Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, subriemannian, and Finslerian manifolds. These results generalize the results of Nielsen, Dowling, Gu, and Doherty, Science 311, 1133-1135 (2006), which showed that the gate complexity can be related to distances on a Riemannian manifoldComment: 7 Pages Added Full Names to Author

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

On the suppression of the diffusion and the quantum nature of a cavity mode. Optical bistability; forces and friction in driven cavities

A new analytical method is presented here, offering a physical view of driven cavities where the external field cannot be neglected. We introduce a new dimensionless complex parameter, intrinsically linked to the cooperativity parameter of optical bistability, and analogous to the scaled Rabbi frequency for driven systems where the field is classical. Classes of steady states are iteratively constructed and expressions for the diffusion and friction coefficients at lowest order also derived. They have in most cases the same mathematical form as their free-space analog. The method offers a semiclassical explanation for two recent experiments of one atom trapping in a high Q cavity where the excited state is significantly saturated. Our results refute both claims of atom trapping by a quantized cavity mode, single or not. Finally, it is argued that the parameter newly constructed, as well as the groundwork of this method, are at least companions of the cooperativity parameter and its mother theory. In particular, we lay the stress on the apparently more fundamental role of our structure parameter.Comment: 24 pages, 7 figures. Submitted to J. Phys. B: At. Mol. Opt. Phy

Preoperative Narcotic Use, Impaired Ambulation Status, and Increased Intraoperative Blood Loss Are Independent Risk Factors for Complications Following Posterior Cervical Laminectomy and Fusion Surgery.

ObjectiveThis retrospective cohort study seeks to identify risk factors associated with complications following posterior cervical laminectomy and fusion (PCLF) surgery.MethodsAdults undergoing PCLF from 2012 through 2018 at a single center were identified. Demographic and radiographic data, surgical characteristics, and complication rates were compared. Multivariate logistic regression models identified independent predictors of complications following surgery.ResultsA total of 196 patients met the inclusion criteria and were included in the study. The medical, surgical, and overall complication rates were 10.2%, 23.0%, and 29.1% respectively. Risk factors associated with medical complications in multivariate analysis included impaired ambulation status (odds ratio [OR], 2.27; p=0.02) and estimated blood loss over 500 mL (OR, 3.67; p=0.02). Multivariate analysis revealed preoperative narcotic use (OR, 2.43; p=0.02) and operative time (OR, 1.005; p=0.03) as risk factors for surgical complication, whereas antidepressant use was a protective factor (OR, 0.21; p=0.01). Overall complication was associated with preoperative narcotic use (OR, 1.97; p=0.04) and higher intraoperative blood loss (OR, 1.0007; p=0.03).ConclusionPreoperative narcotic use and estimated blood loss predicted the incidence of complications following PCLF for CSM. Ambulation status was a significant predictor of the development of a medical complication specifically. These results may help surgeons in counseling patients who may be at increased risk of complication following surgery

A time-dependent Tsirelson's bound from limits on the rate of information gain in quantum systems

We consider the problem of distinguishing between a set of arbitrary quantum states in a setting in which the time available to perform the measurement is limited. We provide simple upper bounds on how well we can perform state discrimination in a given time as a function of either the average energy or the range of energies available during the measurement. We exhibit a specific strategy that nearly attains this bound. Finally, we consider several applications of our result. First, we obtain a time-dependent Tsirelson's bound that limits the extent of the Bell inequality violation that can be in principle be demonstrated in a given time t. Second, we obtain a Margolus-Levitin type bound when considering the special case of distinguishing orthogonal pure states.Comment: 15 pages, revtex, 1 figur

Cognitive demands of face monitoring: Evidence for visuospatial overload

Young children perform difficult communication tasks better face to face than when they cannot see one another (e.g., Doherty-Sneddon & Kent, 1996). However, in recent studies, it was found that children aged 6 and 10 years, describing abstract shapes, showed evidence of face-to-face interference rather than facilitation. For some communication tasks, access to visual signals (such as facial expression and eye gaze) may hinder rather than help children’s communication. In new research we have pursued this interference effect. Five studies are described with adults and 10- and 6-year-old participants. It was found that looking at a face interfered with children’s abilities to listen to descriptions of abstract shapes. Children also performed visuospatial memory tasks worse when they looked at someone’s face prior to responding than when they looked at a visuospatial pattern or at the floor. It was concluded that performance on certain tasks was hindered by monitoring another person’s face. It is suggested that processing of visual communication signals shares certain processing resources with the processing of other visuospatial information

Optimal Unravellings for Feedback Control in Linear Quantum Systems

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case, such as: given a fixed interaction between the system and the environment what is the optimal measurement on the environment for a particular control problem? We show that for a broad class of optimal (state-based) control problems (the stationary Linear-Quadratic-Gaussian class), this question is a semi-definite program. Moreover, the answer also applies to Markovian (current-based) feedback.Comment: 5 pages. Version published by Phys. Rev. Let

Feedback cooling of a nanomechanical resonator

Cooled, low-loss nanomechanical resonators offer the prospect of directly observing the quantum dynamics of mesoscopic systems. However, the present state of the art requires cooling down to the milliKelvin regime in order to observe quantum effects. Here we present an active feedback strategy based on continuous observation of the resonator position for the purpose of obtaining these low temperatures. In addition, we apply this to an experimentally realizable configuration, where the position monitoring is carried out by a single-electron transistor. Our estimates indicate that with current technology this technique is likely to bring the required low temperatures within reach.Comment: 10 pages, RevTex4, 4 color eps figure