Parallelism for Quantum Computation with Qudits

Published

March 31, 2006

Author(s)

Dianne M. O'Leary

Abstract

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.

Citation

Physical Review A (Atomic, Molecular and Optical Physics)

Volume

74

Issue

3

Pub Type

Journals

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Keywords

quantum computing, qudit, universal quantum computation

Citation

O'Leary, D. (2006), Parallelism for Quantum Computation with Qudits, Physical Review A (Atomic, Molecular and Optical Physics), [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150616 (Accessed April 19, 2024)