TY - JOUR

T1 - Parallelism for quantum computation with qudits

AU - O'Leary, Dianne P.

AU - Brennen, Gavin K.

AU - Bullock, Stephen S.

PY - 2006

Y1 - 2006

N2 - 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 (time) 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 alkali-metal atoms Rb87 and Cs133. Second, we provide a protocol for implementing parallelized nonlocal two-qudit gates using the assistance of entangled qubit pairs. Using known protocols for qubit entanglement purification, this offers the possibility of high-fidelity two-qudit gates.

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 (time) 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 alkali-metal atoms Rb87 and Cs133. Second, we provide a protocol for implementing parallelized nonlocal two-qudit gates using the assistance of entangled qubit pairs. Using known protocols for qubit entanglement purification, this offers the possibility of high-fidelity two-qudit gates.

UR - http://www.scopus.com/inward/record.url?scp=33749357062&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.74.032334

DO - 10.1103/PhysRevA.74.032334

M3 - Article

AN - SCOPUS:33749357062

VL - 74

SP - 1

EP - 11

JO - Physical Review A: covering atomic, molecular, and optical physics and quantum information

JF - Physical Review A: covering atomic, molecular, and optical physics and quantum information

SN - 2469-9926

IS - 3

M1 - 032334

ER -