88 (3) ◽  
Author(s):  
Fei Yang ◽  
Shuang Cong ◽  
Ruixing Long ◽  
Tak-San Ho ◽  
Rebing Wu ◽  
...  
Keyword(s):  
Open Quantum Systems ◽  
Transition Probability ◽  
Quantum Systems ◽  
Open Quantum ◽  
Control Landscape

scholarly journals Common foundations of optimal control across the sciences: evidence of a free lunch

2017 ◽  
Vol 375 (2088) ◽  
pp. 20160210 ◽  
Author(s):  
Benjamin Russell ◽  
Herschel Rabitz
Keyword(s):  
Evolutionary Biology ◽  
Quantum Control ◽  
Mathematical Framework ◽  
Optimal Controls ◽  
Control Variables ◽  
Common Control ◽  
Algorithmic Search ◽  
Set Up ◽  
Open Question ◽  
Control Landscape

A common goal in the sciences is optimization of an objective function by selecting control variables such that a desired outcome is achieved. This scenario can be expressed in terms of a control landscape of an objective considered as a function of the control variables. At the most basic level, it is known that the vast majority of quantum control landscapes possess no traps, whose presence would hinder reaching the objective. This paper reviews and extends the quantum control landscape assessment, presenting evidence that the same highly favourable landscape features exist in many other domains of science. The implications of this broader evidence are discussed. Specifically, control landscape examples from quantum mechanics, chemistry and evolutionary biology are presented. Despite the obvious differences, commonalities between these areas are highlighted within a unified mathematical framework. This mathematical framework is driven by the wide-ranging experimental evidence on the ease of finding optimal controls (in terms of the required algorithmic search effort beyond the laboratory set-up overhead). The full scope and implications of this observed common control behaviour pose an open question for assessment in further work. This article is part of the themed issue ‘Horizons of cybernetical physics’.

Sign in / Sign up

Export Citation Format

Share Document