Introduction

The construction of computer algorithms and software models that simulate physical systems plays a fundamental role in all branches of science and engineering. The physicist and Nobel laureate Richard Feynman, among others, observed in the 1980s that the important task of simulating quantum-mechanical processes on a standard computer requires an extraordinary amount of computer memory and runtime [41]. Such observations gave rise to the notion of quantum computing, where quantum mechanics itself is used to simulate quantum behavior. The key insight is to replace the familiar 0 and 1 bits of conventional or classical computing with information units called qubits (quantum bits) that capture quantum states of elementary particles or atomic nuclei. By operating on qubits, a quantum computer can, in principle, process exponentially more data than a classical computer in a similar number of steps. In the 1990s, several fast quantum methods were discovered for such applications as searching large databases [38] and factoring large numbers [82]; the latter is a basic step in some forms of codebreaking.