Quantum Algorithms: A Decade in Review

Rafael Lahoz-Beltrá

Genetic algorithms (GAs) are a class of evolutionary algorithms inspired by Darwinian natural selection. They are popular heuristic optimisation methods based on simulated genetic mechanisms, i.e., mutation, crossover, etc. and population dynamical processes such as reproduction, selection, etc. Over the last decade, the possibility to emulate a quantum computer (a computer using quantum-mechanical phenomena to perform operations on data) has led to a new class of GAs known as “Quantum Genetic Algorithms” (QGAs). In this review, we present a discussion, future potential, pros and cons of this new class of GAs. The review will be oriented towards computer scientists interested in QGAs “avoiding” the possible difficulties of quantum-mechanical phenomena.

Duong Bui, Kimmo Halunen, Nhan Nguyen +1 more

Synge Todo

The quantum Monte Carlo technique for quantum magnets has been greatly improved during the last decade. In this paper, we review the quantum cluster algorithm (loop algorithm) for higher-spin Heisenberg antiferromagnets, together with some technical aspects including parallelization technique and with its application to low-dimensional Heisenberg antiferromagnets.

Andris Ambainis

Peter W. Shor

Wenda Zhou

Abstract Quantum walk is the quantum version of classical random walk, which has shown great advantage over classical algorithms. In this article, main discoveries and breakthroughs along with several applications in the last two decades are reviewed and discussed. Reducing hitting time and diminishing mixing time, as two hot research fields, are addressed. Possibility of universal computation with more generic case of quantum walk is also mentioned. In the future, we can expect new methods and models being feasible ways to approach the theoretical lower bounds of related problems, as well as more efficient applications on specific scene.