Parallelism for quantum computation with qudits
- Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland 20742, USA and Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020, Innsbruck (Austria)
- IDA Center for Computing Sciences, 17100 Science Drive, Bowie, Maryland 20715-4300 (United States)
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 {sup 87}Rb and {sup 133}Cs. 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.
- OSTI ID:
- 20857687
- Journal Information:
- Physical Review. A, Vol. 74, Issue 3; Other Information: DOI: 10.1103/PhysRevA.74.032334; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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