An Explicit Universal Gate-set for Exchange-Only Quantum Computation

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dc.creatorHsieh, M.
dc.creatorKempe, J.
dc.creatorMyrgren, S.
dc.creatorWhaley, K. B.
dc.date2003-08-30
dc.date2003-12-23
dc.date.accessioned2026-07-07T06:07:43Z
dc.date.available2026-07-07T06:07:43Z
dc.descriptionA single physical interaction might not be universal for quantum computation in general. It has been shown, however, that in some cases it can generate universal quantum computation over a subspace. For example, by encoding logical qubits into arrays of multiple physical qubits, a single isotropic or anisotropic exchange interaction can generate a universal logical gate-set. Recently, encoded universality for the exchange interaction was explicitly demonstrated on three-qubit arrays, the smallest nontrivial encoding. We now present the exact specification of a discrete universal logical gate-set on four-qubit arrays. We show how to implement the single qubit operations exactly with at most 3 nearest neighbor exchange operations and how to generate the encoded controlled-not with 29 parallel nearest neighbor exchange interactions or 54 serial gates, obtained from extensive numerical optimization using genetic algorithms and Nelder-Mead searches. Our gate-sequences are immediately applicable to implementations of quantum circuits with the exchange interaction.
dc.description16 pages, 6 figures, new appendix and figures, revised version as accepted for publication
dc.identifierhttps://arxiv.org/abs/quant-ph/0309002
dc.identifierhttp://arxiv.org/abs/quant-ph/0309002
dc.identifierQuantum Information Processing, Vol. 2 (4), p. 289-307, 2003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/91386
dc.subjectQuantum Physics
dc.titleAn Explicit Universal Gate-set for Exchange-Only Quantum Computation
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