Algorithmic Quantum Simulation

Three decades ago, quantum computing was first proposed as an efficient simulator of quantum dynamics. Since then new algorithms have been discovered, such as Shor's factorization and Grover's search algorithms, but quantum simulation is returning to the fore because resource demands (such as space cost and run-time) are lower than for other algorithms. Furthermore quantum simulation algorithms solve interesting, important problems, and the algorithms reach beyond simulating quantum dynamics to more generic problems such as solving huge systems of linear equations. This tutorial explores the history and nature of algorithmic quantum simulation, which assumes that the algorithms are run on a fault-tolerant quantum computer, and explains the methods and techniques. Participants will understand the motivation for algorithmic quantum simulation research and have a basic background so that papers in the field become comprehensible.