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TT: Fachverband Tiefe Temperaturen
TT 71: Many-Body Quantum Dynamics I (joint session DY/TT)
TT 71.11: Talk
Thursday, March 21, 2024, 12:15–12:30, A 151
Conserved Superoperators and Non-Universality in Unitary Circuits — •Marco Lastres1,2, Frank Pollmann1,2, and Sanjay Moudgalya1,2 — 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
An important result in the theory of quantum control is the “universality” of 2-local unitary gates, i.e. the fact that any global unitary evolution of a system of L qudits can be implemented by composition of 2-local unitary gates. Surprisingly, recent results show that universality can break down in the presence of symmetries: in general, not all globally symmetric unitaries can be constructed using k-local symmetric unitary gates. This also restricts the dynamics that can be implemented by symmetric local Hamiltonians.
In this study, we show that these obstructions to universality can in general be understood in terms of unconventional superoperator symmetries associated with unitary evolution by k-local gates. We demonstrate this explicitly in several examples by systematically deriving the superoperator symmetries using the framework of commutant algebras, which has recently been applied to derive the unconventional symmetries responsible for weak ergodicity breaking phenomena, such as quantum many body scars and Hilbert space fragmentation. In all, our work establishes a new comprehensive approach to explore the universality of unitary circuits and derive physical consequences of its absence.
Keywords: gate universality; symmetric gates; dynamical lie algebra; commutant algebra; quantum many body scars