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arXiv:quant-ph/0105147 · Applied Physics Letters

Non-thermal nuclear magnetic resonance quantum computing using hyperpolarized xenon

Anne S. Verhulst, Oskar Liivak, Mark H. Sherwood, Hans-Martin Vieth, Isaac L. Chuang

Published Oct 8, 2001• 39 citations
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Abstract

Current experiments in liquid-state nuclear magnetic resonance (NMR) quantum computing are limited by low initial polarization. To address this problem, we have investigated the use of optical pumping techniques to enhance the polarization of a 2-qubit NMR quantum computer (C13 and H1 in CHCl313). We have generalized the procedure for effective pure state preparation in order to efficiently use the increased polarization. With this more flexible scheme, an effective pure state is prepared with polarization enhancement of a factor of 10 compared to the thermal state. An implementation of Grover’s quantum search algorithm with a polarization-enhanced spin system is demonstrated.

DOI
10.1063/1.1409279

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Current experiments in liquid-state nuclear magnetic resonance (NMR) quantum computing are limited by low initial polarization. To address this problem, we have investigated the use of optical pumping techniques to enhance the polarization of a 2-qubit NMR quantum computer (C13 and H1 in CHCl313). We have generalized the procedure for effective pure state preparation in order to efficiently use the increased polarization. With this more flexible scheme, an effective pure state is prepared with polarization enhancement of a factor of 10 compared to the thermal state. An implementation of Grover’s quantum search algorithm with a polarization-enhanced spin system is demonstrated.
Current experiments in liquid-state nuclear magnetic resonance quantum computing are limited by low initial polarization. To address this problem, we have investigated the use of optical pumping techniques to enhance the polarization of a 2-qubit NMR quantum computer (13C and 1H in 13CHCl3). To efficiently use the increased polarization, we have generalized the procedure for effective pure state preparation. With this new, more flexible scheme, an effective pure state was prepared with polarization-enhancement of a factor of 10 compared to the thermal state. An implementation of Grover's quantum search algorithm was demonstrated using this new technique.
While quantum computing offers the potential of using new quantum algorithms to tackle problems that are intractable for classical processors, its implementation requires the development of quantum devices, which are as yet unavailable. The most complex implementations of quantum algorithms to date have used techniques adapted from nuclear magnetic resonance (NMR) spectroscopy, but current liquid state NMR approaches cannot be extended to systems with many quantum bits, as it is not possible to prepare pure initial states by directly cooling the spin system into its ground state. Furthermore, it has been shown that current NMR experiments involve only separable states, and thus could in principle be described by local hidden variable models. Here we demonstrate how para-hydrogen can be used to prepare a two-spin system in an almost pure state and so overcome these two objections. To achieve polarisation comparable to our observed value of epsilon=0.916pm0.019\\epsilon = 0.916 \\pm 0.019epsilon=0.916pm0.019 by thermal means would require cooling to 6.4 mK in the 9.6 T field used, or a magnetic field of 0.45 MT at room temperature.
We consider two new quantum gate mechanisms based on nuclear spins in hyperpolarized solid 129Xe^{129}Xe129Xe and HCl mixtures and inorganic semiconductors. We propose two schemes for implementing a controlled NOT (CNOT) gate based on nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) from hyperpolarized solid 129Xe^{129}Xe129Xe and HCl mixtures and optically pumped NMR in semiconductors. Such gates might be built up with particular spins addressable based on MRI techniques and optical pumping and optical detection techniques. The schemes could be useful for implementing actual quantum computers in terms of a cellular automata architecture.
Nuclear magnetic resonance (NMR) is well-suited to implement quantum algorithms experimentally. However, there are serious problems associated with the noisy mixed initial state that is described by the thermal equilibrium density operator of NMR spectroscopy. Here we present a new strategy to dramatically increase the sensitivity of a NMR quantum computing experiment. Para hydrogen can be used to prepare a density operator in a suitable molecule that is very close to a pure state, an improvement on the order of 104 compared to “conventional” NMR quantum computing. Our strategy is demonstrated experimentally solving the Deutsch–Jozsa problem based on para hydrogen and Vaska’s complex.
A new method of preparing the pseudo-pure state of a spin system for quantum computation in liquid nuclear magnetic resonance (NMR) was put forward and demonstrated experimentally. Applying appropriately connected line-selective pulses simultaneously and a field gradient pulse techniques we acquired straightforwardly all pseudo-pure states for two qubits in a single experiment much efficiently. The signal intensity with the pseudo-pure state prepared in this way is the same as that of temporal averaging. Our method is suitable for the system with arbitrary numbers of qubits. As an example of application, a highly structured search algorithm—-Hogg’s algorithm was also performed on the pseudo-pure state | 00 〉 prepared by our method.