3 research outputs found
Matrix manipulations via unitary transformations and ancilla-state measurements
We propose protocols for calculating inner product, matrix addition and
matrix multiplication based on multiqubit Toffoli-type and the simplest
one-qubit operations and employ ancilla measurements to remove all garbage of
calculations. The depth (runtime) of the addition protocol is and that
of other protocols logarithmically increases with the dimensionality of the
considered matrices.Comment: 5 pages, 1 figur
Multiple quantum NMR of spin-carrying molecules in nanopores: high order corrections to the two-spin/two-quantum Hamiltonian
This paper is devoted to the multiple-quantum (MQ) NMR spectroscopy in
nanopores filled by a gas of spin-carrying molecules (s=1/2) in a strong
external magnetic field. It turned out that the high symmetry of the spin
system in nanopores yields a possibility to overcome the problem of the
exponential growth of the Hilbert space dimension with an increase in the
number of spins and to investigate MQ NMR dynamics in systems consisting of
several hundred spins. We investigate the dependence of the MQ coherence
intensities on their order (the profile of the MQ coherence intensities) for a
spin system governed by the standard MQ NMR Hamiltonian (the nonsecular
two-quantum/two-spin Hamiltonian) together with the second order correction of
the average Hamiltonian theory. It is shown that the profile depends on the
value of this correction and varies from the exponential to the logarithmic
one.Comment: 7 pages, 3 figure