Parallelism for quantum computation with qudits

Dianne P. O'Leary*, Gavin K. Brennen, Stephen S. Bullock

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


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.

Original languageEnglish
Article number032334
Pages (from-to)1-11
Number of pages11
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number3
Publication statusPublished - 2006
Externally publishedYes


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