Preparing High Purity Initial States for Nuclear Magnetic Resonance Quantum Computing

Abstract

Here we demonstrate how para-hydrogen can be used to prepare a two-spin system in an almost pure state which is suitable for implementing nuclear magnetic resonance (NMR) quantum computation. A 12 ns laser pulse is used to initiate a chemical reaction involving pure para-hydrogen (the nuclear spin singlet of H2). The product, formed on the µs timescale, contains a hydrogen-derived two-spin system with an effective spin-state purity of 0.916. To achieve a comparable result by direct cooling would require an unmanageable (in the liquid state) temperature of 6.4 mK or an impractical magnetic field of 0.45 MT at room temperature. The resulting spin state has an entanglement of formation of 0.822 and cannot be described by local hidden variable models.PACS numbers: 03.67. Lx, 03.67.Mn, Introduction. While quantum computing [1] 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 [2,3,4,5], 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 [6]. Furthermore, it has been shown that current NMR experiments involve only separable states [7], and thus could in principle be described by local hidden variable models.The conventional approach in NMR quantum computing [4] is to use an ensemble of spins, and to prepare a pseudo-pure ground state [2,4] of the form

Implementing Grover’s quantum search on a para-hydrogen based pure state NMR quantum computer

“…We have recently shown how high purity initial states can be prepared using para-hydrogen techniques [12,13], and that these states can be used to perform the simplest quantum computation, Deutsch's algorithm [14]. Similar results have been obtained by Hübler et al [15], albeit with a lower spin state purity.…”

“…We have, therefore, prepared a novel but closely related system, Ru(H) 2 (CO) 2 (dpae), where dpae indicates 1,2-bis(diphenylarsino)ethane. This system has a slightly longer 1 H spin-spin relaxation time (T 2 = 0.67 s), and has the further advantage that the initial state can be prepared with a purity indistinguishable from one (the purity was measured using techniques described previously [12,13] and was found to be ε = 1.06 ± 0.04). Thus we describe our new system as a pure state NMR quantum computer.…”

“…Intermediates of this type have been shown to react with hydrogen on the sub-microsecond timescale [25], which would in this case lead to the formation of Ru(H) 2 (CO) 2 (dpae). For further details see [12,13,14].…”

“…The para-hydrogen molecule cannot be used directly for NMR quantum computing, due to its high symmetry, but this can be overcome by using a chemical reaction to prepare a new molecule, in which the two hydrogen atoms can be made distinct and can be separately addressed. For further details see [12,13,14,15,17,18,19,20]. In our previous work we have used the two hydride 1 H nuclei in Ru(H) 2 (CO) 2 (dppe), where dppe indicates 1,2-bis(diphenylphosphino)ethane, as our NMR quantum computer.…”

“…The precursor compound Ru(CO) 3 (dpae) was prepared from Ru 3 (CO) 12 and dpae using techniques described previously [12,23]. Essentially pure para-hydrogen was prepared at a temperature of 18 K using a charcoal-based catalyst, and was introduced into a 5 mm NMR tube containing Ru(CO) 3 (dpae) dissolved in d 6 -benzene.…”