How Dynamical Quantum Memories Forget
- URL: http://arxiv.org/abs/2008.10611v3
- Date: Sat, 30 Jul 2022 14:21:24 GMT
- Title: How Dynamical Quantum Memories Forget
- Authors: Lukasz Fidkowski, Jeongwan Haah, Matthew B. Hastings
- Abstract summary: We show that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements.
In particular, a volume law phase for the entanglement entropy cannot be sustained in a free fermion system.
- Score: 0.2578242050187029
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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