Dresden 2026 – wissenschaftliches Programm
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QI: Fachverband Quanteninformation
QI 1: Quantum Computing and Algorithms I
QI 1.9: Vortrag
Montag, 9. März 2026, 12:00–12:15, BEY/0137
Generation of Fermionic Gaussian States: Optimal and Approximate Matchgate Circuits — •Marc Langer1,2, Raúl Morral-Yepes1,2, Adam Gammon-Smith3,4, Frank Pollmann1,2, and Barbara Kraus1,2 — 1Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany — 2Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 München, Germany — 3School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK — 4Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, UK
Fermionic Gaussian states (FGS), and the related matchgates, play an important role in the study of various phenomena. Despite being able to represent highly entangled states, they are still tractable on classical computers. A naturally arising question is how to optimally create such states, for instance when using matchgate circuits acting on product states. In this work, we present algorithms for explicitly constructing such circuits that provably yield the minimal number of gates. Our techniques furthermore allow us to characterize which states can be represented exactly with a low depth matchgate circuit. Some applications of these results include approximate state preparation, robust disentangling algorithms and classical simulation methods.
Keywords: matchgate; circuit complexity; fermionic Gaussian; covariance matrix; classical simulation