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Measuring Non-Gaussian Magic in Fermions

Event Type
Seminar/Symposium
Sponsor
Quantum Working Group
Location
205 Gregory Hall
Date
Apr 2, 2025   4:00 - 5:00 pm  
Speaker
Luke Coffman
Contact
Felix Leditzky
E-Mail
leditzky@illinois.edu
Originating Calendar
Quantum Working Group Calendar

Speaker: Luke Coffman (University of Colorado Boulder)
Title: Measuring Non-Gaussian Magic in Fermions

Abstract:
Classically hard to simulate quantum states, or "magic states", are prerequisites to quantum advantage, highlighting an apparent separation between classically and quantumly tractable problems. Classically simulable states such as Clifford circuits on stabilizer states, free bosonic states, free fermions, and matchgate circuits are all in some sense Gaussian. While free bosons and fermions arise from quadratic Hamiltonians, recent works have demonstrated that bosonic and qudit systems converge to Gaussians and stabilizers under convolution. In this work, we similarly identify convolution for fermions and find efficient measures of non-Gaussian magic in pure fermionic states. We demonstrate that three natural notions for the Gaussification of a state, (1) the Gaussian state with the same covariance matrix, (2) the fixed point of convolution, and (3) the closest Gaussian in relative entropy, coincide by proving a central limit theorem for fermionic systems. We then utilize the violation of Wick's theorem and the matchgate identity to quantify non-Gaussian magic in addition to a SWAP test.
Pre-print: https://arxiv.org/abs/2501.06179

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