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Non-thermal nuclear magnetic resonance quantum computing using hyperpolarized Xenon

Verhulst, A S, Liivak, O, Sherwood, M H, Vieth, H M, Isaac L. Chuang

Published May 30, 2001• 34 citations
OpenAlex

Abstract

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.

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•Jan 1, 2000•38 citations
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.
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.
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.
Liquid crystals offer several advantages as solvents for molecules used for nuclear magnetic resonance quantum computing (NMRQC). The dipolar coupling between nuclear spins manifest in the NMR spectra of molecules oriented by a liquid crystal permits a significant increase in clock frequency, while short spin-lattice relaxation times permit fast recycling of algorithms, and save time in calibration and signal-enhancement experiments. Furthermore, the use of liquid crystal solvents offers scalability in the form of an expanded library of spin-bearing molecules suitable for NMRQC. These ideas are demonstrated with the successful execution of a two-qubit Grover search using a molecule (13C 1HCl3) oriented in a liquid crystal and a clock speed eight times greater than in an isotropic solvent. Perhaps more importantly, five times as many logic operations can be executed within the coherence time using the liquid crystal solvent.
This thesis addresses the problems of initialization and separability in liquid state NMR based quantum information processors. We prepare pure quantum states lying above the entanglement threshold. Our pure state quantum computer derives its purity from the highly polarized nuclear spin states in the para-hydrogen molecule. The thesis begins with a critique of conventional NMR based quantum information processing outlining the major strengths and weaknesses of the technology. We describe the enhanced magnetic ordering of the nuclear spin states in para-hydrogen and an initialization experiment exploiting this effect to achieve pure, entangled states. These states can indeed be used as initial states in implementing quantum algorithms: we describe mplementations of the Deutsch and the Grover quantum algorithms. The "twirl" operation converts a completely arbitrary input state to a Werner singlet. The NMR implementation of this operation is taken up. We also analyze the possibility of sharing the purity of some highly polarized qubits in a quantum computer onto quantum subspaces of arbitrary dimensions, and whether these sharing operations increase or decrease the likelihood of entanglement.
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.