  We present experimental results which demonstrate that nuclear magnetic
resonance spectroscopy is capable of efficiently emulating many of the
capabilities of quantum computers, including unitary evolution and coherent
superpositions, but without attendant wave-function collapse. Specifically, we
have: (1) Implemented the quantum XOR gate in two different ways, one using
Pound-Overhauser double resonance, and the other using a spin-coherence double
resonance pulse sequence; (2) Demonstrated that the square root of the
Pound-Overhauser XOR corresponds to a conditional rotation, thus obtaining a
universal set of gates; (3) Devised a spin-coherence implementation of the
Toffoli gate, and confirmed that it transforms the equilibrium state of a
four-spin system as expected; (4) Used standard gradient-pulse techniques in
NMR to equalize all but one of the populations in a two-spin system, so
obtaining the pseudo-pure state that corresponds to |00>; (5) Validated that
one can identify which basic pseudo-pure state is present by transforming it
into one-spin superpositions, whose associated spectra jointly characterize the
state; (6) Applied the spin-coherence XOR gate to a one-spin superposition to
create an entangled state, and confirmed its existence by detecting the
associated double-quantum coherence via gradient-echo methods.
