The construction of computer algorithms and software models that simulatephysical 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 quantummechanicalprocesses on a standard computer requires an extraordinaryamount of computer memory and runtime [41]. Such observations gave rise tothe notion of quantum computing, where quantum mechanics itself is used tosimulate quantum behavior. The key insight is to replace the familiar 0 and1 bits of conventional or classical computing with information units calledqubits (quantum bits) that capture quantum states of elementary particles oratomic nuclei. By operating on qubits, a quantum computer can, in principle,process exponentially more data than a classical computer in a similar numberof steps. In the 1990s, several fast quantum methods were discovered for suchapplications as searching large databases [38] and factoring large numbers [82];the latter is a basic step in some forms of codebreaking.