dorsal/arxiv
View SchemaAn Explicit Universal Gate-set for Exchange-Only Quantum Computation
| Authors | M. Hsieh, J. Kempe, S. Myrgren, K. B. Whaley |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0309002 |
| URL | https://arxiv.org/abs/quant-ph/0309002 |
| Journal | Quantum Information Processing, Vol. 2 (4), p. 289-307, 2003 |
Abstract
A 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.
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"abstract": "A single physical interaction might not be universal for quantum computation\nin general. It has been shown, however, that in some cases it can generate\nuniversal quantum computation over a subspace. For example, by encoding logical\nqubits into arrays of multiple physical qubits, a single isotropic or\nanisotropic exchange interaction can generate a universal logical gate-set.\nRecently, encoded universality for the exchange interaction was explicitly\ndemonstrated on three-qubit arrays, the smallest nontrivial encoding. We now\npresent the exact specification of a discrete universal logical gate-set on\nfour-qubit arrays. We show how to implement the single qubit operations exactly\nwith at most 3 nearest neighbor exchange operations and how to generate the\nencoded controlled-not with 29 parallel nearest neighbor exchange interactions\nor 54 serial gates, obtained from extensive numerical optimization using\ngenetic algorithms and Nelder-Mead searches. Our gate-sequences are immediately\napplicable to implementations of quantum circuits with the exchange\ninteraction.",
"arxiv_id": "quant-ph/0309002",
"authors": [
"M. Hsieh",
"J. Kempe",
"S. Myrgren",
"K. B. Whaley"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quantum Information Processing, Vol. 2 (4), p. 289-307, 2003",
"title": "An Explicit Universal Gate-set for Exchange-Only Quantum Computation",
"url": "https://arxiv.org/abs/quant-ph/0309002"
},
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