Nuclear Magnetic Resonance Spectroscopy: An Experimentally Accessible Paradigm for Quantum Computing

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. 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 pseudo-pure 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 pseudo-pure 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 Pound-Overhauser double resonance, and the other using a spin-coherence double resonance pulse sequence. • Demonstrated that the square root of the Pound-Overhauser XOR corresponds to a conditional rotation, thus obtaining a universal set of gates. • Devised a spin-coherence implementation of the Toffoli gate, and confirmed that it transforms the equilibrium state of a four-spin system as expected. • 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〉. • 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. • 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.