Entanglement dynamics in U(1) symmetric hybrid quantum automaton circuits

Yiqiu Han and Xiao Chen

Department of Physics, Boston College, Chestnut Hill, MA 02467, USA

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


We study the entanglement dynamics of quantum automaton (QA) circuits in the presence of U(1) symmetry. We find that the second Rényi entropy grows diffusively with a logarithmic correction as $\sqrt{t\ln{t}}$, saturating the bound established by Huang [1]. Thanks to the special feature of QA circuits, we understand the entanglement dynamics in terms of a classical bit string model. Specifically, we argue that the diffusive dynamics stems from the rare slow modes containing extensively long domains of spin 0s or 1s. Additionally, we investigate the entanglement dynamics of monitored QA circuits by introducing a composite measurement that preserves both the U(1) symmetry and properties of QA circuits. We find that as the measurement rate increases, there is a transition from a volume-law phase where the second Rényi entropy persists the diffusive growth (up to a logarithmic correction) to a critical phase where it grows logarithmically in time. This interesting phenomenon distinguishes QA circuits from non-automaton circuits such as U(1)-symmetric Haar random circuits, where a volume-law to an area-law phase transition exists, and any non-zero rate of projective measurements in the volume-law phase leads to a ballistic growth of the Rényi entropy.

Quantum entanglement is an important measure of the correlation between particles inside a quantum system. In typical systems with local interactions, the entanglement entropy grows linearly in time, indicating a ballistic propagation of quantum information. When charge-conservation, i.e., U(1) symmetry is imposed, it is found that while the von-Neumann entropy still exhibits a linear growth, higher Renyi entropies are limited by a diffusive growth with a logarithmic correction.

In this work, we use random circuit models to study U(1)-symmetric quantum systems. Specifically, we focus on quantum automaton (QA) circuits, one of the few circuit models that allow an analytic understanding of the entanglement dynamics, and demonstrate that the second Renyi entropy scales as $\sqrt{t\ln{t}}$, saturating the bound mentioned above. By mapping the second Renyi entropy to the quantity of a classical particle model, we show that this diffusive dynamics is the consequence of the emergence of rare slow modes under U(1) symmetry.

In addition, we introduce measurements into QA circuits and examine the monitored entanglement dynamics. Interestingly, as we manipulate the measurement rate, we observe a phase transition from a volume-law phase where the second Renyi entropy persists the diffusive growth, to a critical phase where it grows logarithmically. This is different from non-automaton U(1)-symmetric hybrid quantum circuits where a volume-law to area-law entanglement phase transition exists, and any non-zero rate of measurements below the critical point induces a linear growth of the Renyi entropy.

► BibTeX data

► References

[1] Yichen Huang. ``Dynamics of rényi entanglement entropy in diffusive qudit systems''. IOP SciNotes 1, 035205 (2020).

[2] Hyungwon Kim and David A. Huse. ``Ballistic spreading of entanglement in a diffusive nonintegrable system''. Phys. Rev. Lett. 111, 127205 (2013).

[3] Elliott H. Lieb and Derek W. Robinson. ``The finite group velocity of quantum spin systems''. Communications in Mathematical Physics 28, 251–257 (1972).

[4] Pasquale Calabrese and John Cardy. ``Evolution of entanglement entropy in one-dimensional systems''. Journal of Statistical Mechanics: Theory and Experiment 2005, P04010 (2005).

[5] Christian K. Burrell and Tobias J. Osborne. ``Bounds on the speed of information propagation in disordered quantum spin chains''. Phys. Rev. Lett. 99, 167201 (2007).

[6] Adam Nahum, Jonathan Ruhman, Sagar Vijay, and Jeongwan Haah. ``Quantum entanglement growth under random unitary dynamics''. Phys. Rev. X 7, 031016 (2017).

[7] Winton Brown and Omar Fawzi. ``Scrambling speed of random quantum circuits'' (2013). arXiv:1210.6644.

[8] Tibor Rakovszky, Frank Pollmann, and C. W. von Keyserlingk. ``Sub-ballistic growth of rényi entropies due to diffusion''. Phys. Rev. Lett. 122, 250602 (2019).

[9] Marko Žnidarič. ``Entanglement growth in diffusive systems''. Communications Physics 3, 100 (2020).

[10] Tianci Zhou and Andreas W. W. Ludwig. ``Diffusive scaling of rényi entanglement entropy''. Phys. Rev. Res. 2, 033020 (2020).

[11] Yiqiu Han and Xiao Chen. ``Measurement-induced criticality in ${\mathbb{z}}_{2}$-symmetric quantum automaton circuits''. Phys. Rev. B 105, 064306 (2022).

[12] Yiqiu Han and Xiao Chen. ``Entanglement structure in the volume-law phase of hybrid quantum automaton circuits''. Phys. Rev. B 107, 014306 (2023).

[13] Jason Iaconis, Andrew Lucas, and Xiao Chen. ``Measurement-induced phase transitions in quantum automaton circuits''. Phys. Rev. B 102, 224311 (2020).

[14] Brian Skinner, Jonathan Ruhman, and Adam Nahum. ``Measurement-induced phase transitions in the dynamics of entanglement''. Phys. Rev. X 9, 031009 (2019).

[15] Amos Chan, Rahul M. Nandkishore, Michael Pretko, and Graeme Smith. ``Unitary-projective entanglement dynamics''. Phys. Rev. B 99, 224307 (2019).

[16] Yaodong Li, Xiao Chen, and Matthew P. A. Fisher. ``Quantum zeno effect and the many-body entanglement transition''. Phys. Rev. B 98, 205136 (2018).

[17] Yaodong Li, Xiao Chen, and Matthew P. A. Fisher. ``Measurement-driven entanglement transition in hybrid quantum circuits''. Phys. Rev. B 100, 134306 (2019).

[18] Michael J. Gullans and David A. Huse. ``Dynamical purification phase transition induced by quantum measurements''. Phys. Rev. X 10, 041020 (2020).

[19] Yimu Bao, Soonwon Choi, and Ehud Altman. ``Theory of the phase transition in random unitary circuits with measurements''. Phys. Rev. B 101, 104301 (2020).

[20] Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, and Andreas W. W. Ludwig. ``Measurement-induced criticality in random quantum circuits''. Phys. Rev. B 101, 104302 (2020).

[21] Xiao Chen, Yaodong Li, Matthew P. A. Fisher, and Andrew Lucas. ``Emergent conformal symmetry in nonunitary random dynamics of free fermions''. Phys. Rev. Res. 2, 033017 (2020).

[22] O. Alberton, M. Buchhold, and S. Diehl. ``Entanglement transition in a monitored free-fermion chain: From extended criticality to area law''. Physical Review Letters 126 (2021).

[23] Matteo Ippoliti, Michael J. Gullans, Sarang Gopalakrishnan, David A. Huse, and Vedika Khemani. ``Entanglement phase transitions in measurement-only dynamics''. Phys. Rev. X 11, 011030 (2021).

[24] Shengqi Sang and Timothy H. Hsieh. ``Measurement-protected quantum phases''. Phys. Rev. Res. 3, 023200 (2021).

[25] Ali Lavasani, Yahya Alavirad, and Maissam Barkeshli. ``Measurement-induced topological entanglement transitions in symmetric random quantum circuits''. Nature Physics 17, 342–347 (2021).

[26] Utkarsh Agrawal, Aidan Zabalo, Kun Chen, Justin H. Wilson, Andrew C. Potter, J. H. Pixley, Sarang Gopalakrishnan, and Romain Vasseur. ``Entanglement and charge-sharpening transitions in u(1) symmetric monitored quantum circuits''. Phys. Rev. X 12, 041002 (2022).

[27] Matthew B. Hastings, Iván González, Ann B. Kallin, and Roger G. Melko. ``Measuring renyi entanglement entropy in quantum monte carlo simulations''. Phys. Rev. Lett. 104, 157201 (2010).

[28] Zhi-Cheng Yang. ``Distinction between transport and rényi entropy growth in kinetically constrained models''. Phys. Rev. B 106, L220303 (2022).

[29] Richard Arratia. ``The motion of a tagged particle in the simple symmetric exclusion system on $z$''. The Annals of Probability 11, 362 – 373 (1983).

[30] Soonwon Choi, Yimu Bao, Xiao-Liang Qi, and Ehud Altman. ``Quantum error correction in scrambling dynamics and measurement-induced phase transition''. Phys. Rev. Lett. 125, 030505 (2020).

[31] Ruihua Fan, Sagar Vijay, Ashvin Vishwanath, and Yi-Zhuang You. ``Self-organized error correction in random unitary circuits with measurement''. Phys. Rev. B 103, 174309 (2021).

[32] Yaodong Li and Matthew P. A. Fisher. ``Statistical mechanics of quantum error correcting codes''. Phys. Rev. B 103, 104306 (2021).

[33] Yaodong Li, Sagar Vijay, and Matthew P.A. Fisher. ``Entanglement domain walls in monitored quantum circuits and the directed polymer in a random environment''. PRX Quantum 4, 010331 (2023).

[34] Rajibul Islam, Ruichao Ma, Philipp M. Preiss, M. Eric Tai, Alexander Lukin, Matthew Rispoli, and Markus Greiner. ``Measuring entanglement entropy in a quantum many-body system''. Nature 528, 77–83 (2015).

[35] Scott Aaronson and Daniel Gottesman. ``Improved simulation of stabilizer circuits''. Phys. Rev. A 70, 052328 (2004).

[36] Hansveer Singh, Brayden A. Ware, Romain Vasseur, and Aaron J. Friedman. ``Subdiffusion and many-body quantum chaos with kinetic constraints''. Phys. Rev. Lett. 127, 230602 (2021).

Cited by

[1] Shuo Liu, Ming-Rui Li, Shi-Xin Zhang, and Shao-Kai Jian, "Entanglement Structure and Information Protection in Noisy Hybrid Quantum Circuits", Physical Review Letters 132 24, 240402 (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-22 04:13:03). The list may be incomplete as not all publishers provide suitable and complete citation data.

On SAO/NASA ADS no data on citing works was found (last attempt 2024-06-22 04:13:03).