Exact Synthesis of Qutrit Toffoli+Hadamard and Clifford+T
Lia Yeh from Oxford University (@CompSciOxford ) presents at the QuDits for Quantum Technology workshop, hosted by the Quantum Interactions Theory Group at the Institute for Quantum Computing, University of Waterloo. Learn more: https://quantum-interactions.com/
This talk is about two papers. In the first paper, we introduce the qudit ZH-calculus and generalize all the qubit phase-free ZH-calculus rules to qudits of prime dimension d. We prove that the phase-free qudit ZH-calculus is universal for matrices over the ring. We define the qudit Toffoli+Hadamard gate set and justify this definition, by constructing all d-ary classical reversible circuits from just the Toffoli gate, and by showing that Toffoli+Hadamard is moreover also approximately universal for quantum computation in any odd prime qudit dimension. Furthermore, we show that as is the case for qubits, qudit phase-free ZH-calculus diagrams correspond precisely to circuits allowing post-selections over this Toffoli+Hadamard gate set.
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