Tracking Quantum Error Correction

To implement fault-tolerant quantum computation with continuous variables, the Gottesman--Kitaev--Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to realize large scale quantum computation with the GKP qubit [Phys. Rev. X. {\bf 8}, 021054 (2018)], harnessing the virtue of analog information in the GKP qubits. In the present work, to reduce the number of qubits required for large scale quantum computation, we propose the tracking quantum error correction, where the logical-qubit level quantum error correction is partially substituted by the single-qubit level quantum error correction. In the proposed method, the analog quantum error correction is utilized to make the performances of the single-qubit level quantum error correction almost identical to those of the logical-qubit level quantum error correction in a practical noise level. The numerical results show that the proposed tracking quantum error correction reduces the number of qubits during a quantum error correction process by the reduction rate $\left\{{2(n-1)\times4^{l-1}-n+1}\right\}/({2n \times 4^{l-1}})$ for $n$-cycles of the quantum error correction process using the Knill's $C_{4}/C_{6}$ code with the concatenation level $l$. Hence, the proposed tracking quantum error correction has great advantage in reducing the required number of physical qubits, and will open a new way to bring up advantage of the GKP qubits in practical quantum computation

Predictive information and error processing : the role of medial-frontal cortex during motor control

We have recently provided evidence that an error-related negativity (ERN), an ERP component generated within medial-frontal cortex, is elicited by errors made during the performance of a continuous tracking task (O.E. Krigolson & C.B. Holroyd, 2006). In the present study we conducted two experiments to investigate the ability of the medial-frontal error system to evaluate predictive error information. In two experiments participants used a joystick to perform a computer-based continuous tracking task in which some tracking errors were inevitable. In both experiments, half of these errors were preceded by a predictive cue. The results of both experiments indicated that an ERN-like waveform was elicited by tracking errors. Furthermore, in both experiments the predicted error waveforms had an earlier peak latency than the unpredicted error waveforms. These results demonstrate that the medial-frontal error system can evaluate predictive error information

Error rate information in attention allocation pilot models

The Northrop urgency decision pilot model was used in a command tracking task to compare the optimized performance of multiaxis attention allocation pilot models whose urgency functions were (1) based on tracking error alone, and (2) based on both tracking error and error rate. A matrix of system dynamics and command inputs was employed, to create both symmetric and asymmetric two axis compensatory tracking tasks. All tasks were single loop on each axis. Analysis showed that a model that allocates control attention through nonlinear urgency functions using only error information could not achieve performance of the full model whose attention shifting algorithm included both error and error rate terms. Subsequent to this analysis, tracking performance predictions for the full model were verified by piloted flight simulation. Complete model and simulation data are presented

Model-Based Iterative Learning Control Applied to an Industrial Robot with Elasticity

In this paper model-based Iterative Learning Control (ILC) is applied to improve the tracking accuracy of an industrial robot with elasticity. The ILC algorithm iteratively updates the reference trajectory for the robot such that the predicted tracking error in the next iteration is minimised. The tracking error is predicted by a model of the closed-loop dynamics of the robot. The model includes the servo resonance frequency, the first resonance frequency caused by elasticity in the mechanism and the variation of both frequencies along the trajectory. Experimental results show that the tracking error of the robot can be reduced, even at frequencies beyond the first elastic resonance frequency

A simulator evaluation of a rate-enhanced instrument landing system display

A piloted simulation study was conducted to evaluate the effect on instrument landing system tracking performance of integrating localizer error rate information with the raw localizer error display. The resulting display was named the pseudo command tracking indicator (PCTI) because it provides an indication of any changes of heading required to track the localizer. Eight instrument-rated pilots each flew five instrument approaches with the PCTI and five instrument approaches with a conventional course deviation indicator. The results show good overall pilot acceptance of the PCTI and a significant reduction in localizer tracking error

Experimental comparison of parameter estimation methods in adaptive robot control

In the literature on adaptive robot control a large variety of parameter estimation methods have been proposed, ranging from tracking-error-driven gradient methods to combined tracking- and prediction-error-driven least-squares type adaptation methods. This paper presents experimental data from a comparative study between these adaptation methods, performed on a two-degrees-of-freedom robot manipulator. Our results show that the prediction error concept is sensitive to unavoidable model uncertainties. We also demonstrate empirically the fast convergence properties of least-squares adaptation relative to gradient approaches. However, in view of the noise sensitivity of the least-squares method, the marginal performance benefits, and the computational burden, we (cautiously) conclude that the tracking-error driven gradient method is preferred for parameter adaptation in robotic applications

Biplane Fluoroscopy for Hindfoot Motion Analysis during Gait: A Model-based Evaluation

The purpose of this study was to quantify the accuracy and precision of a biplane fluoroscopy system for model-based tracking of in vivo hindfoot motion during over-ground gait. Gait was simulated by manually manipulating a cadaver foot specimen through a biplane fluoroscopy system attached to a walkway. Three 1.6-mm diameter steel beads were implanted into the specimen to provide marker-based tracking measurements for comparison to model-based tracking. A CT scan was acquired to define a gold standard of implanted bead positions and to create 3D models for model-based tracking. Static and dynamic trials manipulating the specimen through the capture volume were performed. Marker-based tracking error was calculated relative to the gold standard implanted bead positions. The bias, precision, and root-mean-squared (RMS) error of model-based tracking was calculated relative to the marker-based measurements. The overall RMS error of the model-based tracking method averaged 0.43 ± 0.22 mm and 0.66 ± 0.43° for static and 0.59 ± 0.10 mm and 0.71 ± 0.12° for dynamic trials. The model-based tracking approach represents a non-invasive technique for accurately measuring dynamic hindfoot joint motion during in vivo, weight bearing conditions. The model-based tracking method is recommended for application on the basis of the study results

Prediction of pilot reserve attention capacity during air-to-air target tracking

Reserve attention capacity of a pilot was calculated using a pilot model that allocates exclusive model attention according to the ranking of task urgency functions whose variables are tracking error and error rate. The modeled task consisted of tracking a maneuvering target aircraft both vertically and horizontally, and when possible, performing a diverting side task which was simulated by the precise positioning of an electrical stylus and modeled as a task of constant urgency in the attention allocation algorithm. The urgency of the single loop vertical task is simply the magnitude of the vertical tracking error, while the multiloop horizontal task requires a nonlinear urgency measure of error and error rate terms. Comparison of model results with flight simulation data verified the computed model statistics of tracking error of both axes, lateral and longitudinal stick amplitude and rate, and side task episodes. Full data for the simulation tracking statistics as well as the explicit equations and structure of the urgency function multiaxis pilot model are presented

A general aviation simulator evaluation of a rate-enhanced instrument landing system display

A piloted-simulation study was conducted to evaluate the effect on instrument landing system tracking performance of integrating localizer-error rate with raw localizer and glide-slope error. The display was named the pseudocommand tracking indicator (PCTI) because it provides an indication of the change of heading required to track the localizer center line. Eight instrument-rated pilots each flew five instrument approaches with the PCTI and five instrument approaches with a conventional course deviation indicator. The results show good overall pilot acceptance of the display, a significant improvement in localizer tracking error, and no significant changes in glide-slope tracking error or pilot workload

Tracking Error and Active Portfolio Management

Persistent bear market conditions have led to a shift of focus in the tracking error literature. Until recently the portfolio allocation literature focused on tracking error minimization as a consequence of passive benckmark management under portfolio weights, transaction costs and short selling constraints. Abysmal benchmark performance shifted the literature's focus towards active portfolio strategies that aim at beating the benchmark while keeping tracking error within acceptable bounds. We investigate an active (dynamic) portfolio allocation strategy that exploits the predictability in the conditional variance-covariance matrix of asset returns. To illustrate our procedure we use Jorion's (2002) tracking error frontier methodology. We apply our model to a representative portfolio of Australian stocks over the period January 1999 through November 2002.