Quantum Annealing - Foundations and Frontiers

We briefly review various computational methods for the solution of optimization problems. First, several classical methods such as Metropolis algorithm and simulated annealing are discussed. We continue with a description of quantum methods, namely adiabatic quantum computation and quantum annealing. Next, the new D-Wave computer and the recent progress in the field claimed by the D-Wave group are discussed. We present a set of criteria which could help in testing the quantum features of these computers. We conclude with a list of considerations with regard to future research.Comment: 22 pages, 6 figures. EPJ-ST Discussion and Debate Issue: Quantum Annealing: The fastest route to large scale quantum computation?, Eds. A. Das, S. Suzuki (2014

Communication Complexity Protocol for Q-trits

Consider a function where its entries are distributed among many parties. Suppose each party is allowed to transmit only a limited amount of information to a net. One can use a classical protocol to guess the value of the global function. Is there a quantum protocol improving the results of all classical protocols? Brukner et. al. showed the deep connection between such problems and the theory of Bell's inequalities. Here we generalize the theory to trits. There the best classical protocol fails whereas the quantum protocol yields the correct answer.Comment: 8 page

A Holevo-Type Bound for a Hilbert Schmidt Distance Measure

We prove a new version of the Holevo bound employing the Hilbert-Schmidt norm instead of the Kullback-Leibler divergence. Suppose Alice is sending classical information to Bob using a quantum channel, while Bob is performing some projective measurement. We bound the classical mutual information in terms of the Hilbert-Schmidt norm by its quantum Hilbert-Schmidt counterpart. This constitutes a Holevo-type upper bound on the classical information transmission rate via a quantum channel. The resulting inequality is rather natural and intuitive relating classical and quantum expressions using the same measure.Comment: 8 pages. Accepted to Journal of Quantum Information Scienc

Introduction to Weak Measurements and Weak Values

We present a short review of the theory of weak measurement. This should serve as a map for the theory and an easy way to get familiar with the main results, problems and paradoxes raised by the theory.Quanta 2013; 2: 7–17