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Noise-Induced Entanglement Transition in One-Dimensional Random Quantum Circuits |
| Qi Zhang1 and Guang-Ming Zhang1,2* |
1State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
2Frontier Science Center for Quantum Information, Beijing 100084, China
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| Cite this article: |
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Qi Zhang and Guang-Ming Zhang 2022 Chin. Phys. Lett. 39 050302 |
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Abstract A random quantum circuit is a minimally structured model to study entanglement dynamics of many-body quantum systems. We consider a one-dimensional quantum circuit with noisy Haar-random unitary gates using density matrix operator and tensor contraction methods. It is shown that the entanglement evolution of the random quantum circuits is properly characterized by the logarithmic entanglement negativity. By performing exact numerical calculations, we find that, as the physical error rate is decreased below a critical value $p_{\rm c} \approx 0.056$, the logarithmic entanglement negativity changes from the area law to the volume law, giving rise to an entanglement transition. The critical exponent of the correlation length can be determined from the finite-size scaling analysis, revealing the universal dynamic property of the noisy intermediate-scale quantum devices.
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Received: 04 March 2022
Editors' Suggestion
Published: 26 April 2022
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| PACS: |
03.67.Lx
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(Quantum computation architectures and implementations)
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| [1] | Arute F, Arya K, Babbush R et al. 2019 Nature 574 505 |
| [2] | Wu Y, Bao W S, Cao S et al. 2021 Phys. Rev. Lett. 127 180501 |
| [3] | Zhou Y, Stoudenmire E M, and Waintal X 2020 Phys. Rev. X 10 041038 |
| [4] | Nahum A, Vijay S, and Haah J 2018 Phys. Rev. X 8 021014 |
| [5] | Mi X, Roushan P, Quintana C et al. 2021 Science 374 1479 |
| [6] | Xu S and Swingle B 2020 Nat. Phys. 16 199 |
| [7] | Boixo S, Isakov S V, Smelyanskiy V N, Babbush R, Ding N, Jiang Z, Bremner M J, Martinis J M, and Neven H 2018 Nat. Phys. 14 595 |
| [8] | Neill C, Roushan P, Kechedzhi K, Boixo S, Isakov S V, Smelyanskiy V, Megrant A, Chiaro B, Dunsworth A, and Arya K 2018 Science 360 195 |
| [9] | Noh K, Jiang L, and Fefferman B 2020 Quantum 4 318 |
| [10] | Cheng S, Cao C, Zhang C, Liu Y, Hou S Y, Xu P, and Zeng B 2021 Phys. Rev. Res. 3 023005 |
| [11] | Nahum A, Ruhman J, Vijay S, and Haah J 2017 Phys. Rev. X 7 031016 |
| [12] | Napp J, La P R L, Dalzell A M, Brandao F G S L, and Harrow A W 2019 arXiv:2001.00021 [quant-ph] |
| [13] | Markov I L and Shi Y 2008 SIAM J. Comput. 38 963 |
| [14] | Li Y, Chen X, and Fisher M P A 2018 Phys. Rev. B 98 205136 |
| [15] | Skinner B, Ruhman J, and Nahum A 2019 Phys. Rev. X 9 031009 |
| [16] | Bao Y, Choi S, and Altman E 2020 Phys. Rev. B 101 104301 |
| [17] | Zabalo A, Gullans M J, Wilson J H, Gopalakrishnan S, Huse D A, and Pixley J H 2020 Phys. Rev. B 101 060301 |
| [18] | Choi S, Bao Y, Qi X L, and Altman E 2020 Phys. Rev. Lett. 125 030505 |
| [19] | Lunt O, Richter J, and Pal A 2021 arXiv:2112.06682 [quant-ph] |
| [20] | Sang S and Hsieh T H 2021 Phys. Rev. Res. 3 023200 |
| [21] | Lavasani A, Alavirad Y, and Barkeshli M 2021 Nat. Phys. 17 342 |
| [22] | Li Y and Fisher M P A 2021 Phys. Rev. B 103 104306 |
| [23] | Adami C and Cerf N J 1997 Phys. Rev. A 56 3470 |
| [24] | Groisman B, Popescu S, and Winter A 2005 Phys. Rev. A 72 032317 |
| [25] | Žnidarič M, Prosen T, and Pižorn I 2008 Phys. Rev. A 78 022103 |
| [26] | Shapourian H, Liu S, Kudler-Flam J, and Vishwanath A 2021 PRX Quantum 2 030347 |
| [27] | Zanardi P 2001 Phys. Rev. A 63 040304 |
| [28] | Prosen T and Pižorn I 2007 Phys. Rev. A 76 032316 |
| [29] | Alba V, Dubail J, and Medenjak M 2019 Phys. Rev. Lett. 122 250603 |
| [30] | Peres A 1996 Phys. Rev. Lett. 77 1413 |
| [31] | Horodecki M, Horodecki P, and Horodecki R 1996 Phys. Lett. A 223 1 |
| [32] | Życzkowski K, Horodecki P, Sanpera A, and Lewenstein M 1998 Phys. Rev. A 58 883 |
| [33] | Eisert J and Plenio M B 1999 J. Mod. Opt. 46 145 |
| [34] | Vidal G and Werner R F 2002 Phys. Rev. A 65 032314 |
| [35] | Plenio M B 2005 Phys. Rev. Lett. 95 090503 |
| [36] | Ruggiero P, Alba V, and Calabrese P 2016 Phys. Rev. B 94 195121 |
| [37] | Shapourian H, Ruggiero P, Ryu S, and Calabrese P 2019 SciPost Phys. 7 37 |
| [38] | Kudler-Flam J, Narovlansky V, and Ryu S 2021 arXiv:2109.02649 [hep-th] |
| [39] | Page D N 1993 Phys. Rev. Lett. 71 1291 |
| [40] | Choi M D 1975 Linear Alg. its Appl. 10 285 |
| [41] | Vidal G 2003 Phys. Rev. Lett. 91 147902 |
| [42] | Verstraete F, García-Ripoll J J, and Cirac J I 2004 Phys. Rev. Lett. 93 207204 |
| [43] | Hastings M B 2006 Phys. Rev. B 73 085115 |
| [44] | Verstraete F, Murg V, and Cirac J I 2008 Adv. Phys. 57 143 |
| [45] | Zwolak M and Vidal G 2004 Phys. Rev. Lett. 93 207205 |
| [46] | Pirvu B, Murg V, Cirac J I, and Verstraete F 2010 New J. Phys. 12 025012 |
| [47] | Elben A, Kueng R, Huang H Y, van Bijnen R, Kokail C, Dalmonte M, Calabrese P, Kraus B, Preskill J, Zoller P, and Vermersch B 2020 Phys. Rev. Lett. 125 200501 |
| [48] | Wang K, Song Z, Zhao X, Wang Z, and Wang X 2020 arXiv:2012.14311 [quant-ph] |
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