Rapid Measurement of Quantum Systems using Feedback Control

We introduce a feedback control algorithm that increases the speed at which a measurement extracts information about a $d$-dimensional system by a factor that scales as $d^2$. Generalizing this algorithm, we apply it to a register of $n$ qubits and show an improvement O(n). We derive analytical bounds on the benefit provided by the feedback and perform simulations that confirm that this speedup is achieved.Comment: 4 pages, 4 figures. V2: Minor correction

Numerical Analysis of Boosting Scheme for Scalable NMR Quantum Computation

Among initialization schemes for ensemble quantum computation beginning at thermal equilibrium, the scheme proposed by Schulman and Vazirani [L. J. Schulman and U. V. Vazirani, in Proceedings of the 31st ACM Symposium on Theory of Computing (STOC'99) (ACM Press, New York, 1999), pp. 322-329] is known for the simple quantum circuit to redistribute the biases (polarizations) of qubits and small time complexity. However, our numerical simulation shows that the number of qubits initialized by the scheme is rather smaller than expected from the von Neumann entropy because of an increase in the sum of the binary entropies of individual qubits, which indicates a growth in the total classical correlation. This result--namely, that there is such a significant growth in the total binary entropy--disagrees with that of their analysis.Comment: 14 pages, 18 figures, RevTeX4, v2,v3: typos corrected, v4: minor changes in PROGRAM 1, conforming it to the actual programs used in the simulation, v5: correction of a typographical error in the inequality sign in PROGRAM 1, v6: this version contains a new section on classical correlations, v7: correction of a wrong use of terminology, v8: Appendix A has been added, v9: published in PR

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first part, we generalize the Hausdorff dimension by defining a family of bi-Lipschitz invariants, called critical parameters, that measure largeness for infinite-dimensional metric spaces. Basic properties of these invariants are given, and they are estimated for a naturel set of spaces generalizing the usual Hilbert cube. In a second part, we estimate the value of these new invariants in the case of some Wasserstein spaces, as well as the dynamical complexity of push-forward maps. The lower bounds rely on several embedding results; for example we provide bi-Lipschitz embeddings of all powers of any space inside its Wasserstein space, with uniform bound and we prove that the Wasserstein space of a d-manifold has "power-exponential" critical parameter equal to d.Comment: v2 Largely expanded version, as reflected by the change of title; all part I on generalized Hausdorff dimension is new, as well as the embedding of Hilbert cubes into Wasserstein spaces. v3 modified according to the referee final remarks ; to appear in Journal of Topology and Analysi

Trajectory generation for road vehicle obstacle avoidance using convex optimization

This paper presents a method for trajectory generation using convex optimization to find a feasible, obstacle-free path for a road vehicle. Consideration of vehicle rotation is shown to be necessary if the trajectory is to avoid obstacles specified in a fixed Earth axis system. The paper establishes that, despite the presence of significant non-linearities, it is possible to articulate the obstacle avoidance problem in a tractable convex form using multiple optimization passes. Finally, it is shown by simulation that an optimal trajectory that accounts for the vehicle’s changing velocity throughout the manoeuvre is superior to a previous analytical method that assumes constant speed

Ordered Measurements of Permutationally-Symmetric Qubit Strings

We show that any sequence of measurements on a permutationally-symmetric (pure or mixed) multi-qubit string leaves the unmeasured qubit substring also permutationally-symmetric. In addition, we show that the measurement probabilities for an arbitrary sequence of single-qubit measurements are independent of how many unmeasured qubits have been lost prior to the measurement. Our results are valuable for quantum information processing of indistinguishable particles by post-selection, e.g. in cases where the results of an experiment are discarded conditioned upon the occurrence of a given event such as particle loss. Furthermore, our results are important for the design of adaptive-measurement strategies, e.g. a series of measurements where for each measurement instance, the measurement basis is chosen depending on prior measurement results.Comment: 13 page

FDTD Simulation of Thermal Noise in Open Cavities

A numerical model based on the finite-difference time-domain (FDTD) method is developed to simulate thermal noise in open cavities owing to output coupling. The absorbing boundary of the FDTD grid is treated as a blackbody, whose thermal radiation penetrates the cavity in the grid. The calculated amount of thermal noise in a one-dimensional dielectric cavity recovers the standard result of the quantum Langevin equation in the Markovian regime. Our FDTD simulation also demonstrates that in the non-Markovian regime the buildup of the intracavity noise field depends on the ratio of the cavity photon lifetime to the coherence time of thermal radiation. The advantage of our numerical method is that the thermal noise is introduced in the time domain without prior knowledge of cavity modes.Comment: 8 pages, 7 figure

Liver fibrosis after extracorporeal shock-wave lithotripsy of gallbladder stones - A case report

We encountered significant liver fibrosis in a healthy young patient undergoing laparoscopic cholecystectomy for symptomatic gallstone disease. Twelve months prior to cholecystectomy the patient underwent multiple extracorporeal shock-wave lithotripsy (ESWL) sessions with adjuvant oral bile-acid therapy. Since the site of fibrosis corresponded clearly to the shock-wave transmission path, which was in accordance with animal studies, it was concluded that this liver fibrosis was a side effect of biliary ESWL. Based on these findings and the literature, we conclude that further assessment of the long-term safety of ESWL is still warranted, especially in patients undergoing multiple ESWL sessions

Handwritten digit recognition by bio-inspired hierarchical networks

The human brain processes information showing learning and prediction abilities but the underlying neuronal mechanisms still remain unknown. Recently, many studies prove that neuronal networks are able of both generalizations and associations of sensory inputs. In this paper, following a set of neurophysiological evidences, we propose a learning framework with a strong biological plausibility that mimics prominent functions of cortical circuitries. We developed the Inductive Conceptual Network (ICN), that is a hierarchical bio-inspired network, able to learn invariant patterns by Variable-order Markov Models implemented in its nodes. The outputs of the top-most node of ICN hierarchy, representing the highest input generalization, allow for automatic classification of inputs. We found that the ICN clusterized MNIST images with an error of 5.73% and USPS images with an error of 12.56%

Evaluating implicit feedback models using searcher simulations

In this article we describe an evaluation of relevance feedback (RF) algorithms using searcher simulations. Since these algorithms select additional terms for query modification based on inferences made from searcher interaction, not on relevance information searchers explicitly provide (as in traditional RF), we refer to them as implicit feedback models. We introduce six different models that base their decisions on the interactions of searchers and use different approaches to rank query modification terms. The aim of this article is to determine which of these models should be used to assist searchers in the systems we develop. To evaluate these models we used searcher simulations that afforded us more control over the experimental conditions than experiments with human subjects and allowed complex interaction to be modeled without the need for costly human experimentation. The simulation-based evaluation methodology measures how well the models learn the distribution of terms across relevant documents (i.e., learn what information is relevant) and how well they improve search effectiveness (i.e., create effective search queries). Our findings show that an implicit feedback model based on Jeffrey's rule of conditioning outperformed other models under investigation