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Entanglement Dynamics in Hybrid Quantum Circuits

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Entanglement in Spin Chains

Part of the book series: Quantum Science and Technology ((QST))

Abstract

The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems are that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal “laws.” This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy quantum circuits—for which classical description of individual circuits is expected to be generically intractable. Here, we review recent progress in understanding the dynamics of quantum information in ensembles of random quantum circuits, through a stat-mech lens. We begin by reviewing discoveries of universal features of entanglement growth, operator spreading, thermalization, and chaos in unitary random quantum circuits, and their relation to stat-mech problems of random surface growth and noisy hydrodynamics. We then explore the dynamics of monitored random circuits, which can loosely be thought of as noisy dynamics arising from an environment monitoring the system, and exhibit new types of measurement-induced phases and criticality. Throughout, we attempt to give a pedagogical introduction to various technical methods and to highlight emerging connections between concepts in stat-mech, quantum information, and quantum communication theory.

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Notes

  1. 1.

    As an aside, we note that if the ancilla qubit, R, is initially entangled non-locally with the system, e.g., by applying a scrambling unitary before undergoing MRC dynamics, then in the L →∞ limit, \(\overline {S_R}\) precisely jumps from log2 for p < pc to 0 for p > pc. On the other hand, if the ancilla qubit is locally entangled with a single system qubit, \(\overline {S_R}\) is not quantized (for example, with probability p that qubit could immediately get measured even for p < pc) and its jump across the transition is non-universal.

  2. 2.

    For example, by continuously turning off the coupling between the stabilizer-state qubits and volume-law entangled trivial degrees of freedom in the above construction, and then dialing the stabilizer measurement probability to unity, which, in the replicated statistical mechanics description corresponds to disentangling two gapped degrees of freedom and then smoothly changing couplings within a gapped phase, respectively, and does not produce a phase transition.

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Acknowledgements

We thank our collaborators Utkarsh Agrawal, Fergus Barratt, Matthew Fisher, Aaron Friedman, Sarang Gopalakrishnan, Michael Gullans, David Huse, Chao-Ming Jian, Yaodong Li, Andreas Ludwig, Adam Nahum, Javier Lopez-Piqueres, Jed Pixley, Hans Singh, Yi-Zhuang You, Brayden Ware, Justin Wilson, and Aidan Zabalo for many insightful discussions. We also thank Ehud Altman, Maissam Barkeshli, Xiao Chen, Michael Gullans, Tim Hsieh, Yaodong Li, Adam Nahum, and Jed Pixley for helpful comments on this manuscript. This research was supported in part from the US Department of Energy, Office of Science, Basic Energy Sciences, under Early Career Award No. DE-SC0019168 (RV), from the US National Science Foundation DMR-1653007 (ACP), and the Alfred P. Sloan Foundation through Sloan Research Fellowships (RV and ACP). This research was undertaken thanks, in part, to funding from the Max Planck-UBC-UTokyo Center for Quantum Materials and the Canada First Research Excellence Fund, Quantum Materials and Future Technologies Program (ACP).

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Authors and Affiliations

  1. Department of Physics and Astronomy, and Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada

    Andrew C. Potter

  2. Department of Physics, University of Massachusetts, Amherst, MA, USA

    Romain Vasseur

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  1. Andrew C. Potter
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Editors and Affiliations

  1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China

    Abolfazl Bayat

  2. Department of Physics and Astronomy, University College London, London, UK

    Sougato Bose

  3. Department of Physics, University of Gothenburg, Göteborg, Sweden

    Henrik Johannesson

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Potter, A.C., Vasseur, R. (2022). Entanglement Dynamics in Hybrid Quantum Circuits. In: Bayat, A., Bose, S., Johannesson, H. (eds) Entanglement in Spin Chains. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-031-03998-0_9

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