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

M. Hsieh·J. Kempe·S. Myrgren·K. B. Whaley
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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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M. Hsieh, J. Kempe, S. Myrgren, K. B. Whaley. 2003-12-23. An Explicit Universal Gate-set for Exchange-Only Quantum Computation. https://arxiv.org/abs/quant-ph/0309002

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