Algebraic Methods in Quantum Compiling

IQC Seminar - Sarah Meng Li, University of Amsterdam, Centrum Wiskunde & Informatica (CWI)

Quantum compiling translates a quantum algorithm into a sequence of elementary operations. There exists a correspondence between certain quantum circuits and matrices over some number rings. This number-theoretic perspective reveals important properties of gate sets and leads to improved quantum compiling protocols. Here, we demonstrate several algebraic methods in quantum circuit characterization and optimization, based on my master’s research at IQC.

First, we design two improved synthesis algorithms for Toffoli-Hadamard circuits, achieving an exponential reduction in circuit size. Second, we define a unique normal form for qutrit Clifford operators. This allows us to find a set of relations that suffice to rewrite any qutrit Clifford circuit to its normal form, adding to the family of number-theoretic characterization of quantum operators.

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