The authors introduce a decomposition of exponentials of Weyl-Heisenberg and Gell-Mann strings into single- and two-qutrit gates, apply it to qutrit QAOA for graph k-coloring, and generalize the Steiner-Gauss routing method to qutrits.
On swapping the states of two qudits
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abstract
The SWAP gate has become an integral feature of quantum circuit architectures and is designed to permute the states of two qubits through the use of the well-known controlled-NOT gate. We consider the question of whether a two-qudit quantum circuit composed entirely from instances of the generalised controlled-NOT gate can be constructed to permute the states of two qudits. Arguing via the signature of a permutation, we demonstrate the impossibility of such circuits for dimensions $d \equiv 3$ (mod 4).
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Decomposition of multi-qutrit gates generated by Weyl-Heisenberg strings
The authors introduce a decomposition of exponentials of Weyl-Heisenberg and Gell-Mann strings into single- and two-qutrit gates, apply it to qutrit QAOA for graph k-coloring, and generalize the Steiner-Gauss routing method to qutrits.