Quantum Bayesian Networks

January 4, 2019

A quantum computing paradox, Generalized Toffoli Gates

Filed under: Uncategorized — rrtucci @ 12:32 am

Call me Simplicio.

Let a Generalized Toffoli (GT) gate be a quantum gate, acting coherently on N+1 qubits, that rotates a target qubit subject to the state of the other N qubits acting as controls. If you calculate, with a classical computer, the effect of a GT gate on an input state vector, the larger N is, the fewer multiplications you will have to perform. On the other hand, if you expand a GT gate into a sequence of single qubit rotations and CNOTs, the minimal number of CNOTs in such an expansion will grow exponentially in N. Huh?

This paradox seems to imply that it behooves quantum computerists to find a way of implementing GT gates in their hardware in a single step, as I advocated in this previous blog post of mine.

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