Bellman equations for optimal feedback control of qubit states

Using results from quantum filtering theory and methods from classical control theory, we derive an optimal control strategy for an open two-level system (a qubit in interaction with the electromagnetic field) controlled by a laser. The aim is to optimally choose the laser's amplitude and phase in order to drive the system into a desired state. The Bellman equations are obtained for the case of diffusive and counting measurements for vacuum field states. A full exact solution of the optimal control problem is given for a system with simpler, linear, dynamics. These linear dynamics can be obtained physically by considering a two-level atom in a strongly driven, heavily damped, optical cavity.Comment: 10 pages, no figures, replaced the simpler model in section

Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves

Two-frequency Wigner distribution is introduced to capture the asymptotic behavior of the space-frequency correlation of paraxial waves in the radiative transfer limits. The scaling limits give rises to deterministic transport-like equations. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker-Planck-like differential equation in the phase space. The solutions to these equations have a probabilistic representation which can be simulated by Monte Carlo method. When the medium fluctuates more rapidly in the longitudinal direction, the corresponding Fokker-Planck-like equation can be solved exactly.Comment: typos correcte

A reduced complexity numerical method for optimal gate synthesis

Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate design problem is equivalent to the solution of an associated optimal control problem, the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality free techniques) that determine the optimal control thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, used in previous literature. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on $SU(4)$- a problem that is computationally intractable by grid based approaches.Comment: 8 pages, 4 figure

The filtering equations revisited

The problem of nonlinear filtering has engendered a surprising number of mathematical techniques for its treatment. A notable example is the change-of--probability-measure method originally introduced by Kallianpur and Striebel to derive the filtering equations and the Bayes-like formula that bears their names. More recent work, however, has generally preferred other methods. In this paper, we reconsider the change-of-measure approach to the derivation of the filtering equations and show that many of the technical conditions present in previous work can be relaxed. The filtering equations are established for general Markov signal processes that can be described by a martingale-problem formulation. Two specific applications are treated

Assessment of postoperative nausea and vomiting after bariatric surgery using a validated questionnaire

BACKGROUND: Postoperative nausea and vomiting (PONV) is known to occur after bariatric surgery, with over two thirds of patients affected. However, variability exists in how to objectively measure PONV. OBJECTIVES: The goals of the present study were to use a validated, patient-centered scoring tool, the Rhodes Index of Nausea, Vomiting, and Retching to measure the severity of PONV after bariatric surgery, to directly compare PONV between patients who underwent laparoscopic sleeve gastrectomy (LSG) and laparoscopic Roux-en-Y gastric bypass (LRYGB), and to identify risk factors for the development of PONV after bariatric surgery. SETTING: Barnes-Jewish Hospital/Washington University School of Medicine, St. Louis, Missouri, United States of America. METHODS: The Washington University Weight Loss Surgery team prospectively surveyed patients from January 1, 2017 to December 1, 2018 at the following 6 different timepoints: postoperative day (POD) 0, POD 1, POD 2, POD 3 to 4, the first postoperative outpatient visit (POV 1: POD 5-25), and the second postoperative visit (POV 2: POD 25-50). At each timepoint, a cumulative Rhodes score was calculated from the sum of 8 questions. The American Society for Metabolic and Bariatric Surgery Accreditation and Quality Improvement Program database was used to collect patient demographic characteristics and perioperative clinical data. RESULTS: A total of 274 patients met study criteria and completed 605 Rhodes questionnaires. Two hundred fifty Rhodes questionnaires were completed by patients after SG and 355 were completed by patients after LRYGB. Total Rhodes scores are statistically higher in LSG patients compared with patients who underwent LRYGB (LSG = 5.45 ± 6.27; LRYGB = 3.08 ± 4.19, P = .0002). Additionally, at the earlier timepoints, scores were higher among patients who underwent LSG than those who had undergone LRYGB as follows: POD 0 (LSG = 6.96 ± 6.50; LRYGB = 2.89 ± 2.90, P = .0115), POD 1 (LSG = 8.20 ± 6.76; LRYGB = 2.88 ± 3.44, P \u3c .0001), and POD 2 (LSG = 4.05 ± 4.88; LRYGB = 2.06 ± 3.43, P = .05). On subset analysis, examining patients who either underwent an LSG or LRYGB, both procedures had a statistically significant PONV peak emerge on POV 2. Last, overall Rhodes scores were statistically higher in female patients compared with male patients (female: 4.43 ± 5.46; male: 2.35 ± 3.90, P = .021). Although the magnitude of the difference varied somewhat across POD time intervals, the difference was most pronounced at POV 2. CONCLUSIONS: This is the largest study using a validated nausea and vomiting questionnaire to objectively measure PONV after bariatric surgery. The factors found to be most associated with increased PONV were LSG and female sex. Ultimately, these data can help bariatric surgery programs, including Washington University Weight Loss Surgery, identify patients who may require more intensive treatment of PONV, particularly POD 0 to 2, and help to identify patients that continue to struggle with PONV in the later surgical recovery phase

A Quantum Langevin Formulation of Risk-Sensitive Optimal Control

In this paper we formulate a risk-sensitive optimal control problem for continuously monitored open quantum systems modelled by quantum Langevin equations. The optimal controller is expressed in terms of a modified conditional state, which we call a risk-sensitive state, that represents measurement knowledge tempered by the control purpose. One of the two components of the optimal controller is dynamic, a filter that computes the risk-sensitive state. The second component is an optimal control feedback function that is found by solving the dynamic programming equation. The optimal controller can be implemented using classical electronics. The ideas are illustrated using an example of feedback control of a two-level atom

Theodicy and End-of-Life Care

Acknowledgments The section on Islamic perspective is contributed by information provided by Imranali Panjwani, Tutor in Theology & Religious Studies, King's College London.Peer reviewedPublisher PD

Links between traumatic brain injury and ballistic pressure waves originating in the thoracic cavity and extremities

Identifying patients at risk of traumatic brain injury (TBI) is important because research suggests prophylactic treatments to reduce risk of long-term sequelae. Blast pressure waves can cause TBI without penetrating wounds or blunt force trauma. Similarly, bullet impacts distant from the brain can produce pressure waves sufficient to cause mild to moderate TBI. The fluid percussion model of TBI shows that pressure impulses of 15-30 psi cause mild to moderate TBI in laboratory animals. In pigs and dogs, bullet impacts to the thigh produce pressure waves in the brain of 18-45 psi and measurable injury to neurons and neuroglia. Analyses of research in goats and epidemiological data from shooting events involving humans show high correlations (r > 0.9) between rapid incapacitation and pressure wave magnitude in the thoracic cavity. A case study has documented epilepsy resulting from a pressure wave without the bullet directly hitting the brain. Taken together, these results support the hypothesis that bullet impacts distant from the brain produce pressure waves that travel to the brain and can retain sufficient magnitude to induce brain injury. The link to long-term sequelae could be investigated via epidemiological studies of patients who were gunshot in the chest to determine whether they experience elevated rates of epilepsy and other neurological sequelae

Bayesian optimization for materials design

We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian process regression, which allows predicting the performance of a new design based on previously tested designs. After providing a detailed introduction to Gaussian process regression, we introduce two Bayesian optimization methods: expected improvement, for design problems with noise-free evaluations; and the knowledge-gradient method, which generalizes expected improvement and may be used in design problems with noisy evaluations. Both methods are derived using a value-of-information analysis, and enjoy one-step Bayes-optimality