Hamiltonians for liquid-state NMR quantum computing. Choice of rotating frame

Yasushi Kondo, Mikio Nakahara, Shogo Tanimura

Raymond Laflamme

康 近藤, 幹夫 中原, 和也 畑 +1 more

A Hamiltonian in the rotating frame is derived for NMR quantum computing with homonucleus molecules as its computational resource. It is theoretically shown that control pulses designed for heteronucleus spins can be translated to pulses for homonucleus spins by simply replacing hard pulses by soft pulses with properly chosen pulse width. Several experiments employing cytosine as a homonucleus molecule are conducted and it is proved experimentally that the above Hamiltonian accurately describes the dynamics of the spins.

Yasushi Kondo

Sundaresan Jayanthi, Adonis Lupulescu, Julia Grinshtein +1 more

Recently, Pang et al reported a novel polarization transfer scheme applicable to three-spin systems, whereby a rotating-frame NMR analogue of the cross effect could transfer polarization between; e.g., two 13Cs and an 15N in a single crystal. The present work furthers this scheme to the case of powder NMR under magic angle spinning (MAS) conditions, as well as to solution NMR. It is found that in all such cases a second-order average Hamiltonian can transfer polarization between non-equivalent, coupled abundant spins (e.g., two 1Hs) prepared in anti-longitudinal magnetization states, and the spin-locked magnetization of a rare spins (e.g., one 13C). The average Hamiltonian for such three-spin (S1-S2) to I transfer was derived for both liquids and solids, and found in good quantitative agreement with numerical simulations and experiments. At an optimal transfer condition whereby an I-spin RF irradiation field matches the S1-S2 chemical-shift-difference, a maximum polarization enhancement equal to the ratio of gyromagnetic ratios is achieved; as explained and demonstrated in the study, ca. half of this can be effectively obtained for I = 13C in powdered solids and in multi-spin systems in solutions. All such processes display an oscillatory nature, meaning that the transverse spin-locked polarization of a rare spin can become anti-longitudinal magnetization of abundant spins -without ever pulsing on the latter. The roles played by many-body interactions, RF inhomogeneities, and interferences of other coherences during the execution of these novel forms of cross-polarization were investigated, and are exemplified with experiments and simulations.

Yasushi Kondo, Nakahara, Mikio, Hata, Kazuya +1 more

We derive the Hamiltonian in the rotating frame for NMR quantum computing with homonucleus molecules as its computational resource. The Hamiltonian thus obtained is different from conventional Hamiltonians that appear in literature. It is shown that control pulses designed for heteronucleus spins can be translated to pulses for homonucleus spins by simply replacing hard pulses by soft pulses with properly chosen pulse width. To demonstrate the validity of our Hamiltonian, we conducted several experiments employing cytosine as a homonucleus molecule. All the experimental results demonstrate that our Hamiltonian accurately describes the dynamics of the spins, while the conventional Hamiltonian fails. Finally we use our Hamiltonian for precise control of field inhomogeneity compensation with a pair of $π$-pulses.