Quantum circuits of T-depth one

Peter Selinger
Phys. Rev. A 87, 042302 – Published 1 April 2013

Abstract

We give a Clifford+T representation of the Toffoli gate of T-depth one, using four ancillas. More generally, we describe a class of circuits whose T-depth can be reduced to one by using sufficiently many ancillas. We show that the cost of adding an additional control to any controlled gate is at most eight additional T gates and T-depth two. We also show that the circuit THT does not possess a T-depth one representation with an arbitrary number of ancillas initialized to |0.

  • Figure
  • Received 3 October 2012

DOI:https://doi.org/10.1103/PhysRevA.87.042302

©2013 American Physical Society

Authors & Affiliations

Peter Selinger

  • Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4R2

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Vol. 87, Iss. 4 — April 2013

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