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Quantum Computing in Arrays Coupled by 'Always On' Interactions
It has recently been shown that one can perform quantum computation in a
Heisenberg chain in which the interactions are 'always on', provided that one
can abruptly tune the Zeeman energies of the individual (pseudo-)spins. Here we
provide a more complete analysis of this scheme, including several
generalizations. We generalize the interaction to an anisotropic form
(incorporating the XY, or Forster, interaction as a limit), providing a proof
that a chain coupled in this fashion tends to an effective Ising chain in the
limit of far off-resonant spins. We derive the primitive two-qubit gate that
results from exploiting abrupt Zeeman tuning with such an interaction. We also
demonstrate, via numerical simulation, that the same basic scheme functions in
the case of smoothly shifted Zeeman energies. We conclude with some remarks
regarding generalisations to two- and three-dimensional arrays.Comment: 16 pages (preprint format) inc. 3 figure
Quantum Computing with Globally Controlled Exchange-type Interactions
If the interaction between qubits in a quantum computer has a non-diagonal
form (e.g. the Heisenberg interaction), then one must be able to "switch it
off" in order to prevent uncontrolled propagation of states. Therefore, such QC
schemes typically demand local control of the interaction strength between each
pair of neighboring qubits. Here we demonstrate that this degree of control is
not necessary: it suffices to switch the interaction collectively - something
that can in principle be achieved by global fields rather than with local
manipulations. This observation may offer a significant simplification for
various solid state, optical lattice and NMR implementations.Comment: 3 pages inc. 3 figure
Representations and classification of traveling wave solutions to Sinh-G{\"o}rdon equation
Two concepts named atom solution and combinatory solution are defined. The
classification of all single traveling wave atom solutions to Sinh-G{\"o}rdon
equation is obtained, and qualitative properties of solutions are discussed. In
particular, we point out that some qualitative properties derived intuitively
from dynamic system method aren't true. In final, we prove that our solutions
to Sinh-G{\"o}rdon equation include all solutions obtained in the paper[Fu Z T
et al, Commu. in Theor. Phys.(Beijing) 2006 45 55]. Through an example, we show
how to give some new identities on Jacobian elliptic functions.Comment: 12 pages. accepted by Communications in theoretical physics (Beijing
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