Abstract:
Understanding the computational complexity of quantum states is a
central challenge in quantum many-body physics. Fermionic Gaussian
states, in particular, can be efficiently simulated on classical
computers and therefore provide a natural baseline against which
genuinely quantum complexity can be assessed. I will briefly introduce
the idea of magic state resource theories, and then focus on a
framework for quantifying fermionic magic resources, also known as
fermionic non-Gaussianity. I will introduce fermionic antiflatness
(FAF) [1], an efficiently computable and experimentally accessible
measure of non-Gaussianity with a clear physical interpretation in
terms of Majorana fermion correlation functions, and briefly discuss
its phenomenology in many-body systems [2]. I will then argue that FAF
naturally leads to questions about the matchgate commutant, namely the
space of operators on k replicas that are invariant under the diagonal
action of the matchgate ensemble. I will discuss how to construct an
explicit orthonormal basis of the matchgate commutant for arbitrary
replica number and system size [3]. Finally, I will describe how this
commutant structure can be used to investigate the formation of
unitary designs in doped matchgate circuits [4].
[1] PS, P. Stornati, X. Turkeshi, PRX Quantum 7, 010302 (2026)
[2] P. R. N. Falcão, J. Zakrzewski, PS, arXiv:2602.00245
[3] PS, X. Turkeshi, P. S. Tarabunga, arXiv:2603.12392
[4] F. B. Trigueros, Z.-H. Sun, X. Turkeshi, PS, P. S. Tarabunga, in preparation
Date: May 20, 2026 2 PM CET
Location: Al. Lotników, room D, ground floor
Remote guests are invited via Zoom:
Zoom link:
https://us06web.zoom.us/j/84248911743?pwd=ZsiAOQbRgYCm5IFsArOnb18Fj5IsZh.1Meeting ID: 842 4891 1743
Passcode: 394021
