Brick Wall Quantum Circuits with Global Fermionic Symmetry

• URL: http://arxiv.org/abs/2402.18440v5
• Date: Wed, 18 Sep 2024 08:23:25 GMT
• Title: Brick Wall Quantum Circuits with Global Fermionic Symmetry
• Authors: Pietro Richelli, Kareljan Schoutens, Alberto Zorzato,
• Abstract summary: We study brick wall quantum circuits enjoying a global fermionic symmetry. Fermionic symmetry pins $H_gamma$ to a surface of critical points, whereas breaking that symmetry leads to non-trivial topological phases.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study brick wall quantum circuits enjoying a global fermionic symmetry. The constituent 2-qubit gate, and its fermionic symmetry, derive from a 2-particle scattering matrix in integrable, supersymmetric quantum field theory in 1+1 dimensions. Our 2-qubit gate, as a function of three free parameters, is of so-called free fermionic or matchgate form, allowing us to derive the spectral structure of both the brick wall unitary $U_F$ and its, non-trivial, hamiltonian limit $H_{\gamma}$ in closed form. We find that the fermionic symmetry pins $H_{\gamma}$ to a surface of critical points, whereas breaking that symmetry leads to non-trivial topological phases. We briefly explore quench dynamics for this class of circuits.

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