01661nas a2200217 4500008004100000245007400041210006900115260001400184300001400198490000600212520102000218100001701238700002301255700002501278700002201303700002101325700001901346700002301365700001801388856003701406 2008 eng d00aAnyonic interferometry and protected memories in atomic spin lattices0 aAnyonic interferometry and protected memories in atomic spin lat c2008/4/20 a482 - 4880 v43 a Strongly correlated quantum systems can exhibit exotic behavior called
topological order which is characterized by non-local correlations that depend
on the system topology. Such systems can exhibit remarkable phenomena such as
quasi-particles with anyonic statistics and have been proposed as candidates
for naturally fault-tolerant quantum computation. Despite these remarkable
properties, anyons have never been observed in nature directly. Here we
describe how to unambiguously detect and characterize such states in recently
proposed spin lattice realizations using ultra-cold atoms or molecules trapped
in an optical lattice. We propose an experimentally feasible technique to
access non-local degrees of freedom by performing global operations on trapped
spins mediated by an optical cavity mode. We show how to reliably read and
write topologically protected quantum memory using an atomic or photonic qubit.
Furthermore, our technique can be used to probe statistics and dynamics of
anyonic excitations.
1 aJiang, Liang1 aBrennen, Gavin, K.1 aGorshkov, Alexey, V.1 aHammerer, Klemens1 aHafezi, Mohammad1 aDemler, Eugene1 aLukin, Mikhail, D.1 aZoller, Peter uhttp://arxiv.org/abs/0711.1365v101525nas a2200145 4500008004100000245005200041210005200093260001400145490000700159520109700166100002401263700002301287700002501310856004401335 2006 eng d00aParallelism for Quantum Computation with Qudits0 aParallelism for Quantum Computation with Qudits c2006/9/280 v743 a Robust quantum computation with d-level quantum systems (qudits) poses two
requirements: fast, parallel quantum gates and high fidelity two-qudit gates.
We first describe how to implement parallel single qudit operations. It is by
now well known that any single-qudit unitary can be decomposed into a sequence
of Givens rotations on two-dimensional subspaces of the qudit state space.
Using a coupling graph to represent physically allowed couplings between pairs
of qudit states, we then show that the logical depth of the parallel gate
sequence is equal to the height of an associated tree. The implementation of a
given unitary can then optimize the tradeoff between gate time and resources
used. These ideas are illustrated for qudits encoded in the ground hyperfine
states of the atomic alkalies $^{87}$Rb and $^{133}$Cs. Second, we provide a
protocol for implementing parallelized non-local two-qudit gates using the
assistance of entangled qubit pairs. Because the entangled qubits can be
prepared non-deterministically, this offers the possibility of high fidelity
two-qudit gates.
1 aO'Leary, Dianne, P.1 aBrennen, Gavin, K.1 aBullock, Stephen, S. uhttp://arxiv.org/abs/quant-ph/0603081v101765nas a2200145 4500008004100000245006400041210006300105260001400168490000700182520131400189100002501503700002401528700002301552856004401575 2005 eng d00aAsymptotically Optimal Quantum Circuits for d-level Systems0 aAsymptotically Optimal Quantum Circuits for dlevel Systems c2005/6/140 v943 a As a qubit is a two-level quantum system whose state space is spanned by |0>,
|1>, so a qudit is a d-level quantum system whose state space is spanned by
|0>,...,|d-1>. Quantum computation has stimulated much recent interest in
algorithms factoring unitary evolutions of an n-qubit state space into
component two-particle unitary evolutions. In the absence of symmetry, Shende,
Markov and Bullock use Sard's theorem to prove that at least C 4^n two-qubit
unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa
(VMS) use the QR matrix factorization and Gray codes in an optimal order
construction involving two-particle evolutions. In this work, we note that
Sard's theorem demands C d^{2n} two-qudit unitary evolutions to construct a
generic (symmetry-less) n-qudit evolution. However, the VMS result applied to
virtual-qubits only recovers optimal order in the case that d is a power of
two. We further construct a QR decomposition for d-multi-level quantum logics,
proving a sharp asymptotic of Theta(d^{2n}) two-qudit gates and thus closing
the complexity question for all d-level systems (d finite.) Gray codes are not
required, and the optimal Theta(d^{2n}) asymptotic also applies to gate
libraries where two-qudit interactions are restricted by a choice of certain
architectures.
1 aBullock, Stephen, S.1 aO'Leary, Dianne, P.1 aBrennen, Gavin, K. uhttp://arxiv.org/abs/quant-ph/0410116v201715nas a2200145 4500008004100000245004200041210004200083260001400125490000700139520130700146100002301453700002401476700002501500856004401525 2005 eng d00aCriteria for Exact Qudit Universality0 aCriteria for Exact Qudit Universality c2005/5/160 v713 a We describe criteria for implementation of quantum computation in qudits. A
qudit is a d-dimensional system whose Hilbert space is spanned by states |0>,
|1>,... |d-1>. An important earlier work of Mathukrishnan and Stroud [1]
describes how to exactly simulate an arbitrary unitary on multiple qudits using
a 2d-1 parameter family of single qudit and two qudit gates. Their technique is
based on the spectral decomposition of unitaries. Here we generalize this
argument to show that exact universality follows given a discrete set of single
qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to
the QR-matrix decomposition of numerical linear algebra. We consider a generic
physical system in which the single qudit Hamiltonians are a small collection
of H_{jk}^x=\hbar\Omega (|k>k iff H_{jk}^{x,y} are allowed Hamiltonians. One qudit exact universality
follows iff this graph is connected, and complete universality results if the
two-qudit Hamiltonian H=-\hbar\Omega |d-1,d-1>