## Abstracts

### Stationary phase method in discrete Wigner functions and classical simulation of quantum circuits

Presenting Author: Lucas Kocia, National Institute of Standards and Technology, Maryland
Contributing Author(s): Peter Love

We apply the periodized stationary phase method to discrete Wigner functions of systems with odd prime dimension using results from $$p$$-adic number theory. We derive the Wigner-Weyl-Moyal (WWM) formalism with higher order $$hbar$$ corrections representing contextual corrections to non-contextual Clifford operations. We apply this formalism to a subset of unitaries that include diagonal gates such as the $${\pi}/{8}$$ gates. We characterize the stationary phase critical points as a quantum resource injecting contextuality and show that this resource allows for the replacement of the $$p^{2t}$$ points that represent $$t$$ magic state Wigner functions on $$p$$-dimensional qudits by $$\le p^{t}$$ points. We find that the $${\pi}/{8}$$ gate introduces the smallest higher order $$hbar$$ correction possible, requiring the lowest number of additional critical points compared to the Clifford gates. We then establish a relationship between the stabilizer rank of states and the number of critical points and exploit the stabilizer rank decomposition of two qutrit $${\pi}/{8}$$ gates to develop a classical strong simulation of a single qutrit marginal on $$t$$ qutrit $${\pi}/{8}$$ gates that are followed by Clifford evolution, and show that this only requires calculating $$3^{\frac{t}{2}+1}$$ critical points corresponding to Gauss sums. This outperforms the best alternative qutrit algorithm for any number of $${\pi}/{8}$$ gates to full precision.

(Session 9a : Monday from 5:15pm - 5:45pm)

SQuInT Chief Organizer
Akimasa Miyake, Associate Professor
amiyake@unm.edu

SQuInT Local Organizers
Rafael Alexander, Postdoctoral Fellow
Chris Jackson, Postdoctoral Fellow

Gloria Cordova
gjcordo1@unm.edu
505 277-1850

SQuInT Assistant
Wendy Jay

SQuInT Founder
Ivan Deutsch, Regents' Professor, CQuIC Director
ideutsch@unm.edu