Classical Simulation of Quantum Computation

Abstract

Last but not least, we discuss the classical simulation of quantum computation, where we explore the techniques for efficiently simulating quantum circuits on a classical computer. This is an important subject, in part because it allows us to execute a quantum program and verify its correctness even when no quantum hardware is available. It is thus an essential tool for testing and debugging quantum programs. But it also sheds light on the not-so-well-understood computational power boundary between classical computers and quantum computers. We would like to understand how much of quantum processes (if not all) can be efficiently simulated on a classical computer. In other words, understanding various classical simulation techniques can give us insights on what are the key ingredients in quantum computing that bring the advantage in computing power. For instance, is entanglement responsible for quantum speedup, or is there more to it? Those are the kind of questions raised and hopefully answered when we study the simulation of quantum computation. After defining what classical simulation means, we direct the reader’s attention to some leading techniques, namely simulation using density matrices, stabilizer formalism, and graphical models.