At the heart of the puzzlement induced in many by the quantum theory lies a tension between reality and knowledge, between facts and information. Do the basic entities of the theory, quantum states or their wavefunctions, directly correspond to something in the real world so that something—wavefunction stuff—actually does pass through both slits in a two-slit interference experiment? If so, then either we are faced with the puzzle of how something real can suffer abrupt changes in response to faraway events or, if we banish wavefunction collapse from the theory, we are faced with a reality that absurdly evolves to encompass myriads of alternative histories growing ever more unalike. These puzzles melt away if the basic entities of the theory are merely representations of knowledge, only to be replaced by others. Whose knowledge? Knowledge of what?

The new gedanken technology of quantum computation provides an unfamiliar perspective on such vexing questions, by using the quantum theory, not to expand our understanding and control of the physical world, but to exploit the quantum behavior of the physical world as a novel way to encode and process information. The information is primary; the underlying physical system only matters as a vehicle for that information. Quantum computer scientists view a set of n interacting spins-½ not for the insight it offers into the nature of magnetic materials, but as a way to represent and manipulate integers, through their n-bit binary representations as orthogonal states in a “computational basis” that specifies whether each individual spin is up (1) or down (0).

Quantum computation differs in several crucial ways from ordinary classical computation:

1. • The states of a quantum bit (which I here call a Qbit, in quixotic defiance of the fashionable but orthographically preposterous “qubit”) are not restricted to 0 or 1, as in a classical computer, but can be in arbitrary superpositions of 0 and 1.

2. • Even more foreign to classical intuition, the state of the entire computer can be what Schrödinger called verschränkt (entangled), with individual Qbits having no (pure) states of their own at all. While a classical computation flips classical Cbits between 0 and 1, a quantum computation subjects the Qbits to the much more general unitary transformations that specify the time evolution of quantum states.