Numerical algorithms for use in quantum information

M. S. Ramkarthik, Pranay Barkataki

Masahito Hayashi, Geng Liu

Abstract Quantum information bottleneck was proposed by Grimsmo and Still (2016 Phys. Rev. A 94 012338) as a promising method for quantum supervised machine learning. To study this method, we generalize the quantum Arimoto–Blahut algorithm by Ramakrishnan et al (2021 IEEE Trans. Inf. Theory 67 946) to a function defined over a set of density matrices with linear constraints so that our algorithm can be applied to optimizations of quantum operations. This algorithm has wider applicability, and we apply our algorithm to the quantum information bottleneck with three quantum systems. We numerically compare our obtained algorithm with the existing algorithm by Grimsmo and Still. Our numerical analysis shows that our algorithm is better than their algorithm.

Edmar Nascimento, Francisco de Assis

The quantum discrimination problem is an important topic of quantum information theory. Discriminating among a set of M non-orthogonal quantum states means choosing among one of them based on a quantum measurement. In order to accomplish this task one must choose a measure of information to rank the potential solutions. When the Shannon mutual information is considered as such a measure one has an accessible information problem. The accessible information problem consists on the maximization of the mutual information over all sorts of quantum measurements. Analytical solutions for this optimization problem are not available for the general case. Even numerical solutions are hard to find because of the nonlinear nature of the mutual information function. On the other hand, genetic algorithms work pretty well with "misbehaved" functions. Based on the previous statements, we propose solving the accessible information problem via genetic algorithms.

Mika Hirvensalo

Jamie Smith, Michele Mosca

Purva Thakre

In this paper, we discuss the need for quantum error correction. We also describe some basic techniques used in quantum error correction which includes decoherence-free subspaces and subsystems. These subspaces and subsystems are described in detail. We also introduce a numerical algorithm that was used previously to search for these decoherence-free subspaces and subsystems under collective error. It is useful to search for them as they can be used to store quantum information. We use this algorithm in some specific examples involving qubits and qutrits. The results of these algorithm are then compared with the error algebra obtained using Young tableaux. We use these results to describe how the specific numerical algorithm can be used for the search of approximate decoherence-free subspaces and subsystems and minimal noise subsystems.