3

I was trying to find a reference for the 7 T-gate decomposition of the Toffoli gate given by Cirq. The decomposition originates from the the one used for CCZPowGate as given in the doc string here

https://github.com/quantumlib/Cirq/blob/master/cirq-core/cirq/ops/three_qubit_gates.py#L100

This is mentioned as an adjacency respecting decomposition by which I understand that the CNOTs are nearest neighbour

Most of the literature I have seen on Toffoli gate decompositions seem to use long range CNOTs for example in Neilson and Chuang or here

https://arxiv.org/abs/2101.04764 .

Does anyone have an idea about the source of the decomposition used?

Madhav Vijayan
  • 33
  • 2

1 Answers1

3

I'm the one who added this code to Cirq. I found that decomposition as part self-answering a question from 2018. I found it by messing around in Quirk, trying different strategies.

Norbert Schuch has a comment on the answer saying the decomposition appears in his thesis in 2002. I wasn't able to get his thesis to check as the link he gave is dead now, but I don't doubt he also found it or that the original discovery predates mine by more than a decade.

Craig Gidney
  • 36,389
  • 1
  • 29
  • 95