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How Dynamical Quantum Memories Forget · Around 2020
How Dynamical Quantum Memories Forget Fidkowski, Lukasz, Haah, Jeongwan, Hastings, Matthew B.
Understand 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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1903
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M. J. Gullans and D. A. Huse, “Dynamical purification phase transitions induced by quantum measurements,” Phys. Rev. X 10
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1905
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M. J. Gullans and D. A. Huse, “Scalable probes of measurement-induced criticality,” Phys. Rev. Lett. 125, 070606 (2020) 125
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2002
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J. Haferkamp, F. Montealegre-Mora, M. Heinrich, J. Eisert, D. Gross, and I. Roth, “Quantum homeopathy works: Efficient unitary designs with a system-size independent number of non-clifford gates,” (2020), arXiv:2002.09524
Original
2002
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X. Chen, Y. Li, M. P. A. Fisher, and A. Lucas, “Emergent conformal symmetry in nonunitary random dynamics of free fermions,” Phys. Rev. Research 2
Original
2004
Earlier work this paper cites.
Similar M. Ippoliti, M. J. Gullans, S. Gopalakrishnan, D. A. Huse, and V. Khemani, “Entanglement phase transitions in measurement-only dynamics,” (2020), arXiv:2004.09560
Original
2004
Cited alongside, same era.
S. Bravyi, “Lagrangian representation for fermionic linear optics,” Quantum Inf. and Comp. 5
2005
Cited alongside, same era.
B. Collins and P. Sniady, “Integration with respect to the Haar measure on unitary, orthogonal and symplectic group,” Commun. Math. Phys. 264
2006
Cited alongside, same era.
M. B. Hastings, “Random unitaries give quantum expanders,” Physical Review A 76
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2007
Cited alongside, same era.
Y. Li and M. P. A. Fisher, “Statistical mechanics of quantum error-correcting codes,” (2020), arXiv:2007.03822 [quant-ph]
Original
Then Y. Li, X. Chen, and M. P. A. Fisher, “Quantum zeno effect and the many-body entanglement transition,” Phys. Rev. B 98
Original
2018
Later among the works it cites.
A. Harrow and S. Mehraban, “Approximate unitary t t -designs by short random quantum circuits using nearest-neighbor and long-range gates,” (2018), arXiv:1809.06957
Original
2018
Later among the works it cites.
B. Skinner, J. Ruhman, and A. Nahum, “Measurement-induced phase transitions in the dynamics of entanglement,” Phys. Rev. X 9
Original
2019
Later among the works it cites.
Y. Li, X. Chen, and M. P. A. Fisher, “Measurement-driven entanglement transition in hybrid quantum circuits,” Phys. Rev. B 100
2019
Later among the works it cites.
A. Chan, R. M. Nandkishore, M. Pretko, and G. Smith, “Unitary-projective entanglement dynamics,” Phys. Rev. B 99
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K. M. R. Audenaert, “A sharp fannes-type inequality for the von neumann entropy,” J. Phys. A 40
2007
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A. Nahum, P. Serna, A. M. Somoza, and M. Ortuño, “Loop models with crossings,” Phys. Rev. B 87
2013
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E. S. Meckes, The random matrix theory of the classical compact groups , Vol. 218 (Cambridge University Press, 2019)
2019
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