Searcharxiv⌕ Search

arXiv subjects

Herschel Rabitz

Publications and source records attributed to Herschel Rabitz.

141 records · Page 8Linked to original sources
arXiv2007

Optimal control of quantum gates and suppression of decoherence in a system of interacting two-level particles

Methods of optimal control are applied to a model system of interacting two-level particles (e.g., spin-half atomic nuclei or electrons or two-level atoms) to produce high-fidelity quantum gates while simultaneously negating the detrimental effect of decoherence. One set of particles functions as the quantum information processor, whose evolution is controlled by a time-dependent external field. The other particles are not directly controlled and serve as an effective environment, coupling to which is the source of decoherence. The control objective is to generate target one- and two-qubit unitary gates in the presence of strong environmentally-induced decoherence and under physically motivated restrictions on the control field. The quantum-gate fidelity, expressed in terms of a novel state-independent distance measure, is maximized with respect to the control field using combined genetic and gradient algorithms. The resulting high-fidelity gates demonstrate the feasibility of precisely guiding the quantum evolution via optimal control, even when the system complexity is exacerbated by environmental coupling. It is found that the gate duration has an important effect on the control mechanism and resulting fidelity. An analysis of the sensitivity of the gate performance to random variations in the system parameters reveals a significant degree of robustness attained by the optimal control solutions.

quant-ph↗
arXiv2006

Quantum control by von Neumann measurements

A general scheme is presented for controlling quantum systems using evolution driven by non-selective von Neumann measurements, with or without an additional tailored electromagnetic field. As an example, a 2-level quantum system controlled by non-selective quantum measurements is considered. The control goal is to find optimal system observables such that consecutive non-selective measurement of these observables transforms the system from a given initial state into a state which maximizes the expected value of a target operator (the objective). A complete analytical solution is found including explicit expressions for the optimal measured observables and for the maximal objective value given any target operator, any initial system density matrix, and any number of measurements. As an illustration, upper bounds on measurement-induced population transfer between the ground and the excited states for any number of measurements are found. The anti-Zeno effect is recovered in the limit of an infinite number of measurements. In this limit the system becomes completely controllable. The results establish the degree of control attainable by a finite number of measurements.

quant-ph↗
arXiv2006

Teaching the Environment to Control Quantum Systems

A non-equilibrium, generally time-dependent, environment whose form is deduced by optimal learning control is shown to provide a means for incoherent manipulation of quantum systems. Incoherent control by the environment (ICE) can serve to steer a system from an initial state to a target state, either mixed or in some cases pure, by exploiting dissipative dynamics. Implementing ICE with either incoherent radiation or a gas as the control is explicitly considered, and the environmental control is characterized by its distribution function. Simulated learning control experiments are performed with simple illustrations to find the shape of the optimal non-equilibrium distribution function that best affects the posed dynamical objectives.

quant-ph↗
arXiv2006

Foundations for Cooperating with Control Noise in the Manipulation of Quantum Dynamics

This paper develops the theoretical foundations for the ability of a control field to cooperate with noise in the manipulation of quantum dynamics. The noise enters as run-to-run variations in the control amplitudes, phases and frequencies with the observation being an ensemble average over many runs as is commonly done in the laboratory. Weak field perturbation theory is developed to show that noise in the amplitude and frequency components of the control field can enhance the process of population transfer in a multilevel ladder system. The analytical results in this paper support the point that under suitable conditions an optimal field can cooperate with noise to improve the control outcome.

quant-ph↗
arXiv2006

Cooperating or Fighting with Control Noise in the Optimal Manipulation of Quantum Dynamics

This paper investigates the impact of control field noise on the optimal manipulation of quantum dynamics. Simulations are performed on several multilevel quantum systems with the goal of population transfer in the presence of significant control noise. The noise enters as run-to-run variations in the control amplitude and phase with the observation being an ensemble average over many runs as is commonly done in the laboratory. A genetic algorithm with an improved elitism operator is used to find the optimal field that either fights against or cooperates with control field noise. When seeking a high control yield it is possible to find fields that successfully fight with the noise while attaining good quality stable results. When seeking modest control yields, fields can be found which are optimally shaped to cooperate with the noise and thereby drive the dynamics more efficiently. In general, noise reduces the coherence of the dynamics, but the results indicate that population transfer objectives can be met by appropriately either fighting or cooperating with noise, even when it is intense.

physics.chem-ph↗
arXiv2006

Cooperating or Fighting with Decoherence in the Optimal Control of Quantum Dynamics

This paper explores the use of laboratory closed-loop learning control to either fight or cooperate with decoherence in the optimal manipulation of quantum dynamics. Simulations of the processes are performed in a Lindblad formulation on multilevel quantum systems strongly interacting with the environment without spontaneous emission. When seeking a high control yield it is possible to find fields that successfully fight with decoherence while attaining a good quality yield. When seeking modest control yields, fields can be found which are optimally shaped to cooperate with decoherence and thereby drive the dynamics more efficiently. In the latter regime when the control field and the decoherence strength are both weak, a theoretical foundation is established to describe how they cooperate with each other. In general, the results indicate that the population transfer objectives can be effectively met by appropriately either fighting or cooperating with decoherence.

quant-ph↗
arXiv2006

On the distance between unitary propagators of quantum systems of differing dimensions

A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process with the propagator of the desired (ideal) process; the former being of a higher dimension then the latter. The proposed measure has the advantage of dealing with possibly correlated inputs, but at the expense of working on the whole space and not just the information bearing part as is usually the case, i.e., no partial trace operation is explicitly involved. It is also shown that the distance measure and an average measure of channel fidelity both depend on the size of the same matrix: as the matrix size increases, distance decreases and fidelity increases.

quant-ph↗
arXiv2006

Encoding a qubit into multilevel subspaces

We present a formalism for encoding the logical basis of a qubit into subspaces of multiple physical levels. The need for this multilevel encoding arises naturally in situations where the speed of quantum operations exceeds the limits imposed by the addressability of individual energy levels of the qubit physical system. A basic feature of the multilevel encoding formalism is the logical equivalence of different physical states and correspondingly, of different physical transformations. This logical equivalence is a source of a significant flexibility in designing logical operations, while the multilevel structure inherently accommodates fast and intense broadband controls thereby facilitating faster quantum operations. Another important practical advantage of multilevel encoding is the ability to maintain full quantum-computational fidelity in the presence of mixing and decoherence within encoding subspaces. The formalism is developed in detail for single-qubit operations and generalized for multiple qubits. As an illustrative example, we perform a simulation of closed-loop optimal control of single-qubit operations for a model multilevel system, and subsequently apply these operations at finite temperatures to investigate the effect of decoherence on operational fidelity.

quant-ph↗
arXiv2004

Optimal Experiment Design for Quantum State and Process Tomography and Hamiltonian Parameter Estimation

A number of problems in quantum state and system identification are addressed. Specifically, it is shown that the maximum likelihood estimation (MLE) approach, already known to apply to quantum state tomography, is also applicable to quantum process tomography (estimating the Kraus operator sum representation (OSR)), Hamiltonian parameter estimation, and the related problems of state and process (OSR) distribution estimation. Except for Hamiltonian parameter estimation, the other MLE problems are formally of the same type of convex optimization problem and therefore can be solved very efficiently to within any desired accuracy. Associated with each of these estimation problems, and the focus of the paper, is an optimal experiment design (OED) problem invoked by the Cramer-Rao Inequality: find the number of experiments to be performed in a particular system configuration to maximize estimation accuracy; a configuration being any number of combinations of sample times, hardware settings, prepared initial states, etc. We show that in all of the estimation problems, including Hamiltonian parameter estimation, the optimal experiment design can be obtained by solving a convex optimization problem. Software to solve the MLE and OED convex optimization problems is available upon request from the first author.

quant-ph↗
arXiv2004

Quantum State Detector Design: Optimal Worst-Case a posteriori Performance

The problem addressed is to design a detector which is maximally sensitive to specific quantum states. Here we concentrate on quantum state detection using the worst-case a posteriori probability of detection as the design criterion. This objective is equivalent to asking the question: if the detector declares that a specific state is present, what is the probability of that state actually being present? We show that maximizing this worst-case probability (maximizing the smallest possible value of this probability) is a quasiconvex optimization over the matrices of the POVM (positive operator valued measure) which characterize the measurement apparatus. We also show that with a given POVM, the optimization is quasiconvex in the matrix which characterizes the Kraus operator sum representation (OSR) in a fixed basis. We use Lagrange Duality Theory to establish the optimality conditions for both deterministic and randomized detection. We also examine the special case of detecting a single pure state. Numerical aspects of using convex optimization for quantum state detection are also discussed.

quant-ph↗
arXiv2002

Beable trajectories for revealing quantum control mechanisms

The dynamics induced while controlling quantum systems by optimally shaped laser pulses have often been difficult to understand in detail. A method is presented for quantifying the importance of specific sequences of quantum transitions involved in the control process. The method is based on a ``beable'' formulation of quantum mechanics due to John Bell that rigorously maps the quantum evolution onto an ensemble of stochastic trajectories over a classical state space. Detailed mechanism identification is illustrated with a model 7-level system. A general procedure is presented to extract mechanism information directly from closed-loop control experiments. Application to simulated experimental data for the model system proves robust with up to 25% noise.

quant-ph↗
arXiv2001

Optimal use of time dependent probability density data to extract potential energy surfaces

A novel algorithm was recently presented to utilize emerging time dependent probability density data to extract molecular potential energy surfaces. This paper builds on the previous work and seeks to enhance the capabilities of the extraction algorithm: An improved method of removing the generally ill-posed nature of the inverse problem is introduced via an extended Tikhonov regularization and methods for choosing the optimal regularization parameters are discussed. Several ways to incorporate multiple data sets are investigated, including the means to optimally combine data from many experiments exploring different portions of the potential. Results are presented on the stability of the inversion procedure, including the optimal combination scheme, under the influence of data noise. The method is applied to the simulated inversion of a double well system.

physics.chem-ph↗
arXiv2000

Optimal Control of Molecular Motion Expressed Through Quantum Fluid Dynamics

A quantum fluid dynamic control formulation is presented for optimally manipulating atomic and molecular systems. In quantum fluid dynamic the control quantum system is expressed in terms of the probability density and the quantum current. This choice of variables is motivated by the generally expected slowly varying spatial-temporal dependence of the fluid dynamical variables. The quantum fluid dynamic approach is illustrated for manipulation of the ground electronic state dynamics of HCl induced by an external electric field.

physics.chem-ph↗
arXiv1996

A Simplified Approach to Optimally Controlled Quantum Dynamics

A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously[J. Botina, H. Rabitz and N. Rahman, J. chem. Phys. Vol. 102, pag. 226 (1995)]. Quantum Lagrange multiplier functions are used to preserve a chosen subset of the observable dynamics of interest. As a result, a corresponding small set of Lagrange multipliers needs to be calculated and they are only a function of time. This is a considerable simplification over traditional quantum optimal control theory[S. shi and H. Rabitz, comp. Phys. Comm. Vol. 63, pag. 71 (1991)]. The success of the new approach is based on taking advantage of the multiplicity of solutions to virtually any problem of quantum control to meet a physical objective. A family of such simplified formulations is introduced and numerically tested. Results are presented for these algorithms and compared with previous reported work on a model problem for selective unimolecular reaction induced by an external optical electric field.

physics.chem-ph↗