Decomposing Quantum Generalized Toffoli with an Arbitrary Number of Ancilla


We present a general decomposition of the Generalized Toffoli, and for completeness, the multi-target gate using an arbitrary number of clean or dirty ancilla. While prior work has shown how to decompose the Generalized Toffoli using 0, 1, or O(n) many clean ancilla and 0, 1, and n−2 dirty ancilla, we provide a generalized algorithm to bridge the gap, i.e. this work gives an algorithm to generate a decomposition for any number of clean or dirty ancilla. While it is hard to guarantee optimality, our decompositions guarantee a decrease in circuit depth as the number of ancilla increases.

Alex Hoover
Alex Hoover
Cryptography PhD Student

A random guy with broad interests across cyrptography, computer security, quantum computing, and more.