The basis of quantum computing

A classical computer has a memory made up of bits, where each bit holds either a one or a zero. A quantum computer maintains a sequence of qubits. A single qubit can hold a one, a zero, or, crucially, a quantum superposition of these, and any two qubits can be in a quantum superposition of 4 states, and three qubits in 8. In general a quantum computer with n qubits can be in up to 2n different states simultaneously (this compares to a normal computer that can only be in one of 2n states at any one time). A quantum computer operates by manipulating those qubits with (possibly a suite of) quantum logic gates.

An example of an implementation of qubits for a quantum computer could start with the use of particles with two spin states: "up" and "down" (typically written |0\rangle and |1\rangle). But in fact any system possessing an observable quantity A which is conserved under time evolution and such that A has at least two discrete and sufficiently spaced consecutive eigenvalues, is a suitable candidate for implementing a qubit. This is true because any such system can be mapped onto an effective spin-1/2.