A quantum computer is a (real or theoretical) computer that exploits superposed and entangled states. Quantum computers can be viewed as sampling from quantum systems. These systems evolve in ways that operate on an enormous number of possibilities simultaneously, though they remain subject to strict computational constraints. By contrast, ordinary ("classical") computers operate according to deterministic rules. (A classical computer can, in principle, be replicated by a classical mechanical device, with only a simple multiple of time cost. On the other hand (it is believed), a quantum computer would require exponentially more time and energy to be simulated classically.) It is widely believed that a quantum computer could perform some calculations exponentially faster than any classical computer. For example, a large-scale quantum computer could break some widely used public-key cryptographic schemes and aid physicists in performing physical simulations. However, current hardware implementations of quantum computation are largely experimental and only suitable for specialized tasks. The basic unit of information in quantum computing...