Beecroft Building, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU
Bruno Bertini, University of Birmingham
Quantum dynamics with random permutation circuits
Characterising the universal phenomena occurring in quantum many-body systems out-of-equilibrium — such as thermalisation or growth of entanglement— and the emergent laws governing them is one of the central themes of modern physics. A particularly interesting question concerns the role played in these processes by quantum mechanics, i.e., are the universal phenomena occurring in quantum many-body systems fundamentally different from those observed in classical many-body systems? If so, which of their features are genuinely quantum?
I will discuss this question considering quantum many-body systems in discrete space-time, i.e. quantum circuits. I will introduce “permutation circuits”, a class of local quantum circuits that act classically — do not generate superpositions — in a special basis. Considering random (or Floquet random) permutation circuits I will show that these systems have dynamical and spectral properties that are remarkably similar to those of generic quantum circuits while I will point out and explain the key differences.
References
BB, Klobas, Kos, Malz, Phys. Rev. X 15, 011015 (2025)
Szász-Schagrin, Mazzoni, BB, Klobas, Piroli, arXiv:2505.06158
BB, Klobas, Kos, Malz, arXiv:2505.06158
BB, Horvath, Klobas, Orlov, Prosen, in preparation.