Nuclear magnetic resonance spectroscopy: An experimentally accessible paradigm for quantum computing
Abstract
We present experimental results which demonstrate that nuclear magnetic resonance spectroscopy is capable of emulating many of the capabilities of quantum computers, including unitary evolution and coherent superpositions, but without attendant wavefunction collapse. This emulation is made possible by two facts. The first is that the spin active nuclei in each molecule of a liquid sample are largely isolated from the spins in all other molecules, so that each molecule is effectively an independent quantum computer. The second is the existence of a manifold of statistical spin states, called pseudopure states, whose transformation properties are identical to those of true pure states. These facts enable us to operate on coherent superpositions over the spins in each molecule using full quantum parallelism, and to combine the results into deterministic macroscopic observables via thermodynamic averaging. We call a device based on these principles an ensemble quantum computer. Our results show that it is indeed possible to prepare a pseudopure state in a macroscopic liquid sample under ambient conditions, to transform it into a coherent superposition, to apply elementary quantum logic gates to this superposition, and to convert it into the equivalent of an entangled state. Specifically, we have:  implemented the quantum XOR gate in two different ways, one using PoundOverhauser double resonance, and the other using a spincoherence double resonance pulse sequence;
 demonstrated that the square root of the PoundOverhauser XOR corresponds to a conditional rotation, thus confirming that NMR spectroscopy provides a universal set of gates;
 devised a spincoherence implementation of the Toffoli gate, and confirmed that it transforms the equilibrium state of a fourspin system as expected;
 used standard gradientpulse techniques in NMR to equalize all but one of the populations in a twospin system, thus obtaining the basic pseudopure state that corresponds to 00>;
 validated that one can identify which basic pseudopure state is present by transforming it into onespin superpositions, whose associated spectra jointly characterize the state;
 applied the spincoherence XOR gate to a onespin superposition to create an entangled state, and confirmed its existence by detecting the associated doublequantum coherence via gradientecho methods.
 Publication:

Physica D Nonlinear Phenomena
 Pub Date:
 September 1998
 DOI:
 10.1016/S01672789(98)000463
 arXiv:
 arXiv:quantph/9709001
 Bibcode:
 1998PhyD..120...82C
 Keywords:

 QUANTUM AND MOLECULAR COMPUTING;
 MACROSCOPIC QUANTUM PHENOMENA;
 NUCLEAR MAGNETIC RESONANCE TECHNIQUES;
 Quantum Physics
 EPrint:
 LaTeX + epsfig + amsmath packages, 27 pages, 12 figures, to appear in Physica D