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Optimal two-qubit quantum circuits using exchange interactions

Heng Fan·Vwani Roychowdhury·Thomas Szkopek
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Abstract

The Heisenberg exchange interaction is a natural method to implement non-local (i.e., multi-qubit) quantum gates in quantum information processing. We consider quantum circuits comprising of $(SWAP)^α$ gates, which are realized through the exchange interaction, and single-qubit gates. A universal two-qubit quantum circuit is constructed from only three $(SWAP)^α$ gates and six single-qubit gates. We further show that three $(SWAP)^α$ gates are not only sufficient, but necessary. Since six single-qubit gates are known to be necessary, our universal two-qubit circuit is optimal in terms of the number of {\em both} $(SWAP)^α$ and single-qubit gates.

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Heng Fan, Vwani Roychowdhury, Thomas Szkopek. 2005-07-15. Optimal two-qubit quantum circuits using exchange interactions. https://doi.org/10.1103/physreva.72.052323

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