Nuclear magnetic resonance quantum computing exploiting the pure spin state of para hydrogen

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.

Geminal parahydrogen-induced polarization: accumulating long-lived singlet order on methylene proton pairs

In the majority of hydrogenative parahydrogen-induced polarization (PHIP) experiments, the hydrogen molecule undergoes pairwise cis addition to an unsaturated precursor to occupy vicinal positions on the product molecule. However, some ruthenium-based hydrogenation catalysts induce geminal hydrogenation, leading to a reaction product in which the two hydrogen atoms are transferred to the same carbon centre, forming a methylene (CH 2 ) group. The singlet order of parahydrogen is substantially retained over the geminal hydrogenation reaction, giving rise to a singlet-hyperpolarized CH 2 group. Although the T 1 relaxation times of the methylene protons are often short, the singlet order has a long lifetime, provided that singlet-triplet mixing is suppressed, either by chemical equivalence of the protons or by applying a resonant radiofrequency field. The long lifetime of the singlet order enables the accumulation of hyperpolarization during the slow hydrogenation reaction. We introduce a kinetic model for the behaviour of the observed hyperpolarized signals, including both the chemical kinetics and the spin dynamics of the reacting molecules. Our work demonstrates the feasibility of producing singlet-hyperpolarized methylene moieties by parahydrogen-induced polarization. This potentially extends the range of molecular agents which may be generated in a hyperpolarized state by chemical reactions of parahydrogen.

Photochemical pump and NMR probe to monitor the formation and kinetics of hyperpolarized metal dihydrides

Pulsed-laser experiments validate photochemical pump-NMR probe spectroscopy for monitoring the rate of rapid H₂ oxidative addition to a metal centre.

On reaction of IrI(CO)(PPh₃)₂1 with para-hydrogen (p-H₂), Ir(H)₂I(CO)(PPh₃)₂2 is formed which exhibits strongly enhanced ¹H NMR signals for its hydride resonances. Complex 2 also shows similar enhancement of its NMR spectra when it is irradiated under p-H₂. We report the use of this photochemical reactivity to measure the kinetics of H₂ addition by laser-synchronized reactions in conjunction with NMR. The single laser pulse promotes the reductive elimination of H₂ from Ir(H)₂I(CO)(PPh₃)₂2 in C₆D₆ solution to form the 16-electron precursor 1, back reaction with p-H₂ then reforms 2 in a well-defined nuclear spin-state. The build up of this product can be followed by incrementing a precisely controlled delay (τ), in millisecond steps, between the laser and the NMR pulse. The resulting signal vs. time profile shows a dependence on p-H₂ pressure. The plot of k_obs against p-H₂ pressure is linear and yields the second order rate constant, k₂, for H₂ addition to 1 of (3.26 ± 0.42) × 10² M^–1 s^–1. Validation was achieved by transient-UV-vis absorption spectroscopy which gives k₂ of (3.06 ± 0.40) × 10² M^–1 s^–1. Furthermore, irradiation of a C₆D₆ solution of 2 with multiple laser shots, in conjunction with p-H₂ derived hyperpolarization, allows the detection and characterisation of two minor reaction products, 2a and 3, which are produced in such low yields that they are not detected without hyperpolarization. Complex 2a is a configurational isomer of 2, while 3 is formed by substitution of CO by PPh₃.

Nuclear spin isomers of guest molecules in H₂@C₆₀, H₂O@C₆₀ and other endofullerenes

Spectroscopic studies of recently synthesized endofullerenes, in which H₂, H₂O and other atoms and small molecules are trapped in cages of carbon atoms, have shown that although the trapped molecules interact relatively weakly with the internal environment they are nevertheless susceptible to appropriately applied external perturbations. These properties have been exploited to isolate and study samples of H₂ in C₆₀ and other fullerenes that are highly enriched in the para spin isomer. Several strategies for spin-isomer enrichment, potential extensions to other endofullerenes and possible applications of these materials are discussed.

Parahydrogen Induced polarization by homogeneous catalysis: theory and applications

The alignment of the nuclear spins in parahydrogen can be transferred to other molecules by a homogeneously catalyzed hydrogenation reaction resulting in dramatically enhanced NMR signals. In this chapter we introduce the involved theoretical concepts by two different approaches: the well known, intuitive population approach and the more complex but more complete density operator formalism. Furthermore, we present two interesting applications of PHIP employing homogeneous catalysis. The first demonstrates the feasibility of using PHIP hyperpolarized molecules as contrast agents in (1)H MRI. The contrast arises from the J-coupling induced rephasing of the NMR signal of molecules hyperpolarized via PHIP. It allows for the discrimination of a small amount of hyperpolarized molecules from a large background signal and may open up unprecedented opportunities to use the standard MRI nucleus (1)H for, e.g., metabolic imaging in the future. The second application shows the possibility of continuously producing hyperpolarization via PHIP by employing hollow fiber membranes. The continuous generation of hyperpolarization can overcome the problem of fast relaxation times inherent in all hyperpolarization techniques employed in liquid-state NMR. It allows, for instance, the recording of a reliable 2D spectrum much faster than performing the same experiment with thermally polarized protons. The membrane technique can be straightforwardly extended to produce a continuous flow of a hyperpolarized liquid for MRI enabling important applications in natural sciences and medicine.

Mechanism of nuclear spin initiated para-H2 to ortho-H2 conversion

In this paper a quantitative explanation for a diamagnetic ortho/para H2 conversion is given. The description is based on the quantum-mechanical density matrix formalism originally developed by Alexander and Binsch for studies of exchange processes in NMR spectra. Only the nuclear spin system is treated quantum-mechanically. Employing the model of a three spin system, the reactions of the hydrogen gas with the catalysts are treated as a phenomenological rate process, described by a rate constant. Numerical calculations reveal that for nearly all possible geometrical arrangements of the three spin system an efficient spin conversion is obtained. Only in the chemically improbable case of a linear group H-X-H no spin conversion is obtained. The efficiency of the spin conversion depends strongly on the lifetime of the H-X-H complex and on the presence of exchange interactions between the two hydrogens. Even moderate exchange couplings cause a quench of the spin conversion. Thus a sufficiently strong binding of the dihydrogen to the S spin is necessary to render the quenching by the exchange interaction ineffective.

Quantum logical operations for spin 3/2 quadrupolar nuclei monitored by quantum state tomography

This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3/2 systems. By doing so, the possibility of controlling relative phases of superimposed pseudo-pure states is demonstrated. In addition, many aspects of the effect of the quadrupolar evolution, occurring during the RF pulses, on the quantum operations performance are discussed. Most of the procedures presented can be easily adapted to describe selective pulses of higher spin systems (>3/2) and for spin 1/2 under J couplings.

Generation and interrogation of a pure nuclear spin state by parahydrogen-enhanced NMR spectroscopy: a defined initial state for quantum computation

We describe a number of studies used to establish that parahydrogen can be used to prepare a two-spin system in a pure state, which is suitable for implementing NMR quantum computation. States are generated by pulsed and continuous-wave (CW) UV laser initiation of a chemical reaction between Ru(CO)(3)(L(2)) [where L(2) = dppe = 1,2-bis(diphenylphosphino)ethane or L(2) = dpae = 1,2-bis(diphenylarsino)ethane] with pure parahydrogen (generated at 18 K). This process forms Ru(CO)(2)(dppe)(H)(2) and Ru(CO)(2)(dpae)(H)(2) on a sub-microsecond time-scale. With the pulsed laser, the spin state of the hydride nuclei in Ru(CO)(2)(dppe)(H)(2) has a purity of 89.8 +/- 2.6% (from 12 measurements). To achieve comparable results by cooling would require a temperature of 6.6 mK, which is unmanageable in the liquid state, or an impractical magnetic field of 0.44 MT at room temperature. In the case of CW initiation, reduced state purities are observed due to natural signal relaxation even when a spin-lock is used to prevent dephasing. When Ru(CO)(3)(dpae) and pulsed laser excitation are utilized, the corresponding dihydride product spin state purity was determined as 106 +/- 4% of the theoretical maximum. In other words, the state prepared using Ru(CO)(3)(dpae) as the precursor is indistinguishable from a pure state.

Preparing high purity initial states for nuclear magnetic resonance quantum computing

Here we demonstrate how parahydrogen can be used to prepare a two-spin system in an almost pure state which is suitable for implementing nuclear magnetic resonance quantum computation. A 12 ns laser pulse is used to initiate a chemical reaction involving pure parahydrogen (the nuclear spin singlet of H2). The product, formed on the micros time scale, 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.