How Dynamical Quantum Memories Forget

Lukasz Fidkowski; Jeongwan Haah; Matthew B. Hastings

doi:10.22331/q-2021-01-17-382

How Dynamical Quantum Memories Forget

Lukasz Fidkowski¹, Jeongwan Haah², and Matthew B. Hastings^3,2

¹Department of Physics, University of Washington, Seattle, WA 98195-1560, USA
²Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA
³Station Q, Microsoft Research, Santa Barbara, CA 93106-6105, USA

Published:	2021-01-17, volume 5, page 382
Eprint:	arXiv:2008.10611v2
Doi:	https://doi.org/10.22331/q-2021-01-17-382
Citation:	Quantum 5, 382 (2021).

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Updated version: The authors have uploaded version v3 of this work to the arXiv which may contain updates or corrections not contained in the published version v2. The authors left the following comment on the arXiv:

24 pages, 2 figures (v3) expanding the proof of Lemma 3

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.

► BibTeX data

@article{Fidkowski2021howdynamicalquantum,
  doi = {10.22331/q-2021-01-17-382},
  url = {https://doi.org/10.22331/q-2021-01-17-382},
  title = {How {D}ynamical {Q}uantum {M}emories {F}orget},
  author = {Fidkowski, Lukasz and Haah, Jeongwan and Hastings, Matthew B.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {382},
  month = jan,
  year = {2021}
}

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