TY - JOUR
T1 - Parallelism for Quantum Computation with Qudits
JF - Physical Review A
Y1 - 2006
A1 - Dianne P. O'Leary
A1 - Gavin K. Brennen
A1 - Stephen S. Bullock
AB - 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.
VL - 74
UR - http://arxiv.org/abs/quant-ph/0603081v1
CP - 3
J1 - Phys. Rev. A
U5 - 10.1103/PhysRevA.74.032334
ER -