Short paths in PU(2)

Parzanchevski--Sarnak \cite{PS} recently adapted an algorithm of Ross--Selinger \cite{RS16} for factorization of $\PU(2)$-diagonal elements to within distance $\eps$ into an efficient probabilistic algorithm for any $\PU(2)$-element, using at most $3\log_p(\nicefrac{1}{\eps^3})$ factors from certain well-chosen sets. The Clifford+$T$ gates are one such set arising from $p=2$. In that setting, we leverage recent work of Carvalho Pinto--Petit \cite{CPP} to improve this to $\frac{7}{3}\log_2(\nicefrac{1}{\eps^3})$, and implement the algorithm in Haskell.

Qubit-Based Clock Synchronization for QKD Systems Using a Bayesian Approach

Quantum key distribution (QKD) systems provide a method for two users to exchange a provably secure key. Synchronizing the users’ clocks is an essential step before a secure key can be distilled. Qubit-based synchronization protocols directly use the transmitted quantum states to achieve synchronization and thus avoid the need for additional classical synchronization hardware. Previous qubit-based synchronization protocols sacrifice secure key either directly or indirectly, and all known qubit-based synchronization protocols do not efficiently use all publicly available information published by the users. Here, we introduce a Bayesian probabilistic algorithm that incorporates all published information to efficiently find the clock offset without sacrificing any secure key. Additionally, the output of the algorithm is a probability, which allows us to quantify our confidence in the synchronization. For demonstration purposes, we present a model system with accompanying simulations of an efficient three-state BB84 prepare-and-measure protocol with decoy states. We use our algorithm to exploit the correlations between Alice’s published basis and mean photon number choices and Bob’s measurement outcomes to probabilistically determine the most likely clock offset. We find that we can achieve a 95 percent synchronization confidence in only 4140 communication bin widths, meaning we can tolerate clock drift approaching 1 part in 4140 in this example when simulating this system with a dark count probability per communication bin width of 8×10−4 and a received mean photon number of 0.01.

Adaptive Probabilistic Optimization Approach for Vibration-Based Structural Health Monitoring

This paper presents a novel adaptive probabilistic algorithm to identify damage characteristics by integrating the use of the frequency response function with an optimization approach. The proposed algorithm evaluates the probability of damage existence and determines salient details such as damage location and damage severity in a probabilistic manner. A multistage sequence is used to determine the probability of damage parameters including crack depth and crack location while minimizing uncertainties. A simply supported beam with an open edge crack was used to demonstrate the application of the algorithm for damage detection. The robustness of the algorithm was tested by incorporating varying levels of noise into the frequency response. All simulation results show successful detection of damage with a relatively high probability even in the presence of noise. Results indicate that the probabilistic algorithm could have significant advantages over conventional deterministic methods since it has the ability to avoid yielding false negatives that are quite common among deterministic damage detection techniques.

On sparse interpolation of rational functions and gcds

In this note, we present a variant of a probabilistic algorithm by Cuyt and Lee for the sparse interpolation of multivariate rational functions. We also present an analogous method for the computation of sparse gcds.

Camera-Driven Probabilistic Algorithm for Multi-Elevator Systems

A fast and reliable vertical transportation system is an important component of modern office buildings. Optimization of elevator control strategies can be easily done using the state-of-the-art artificial intelligence (AI) algorithms. This study presents a novel method for optimal dispatching of conventional passenger elevators using the information obtained by surveillance cameras. It is assumed that a real-time video is processed by an image processing system that determines the number of passengers and items waiting for an elevator car in hallways and riding the lifts. It is supposed that these numbers are also associated with a given uncertainly probability. The efficiency of our novel elevator control algorithm is achieved not only by the probabilistic utilization of the number of people and/or items waiting but also from the demand to exhaustively serve a crowded floor, directing to it as many elevators as there are available and filling them up to the maximum allowed weight. The proposed algorithm takes into account the uncertainty that can take place due to inaccuracy of the image processing system, introducing the concept of effective number of people and items using Bayesian networks. The aim is to reduce the waiting time. According to the simulation results, the implementation of the proposed algorithm resulted in reduction of the passenger journey time. The proposed approach was tested on a 10-storey office building with five elevator cars and traffic size and intensity varying from 10 to 300 and 0.01 to 3, respectively. The results showed that, for the interfloor traffic conditions, the average travel time for scenarios with varying traffic size and intensity improved by 39.94% and 19.53%, respectively.