How Dynamical Quantum Memories Forget

Lukasz Fidkowski1, Jeongwan Haah2, and Matthew B. Hastings3,2

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

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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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Cited by

[1] Matteo Ippoliti and Vedika Khemani, "Postselection-Free Entanglement Dynamics via Spacetime Duality", Physical Review Letters 126 6, 060501 (2021).

[2] Matteo Ippoliti, Michael J. Gullans, Sarang Gopalakrishnan, David A. Huse, and Vedika Khemani, "Entanglement Phase Transitions in Measurement-Only Dynamics", Physical Review X 11 1, 011030 (2021).

[3] Adam Nahum, Sthitadhi Roy, Brian Skinner, and Jonathan Ruhman, "Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory", arXiv:2009.11311.

[4] Michael J. Gullans, Stefan Krastanov, David A. Huse, Liang Jiang, and Steven T. Flammia, "Quantum coding with low-depth random circuits", arXiv:2010.09775.

[5] Jason Iaconis, Andrew Lucas, and Xiao Chen, "Measurement-induced phase transitions in quantum automaton circuits", arXiv:2010.02196, Physical Review B 102 22, 224311 (2020).

[6] Ali Lavasani, Yahya Alavirad, and Maissam Barkeshli, "Topological order and criticality in (2+1)D monitored random quantum circuits", arXiv:2011.06595.

[7] Sarang Gopalakrishnan and Michael J. Gullans, "Entanglement and purification transitions in non-Hermitian quantum mechanics", arXiv:2012.01435.

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The above citations are from Crossref's cited-by service (last updated successfully 2021-03-04 00:57:06) and SAO/NASA ADS (last updated successfully 2021-03-04 00:57:08). The list may be incomplete as not all publishers provide suitable and complete citation data.