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Yaodong Li, Xiao Chen, and Matthew P. A. Fisher, “Measurement-driven entanglement transition in hybrid quantum circuits,” Physical Review B 100
Original
1901
Earlier work this paper cites.
Soonwon Choi, Yimu Bao, Xiao-Liang Qi, and Ehud Altman, “Quantum error correction and entanglement phase transition in random unitary circuits with projective measurements,” arXiv e-prints , arXiv:1903.05124 (2019), arXiv:1903.05124 [quant-ph]
Original
1903
Earlier work this paper cites.
M. Szyniszewski, A. Romito, and H. Schomerus, “Entanglement transition from variable-strength weak measurements,” Phys. Rev. B 100
Original
1903
Earlier work this paper cites.
Michael J. Gullans and David A. Huse, “Dynamical purification phase transition induced by quantum measurements,” arXiv e-prints (2019a), arXiv:1905.05195 [quant-ph]
Original
1905
Earlier work this paper cites.
Yimu Bao, Soonwon Choi, and Ehud Altman, “Theory of the phase transition in random unitary circuits with measurements,” Phys. Rev. B 101
Original
1908
Earlier work this paper cites.
Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, and Andreas W. W. Ludwig, “Measurement-induced criticality in random quantum circuits,” Phys. Rev. B 101
Original
1908
Earlier work this paper cites.
Qicheng Tang and W. Zhu, “Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations,” Physical Review Research 2
Original
1908
Earlier work this paper cites.
Michael J. Gullans and David A. Huse, “Scalable probes of measurement-induced criticality,” arXiv e-prints , arXiv:1910.00020 (2019b), arXiv:1910.00020 [cond-mat.stat-mech]
Original
1910
Earlier work this paper cites.
Todd A. Brun, “Quantum Error Correction,” arXiv e-prints , arXiv:1910.03672 (2019), arXiv:1910.03672 [quant-ph]
Original
1910
Earlier work this paper cites.
Aidan Zabalo, Michael J. Gullans, Justin H. Wilson, Sarang Gopalakrishnan, David A. Huse, and J. H. Pixley, “Critical properties of the measurement-induced transition in random quantum circuits,” Phys. Rev. B 101
Original
1911
Earlier work this paper cites.
Adam Nahum and Brian Skinner, “Entanglement and dynamics of diffusion-annihilation processes with Majorana defects,” arXiv e-prints , arXiv:1911.11169 (2019), arXiv:1911.11169 [cond-mat.stat-mech]
Original
1911
Earlier work this paper cites.
Tianci Zhou and Adam Nahum, “The entanglement membrane in chaotic many-body systems,” arXiv e-prints , arXiv:1912.12311 (2019b), arXiv:1912.12311 [cond-mat.str-el]
Original
1912
Earlier work this paper cites.
F. P. Buff, R. A. Lovett, and F. H. Stillinger, “Interfacial density profile for fluids in the critical region,” Phys. Rev. Lett. 15
1965
Earlier work this paper cites.
John D. Weeks, “Structure and thermodynamics of the liquid–vapor interface,” The Journal of Chemical Physics 67
1977
Earlier work this paper cites.
Matthew P. A. Fisher, Daniel S. Fisher, and John D. Weeks, “Agreement of capillary-wave theory with exact results for the interface profile of the two-dimensional ising model,” Phys. Rev. Lett. 48
1982
Earlier work this paper cites.
Sergey Bravyi and Barbara Terhal, “A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes,” New Journal of Physics 11
Original
1983
Earlier work this paper cites.
David A. Huse and Christopher L. Henley, “Pinning and roughening of domain walls in Ising systems due to random impurities,” Phys. Rev. Lett. 54
1985
Earlier work this paper cites.
Mehran Kardar, “Roughening by impurities at finite temperatures,” Phys. Rev. Lett. 55
1985
Earlier work this paper cites.
David A. Huse, Christopher L. Henley, and Daniel S. Fisher, “Huse, Henley, and Fisher respond,” Phys. Rev. Lett. 55
1985
Earlier work this paper cites.
Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang, “Dynamic scaling of growing interfaces,” Phys. Rev. Lett. 56
1986
Earlier work this paper cites.
Mehran Kardar and Yi-Cheng Zhang, “Scaling of directed polymers in random media,” Phys. Rev. Lett. 58
1987
Earlier work this paper cites.
Peter W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52
1995
Earlier work this paper cites.
Charles H. Bennett, David P. Divincenzo, John A. Smolin, and William K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54
1996
Earlier work this paper cites.

Similar

A. R. Calderbank and Peter W. Shor, “Good quantum error-correcting codes exist,” Phys. Rev. A 54
1996
Cited alongside, same era.
Daniel Gottesman, “Class of quantum error-correcting codes saturating the quantum Hamming bound,” Physical Review A 54
1996
Cited alongside, same era.
A. Ekert and C. Macchiavello, “Error Correction in Quantum Communication,” arXiv e-prints , quant-ph/9602022 (1996), arXiv:quant-ph/9602022 [quant-ph]
1996
Cited alongside, same era.
Emanuel Knill and Raymond Laflamme, “Theory of quantum error-correcting codes,” Phys. Rev. A 55
1997
Cited alongside, same era.
A. Robert Calderbank, Eric M. Rains, Peter W. Shor, and Neil J. A. Sloane, “Quantum Error Correction and Orthogonal Geometry,” Phys. Rev. Lett. 78
1997
Cited alongside, same era.

Then

Ali Lavasani, Yahya Alavirad, and Maissam Barkeshli, “Measurement-induced topological entanglement transitions in symmetric random quantum circuits,” arXiv e-prints , arXiv:2004.07243 (2020), arXiv:2004.07243 [quant-ph]
Original
2004
Later among the works it cites.
Shengqi Sang and Timothy H. Hsieh, “Measurement Protected Quantum Phases,” arXiv e-prints , arXiv:2004.09509 (2020), arXiv:2004.09509 [cond-mat.stat-mech]
Original
2004
Later among the works it cites.
Ori Alberton, Michael Buchhold, and Sebastian Diehl, “Trajectory dependent entanglement transition in a free fermion chain – from extended criticality to area law,” arXiv e-prints , arXiv:2005.09722 (2020), arXiv:2005.09722 [cond-mat.stat-mech]
Original
2005
Later among the works it cites.
Oliver Lunt and Arijeet Pal, “Measurement-induced entanglement transitions in many-body localized systems,” arXiv e-prints , arXiv:2005.13603 (2020), arXiv:2005.13603 [quant-ph]
Original
2005
Later among the works it cites.

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Reading the bibliography…

2020

Statistical mechanics of quantum error correcting codes

Li, Yaodong, Fisher, Matthew P. A.

Understand

We study stabilizer quantum error correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension.

Building upon 1) a general formula relating the error-susceptibility of a subregion to its entanglement properties, and 2) a previously established mapping between entanglement entropies and domain wall free energies of an underlying spin model, we propose a statistical mechanical description of the QECC in terms of "entanglement domain walls".
Free energies of such domain walls generically feature a leading volume law term coming from its "surface energy", and a sub-volume law correction coming from thermodynamic entropies of its transverse fluctuations.
These are most easily accounted for by capillary-wave theory of liquid-gas interfaces, which we use as an illustrative tool.

Built on

Yaodong Li, Xiao Chen, and Matthew P. A. Fisher, “Measurement-driven entanglement transition in hybrid quantum circuits,” Physical Review B 100
Original
1901
Earlier work this paper cites.
Soonwon Choi, Yimu Bao, Xiao-Liang Qi, and Ehud Altman, “Quantum error correction and entanglement phase transition in random unitary circuits with projective measurements,” arXiv e-prints , arXiv:1903.05124 (2019), arXiv:1903.05124 [quant-ph]
Original
1903
Earlier work this paper cites.
M. Szyniszewski, A. Romito, and H. Schomerus, “Entanglement transition from variable-strength weak measurements,” Phys. Rev. B 100
Original
1903
Earlier work this paper cites.
Michael J. Gullans and David A. Huse, “Dynamical purification phase transition induced by quantum measurements,” arXiv e-prints (2019a), arXiv:1905.05195 [quant-ph]
Original
1905
Earlier work this paper cites.
Yimu Bao, Soonwon Choi, and Ehud Altman, “Theory of the phase transition in random unitary circuits with measurements,” Phys. Rev. B 101
Original
1908
Earlier work this paper cites.
Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, and Andreas W. W. Ludwig, “Measurement-induced criticality in random quantum circuits,” Phys. Rev. B 101
Original
1908
Earlier work this paper cites.
Qicheng Tang and W. Zhu, “Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations,” Physical Review Research 2
Original
1908
Earlier work this paper cites.
Michael J. Gullans and David A. Huse, “Scalable probes of measurement-induced criticality,” arXiv e-prints , arXiv:1910.00020 (2019b), arXiv:1910.00020 [cond-mat.stat-mech]
Original
1910
Earlier work this paper cites.
Todd A. Brun, “Quantum Error Correction,” arXiv e-prints , arXiv:1910.03672 (2019), arXiv:1910.03672 [quant-ph]
Original
1910
Earlier work this paper cites.
Aidan Zabalo, Michael J. Gullans, Justin H. Wilson, Sarang Gopalakrishnan, David A. Huse, and J. H. Pixley, “Critical properties of the measurement-induced transition in random quantum circuits,” Phys. Rev. B 101
Original
1911
Earlier work this paper cites.
Adam Nahum and Brian Skinner, “Entanglement and dynamics of diffusion-annihilation processes with Majorana defects,” arXiv e-prints , arXiv:1911.11169 (2019), arXiv:1911.11169 [cond-mat.stat-mech]
Original
1911
Earlier work this paper cites.
Tianci Zhou and Adam Nahum, “The entanglement membrane in chaotic many-body systems,” arXiv e-prints , arXiv:1912.12311 (2019b), arXiv:1912.12311 [cond-mat.str-el]
Original
1912
Earlier work this paper cites.
F. P. Buff, R. A. Lovett, and F. H. Stillinger, “Interfacial density profile for fluids in the critical region,” Phys. Rev. Lett. 15
1965
Earlier work this paper cites.
John D. Weeks, “Structure and thermodynamics of the liquid–vapor interface,” The Journal of Chemical Physics 67
1977
Earlier work this paper cites.
Matthew P. A. Fisher, Daniel S. Fisher, and John D. Weeks, “Agreement of capillary-wave theory with exact results for the interface profile of the two-dimensional ising model,” Phys. Rev. Lett. 48
1982
Earlier work this paper cites.
Sergey Bravyi and Barbara Terhal, “A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes,” New Journal of Physics 11
Original
1983
Earlier work this paper cites.
David A. Huse and Christopher L. Henley, “Pinning and roughening of domain walls in Ising systems due to random impurities,” Phys. Rev. Lett. 54
1985
Earlier work this paper cites.
Mehran Kardar, “Roughening by impurities at finite temperatures,” Phys. Rev. Lett. 55
1985
Earlier work this paper cites.
David A. Huse, Christopher L. Henley, and Daniel S. Fisher, “Huse, Henley, and Fisher respond,” Phys. Rev. Lett. 55
1985
Earlier work this paper cites.
Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang, “Dynamic scaling of growing interfaces,” Phys. Rev. Lett. 56
1986
Earlier work this paper cites.
Mehran Kardar and Yi-Cheng Zhang, “Scaling of directed polymers in random media,” Phys. Rev. Lett. 58
1987
Earlier work this paper cites.
Peter W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52
1995
Earlier work this paper cites.
Charles H. Bennett, David P. Divincenzo, John A. Smolin, and William K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54
1996
Earlier work this paper cites.

Similar

A. R. Calderbank and Peter W. Shor, “Good quantum error-correcting codes exist,” Phys. Rev. A 54
1996
Cited alongside, same era.
Daniel Gottesman, “Class of quantum error-correcting codes saturating the quantum Hamming bound,” Physical Review A 54
1996
Cited alongside, same era.
A. Ekert and C. Macchiavello, “Error Correction in Quantum Communication,” arXiv e-prints , quant-ph/9602022 (1996), arXiv:quant-ph/9602022 [quant-ph]
1996
Cited alongside, same era.
Emanuel Knill and Raymond Laflamme, “Theory of quantum error-correcting codes,” Phys. Rev. A 55
1997
Cited alongside, same era.
A. Robert Calderbank, Eric M. Rains, Peter W. Shor, and Neil J. A. Sloane, “Quantum Error Correction and Orthogonal Geometry,” Phys. Rev. Lett. 78
1997
Cited alongside, same era.

Then

Ali Lavasani, Yahya Alavirad, and Maissam Barkeshli, “Measurement-induced topological entanglement transitions in symmetric random quantum circuits,” arXiv e-prints , arXiv:2004.07243 (2020), arXiv:2004.07243 [quant-ph]
Original
2004
Later among the works it cites.
Shengqi Sang and Timothy H. Hsieh, “Measurement Protected Quantum Phases,” arXiv e-prints , arXiv:2004.09509 (2020), arXiv:2004.09509 [cond-mat.stat-mech]
Original
2004
Later among the works it cites.
Ori Alberton, Michael Buchhold, and Sebastian Diehl, “Trajectory dependent entanglement transition in a free fermion chain – from extended criticality to area law,” arXiv e-prints , arXiv:2005.09722 (2020), arXiv:2005.09722 [cond-mat.stat-mech]
Original
2005
Later among the works it cites.
Oliver Lunt and Arijeet Pal, “Measurement-induced entanglement transitions in many-body localized systems,” arXiv e-prints , arXiv:2005.13603 (2020), arXiv:2005.13603 [quant-ph]
Original
2005
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Daniel Gottesman, Stabilizer codes and quantum error correction , Ph.D. thesis, California Institute of Technology (1997), arXiv:quant-ph/9705052 [quant-ph]

1997

Cited alongside, same era.

Eric M. Rains, R. H. Hardin, Peter W. Shor, and N. J. A. Sloane, “A Nonadditive Quantum Code,” Phys. Rev. Lett. 79

1997

Cited alongside, same era.

Daniel Gottesman, “The Heisenberg Representation of Quantum Computers,” arXiv e-prints , quant-ph/9807006 (1998), arXiv:quant-ph/9807006 [quant-ph]

1998

Cited alongside, same era.

John Preskill, Lecture notes for physics 229: Quantum information and computation (California Institute of Technology, 1998)

1998

Cited alongside, same era.

Benjamin Schumacher and Michael D. Westmoreland, “Approximate quantum error correction,” arXiv e-prints , quant-ph/0112106 (2001), arXiv:quant-ph/0112106 [quant-ph]

2001

Cited alongside, same era.

John Napp, Rolando L. La Placa, Alexander M. Dalzell, Fernando G. S. L. Brandao, and Aram W. Harrow, “Efficient classical simulation of random shallow 2D quantum circuits,” arXiv e-prints , arXiv:2001.00021 (2019), arXiv:2001.00021 [quant-ph]