Adaptive experimental design for one-qubit state estimation with finite data based on a statistical update criterion

We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance-optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum state estimation. In general, A-optimization is a nonlinear minimization problem; however, we find an analytic solution for 1-qubit state estimation using projective measurements, reducing computational effort. We compare numerically two adaptive and two nonadaptive schemes for finite data sets and show that the A-optimality criterion gives more precise estimates than standard quantum tomography.Comment: 15 pages, 7 figure

Experimental Designs for Binary Data in Switching Measurements on Superconducting Josephson Junctions

We study the optimal design of switching measurements of small Josephson junction circuits which operate in the macroscopic quantum tunnelling regime. Starting from the D-optimality criterion we derive the optimal design for the estimation of the unknown parameters of the underlying Gumbel type distribution. As a practical method for the measurements, we propose a sequential design that combines heuristic search for initial estimates and maximum likelihood estimation. The presented design has immediate applications in the area of superconducting electronics implying faster data acquisition. The presented experimental results confirm the usefulness of the method. KEY WORDS: optimal design, D-optimality, logistic regression, complementary log-log link, quantum physics, escape measurement

D-optimal designs via a cocktail algorithm

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey, Titterington and Torsney, 1978), and shares their simplicity and monotonic convergence properties. Numerical examples show that the cocktail algorithm can lead to dramatically improved speed, sometimes by orders of magnitude, relative to either the multiplicative algorithm or the vertex exchange method (a variant of VDM). Key to the improved speed is a new nearest neighbor exchange strategy, which acts locally and complements the global effect of the multiplicative algorithm. Possible extensions to related problems such as nonparametric maximum likelihood estimation are mentioned.Comment: A number of changes after accounting for the referees' comments including new examples in Section 4 and more detailed explanations throughou

Exploring aerospace design in virtual reality with dimension reduction

One of the today’s most propitious immersive technologies is virtual reality (VR). This term is colloquially associated with head-sets that transport users to a bespoke, built-forpurpose immersive 3D virtual environment. It has given rise to the field of immersive visual analytics—a new field of research that aims to use immersive technologies for enhancing and empowering data analytics. In this paper we present a VR aerospace design environment with the objective of aiding the component aerodynamic design process by interactively visualizing performance and geometry. This virtual environment uses ideas from parameter-space dimension reduction to enhance the exploration and exploitation of the design space. We decompose the design of such an environment into function structures, present an implementation of the system, and verify the interface in terms of usability and expressiveness

Break-taking behaviour pattern of long-distance freight vehicles based on GPS trajectory data

This paper focuses on the break-taking behaviour pattern of long-distance freight vehicles, providing a new perspective on the study of behaviour patterns and simultaneously providing a reference for transport management departments and related enterprises. Based on Global Positioning System (GPS) trajectory data, we select stopping points as break-taking sites of long-distance freight vehicles and then classify the stopping points into three different classes based on the break-taking duration. We then explore the relationship of the distribution of the break-taking frequency between the three single classifications and their combinations, on the basis of the break-taking duration distribution. We find that the combination is a Gaussian distribution when each of the three individual classes is a Gaussian distribution, contrasting with the power-law distribution of the break-taking duration. Then we experimental analysis the distribution of the break-taking durations and frequencies, and find that, for the durations, the three single classifications can be fitted individually by an Exponential distribution and together by a Power-law distribution, for the frequencies, both the three single classifications and together can be fitted by a Gaussian distribution,so that can validate the above theoretical analysis. Key words: break-taking behaviour, long-distance freight vehicle, statistical analysi