Brick Wall Quantum Circuits with Global Fermionic Symmetry

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.

42 pages

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Cited by in corpus (2)

• Integrable fishnet circuits and Brownian solitons
• More global randomness from less-random local gates