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Title: How Dynamical Quantum Memories Forget
Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, we study the long time behavior of such systems. We demonstrate that even in the ``mixed'' phase, a maximally mixed initial density matrix is purified on a time scale equal to the Hilbert space dimension (i.e., exponential in system size), albeit with noisy dynamics at intermediate times which we connect to Dyson Brownian motion. In contrast, we show that free fermion systems — i.e., ones where the unitaries are generated by quadratic Hamiltonians and the measurements are of fermion bilinears — purify in a time quadratic in the system size. In particular, a volume law phase for the entanglement entropy cannot be sustained in a free fermion system.  more » « less
Award ID(s):
1939864
PAR ID:
10213553
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Quantum
Volume:
5
ISSN:
2521-327X
Page Range / eLocation ID:
382
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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