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Exact gate-sequences for universal quantum computation using the XY-interaction alone

J. Kempe·K. B. Whaley
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Abstract

In a previous publication [1] we showed that it is possible to implement universal quantum computation with the anisotropic XY-Heisenberg exchange acting as a single interaction. To achieve this we used encodings of the states of the computation into a larger Hilbert space. This proof is non- constructive, however, and did not explicitly give the trade-offs in time that are required to implement encoded single qubit operations and encoded two-qubit gates. Here we explicitly give the gate-sequences needed to simulate these operations on encoded qubits and qutrits (three-level systems) and analyze the trade-offs involved. We also propose a possible layout for the qubits in a triangular arrangement.

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J. Kempe, K. B. Whaley. 2002-05-23. Exact gate-sequences for universal quantum computation using the XY-interaction alone. https://doi.org/10.1103/physreva.65.052330

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