01525nas 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/0603081v1