Statistical Mechanics of Monitored Random Quantum Circuits

ORAL  · Invited

Abstract

The central philosophy of statistical mechanics and random-matrix theory of complex systems is 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 a classical simulation of individual circuits is expected to be generically intractable. In this talk, I will review recent progress in understanding the dynamics of quantum information in ensembles of random monitored quantum circuits through a statistical mechanics lens. In particular, I will describe applications of this formalism to the measurement-induced phase transitions that separate phases characterized by the amount of quantum information that can be extracted from measurements.

*This work was supported in part by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Grants No. DE-SC0019168 and No. DE-SC0023999, and by the Air Force Office of Scientific Research under Grant No. FA9550-21-1-0123.

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Publication: Entanglement transitions from holographic random tensor networks, R. Vasseur, A.C. Potter, Y-Z. You and A.W.W. Ludwig, Phys. Rev. B 100, 134203 (2019).
Measurement-induced criticality in random quantum circuits, C-M. Jian, Y-Z. You, R. Vasseur and A.W.W. Ludwig, Phys. Rev. B 101, 104302 (2020).
Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits, U. Agrawal, A. Zabalo, K. Chen, J.H. Wilson, A.C. Potter, J.H. Pixley, S. Gopalakrishnan and R. Vasseur, Phys. Rev. X 12, 041002 (2022).
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.

Presenters

  • Romain Vasseur

    • University of Massachusetts Amherst

Authors

  • Romain Vasseur

    • University of Massachusetts Amherst