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

Educational Magic Tricks Based on Error-Detection Schemes

Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics

Clustering as an example of optimizing arbitrarily chosen objective functions

This paper is a reflection upon a common practice of solving various types of learning problems by optimizing arbitrarily chosen criteria in the hope that they are well correlated with the criterion actually used for assessment of the results. This issue has been investigated using clustering as an example, hence a unified view of clustering as an optimization problem is first proposed, stemming from the belief that typical design choices in clustering, like the number of clusters or similarity measure can be, and often are suboptimal, also from the point of view of clustering quality measures later used for algorithm comparison and ranking. In order to illustrate our point we propose a generalized clustering framework and provide a proof-of-concept using standard benchmark datasets and two popular clustering methods for comparison

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

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

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

An epitaxial perovskite as a compact neuristor:Electrical self-oscillations in TbMnO₃thin films

Developing materials that can lead to compact versions of artificial neurons (neuristors) and synapses (memristors) is the main aspiration of the nascent neuromorphic materials research field. Oscillating circuits are interesting as neuristors, as they emulate the firing of action potentials. Here we present room-temperature self-oscillating devices fabricated from epitaxial thin films of semiconducting TbMnO3. We show that the negative differential resistance regime observed in these devices, orginates from transitions across the electronic band gap of the semiconductor. The intrinsic nature of the mechanism governing the oscillations gives rise to a high degree of control and repeatability. Obtaining such properties in an epitaxial perovskite oxide opens the way towards combining self-oscillating properties with those of other piezoelectric, ferroelectric, or magnetic perovskite oxides in order to achieve hybrid neuristor-memristor functionality in compact heterostructures

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