Critical properties of the measurement-induced transition in random quantum circuits

By A. Zabalo, Michael J. Gullans, Justin H. Wilson, S. Gopalakrishnan, D. Huse, J. Pixley. Physical review B, 2019

274 citations recorded by the source corpus.

We numerically study the measurement-driven quantum phase transition of Haar-random quantum circuits in $1+1$ dimensions. By analyzing the tripartite mutual information we are able to make a precise estimate of the critical measurement rate $p_c = 0.17(1)$. We extract estimates for the associated bulk critical exponents that are consistent with the values for percolation, as well as those for stabilizer circuits, but differ from previous estimates for the Haar-random case. Our estimates of the surface order parameter exponent appear different from that for stabilizer circuits or percolation, but we are unable to definitively rule out the scenario where all exponents in the three cases match. Moreover, in the Haar case the prefactor for the entanglement entropies $S_n$ depends strongly on the R\'enyi index $n$; for stabilizer circuits and percolation this dependence is absent. Results on stabilizer circuits are used to guide our study and identify measures with weak finite-size effects. We discuss how our numerical estimates constrain theories of the transition.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/27ba6b9c7377cb1366ea60242ec416310709154c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. B. Skinner
5. D. Huse
6. S. Vijay
7. J. Ruhman
8. Yaodong Li

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. D. Huse
5. B. Skinner
6. Yaodong Li
7. J. Ruhman
8. S. Vijay

Citations in the corpus

• Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout (2022, methodology): “Reported values of p∗ and critical exponents vary depending on circuit structure and scaling ansatz [14, 16–18], and estimates from collapses of mutual information [19, 23] differ from those of entanglement entropy.”
• Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “[93] Aidan Zabalo, Michael J Gullans, Justin H Wilson, Sarang Gopalakrishnan, David A Huse, and JH Pixley.”
• Dynamical Purification Phase Transition Induced by Quantum Measurements (2019, background): “There is also considerable numerical and analytical evidence that more general quantum trajectory models with nonstabilizer dynamics undergo a strong purification transition [41, 64, 65].”
• Statistical mechanics of quantum error correcting codes (2020, background): “It would be interesting to see if the entanglement domain wall picture is valid in a broader class of models, such as hybrid random Haar circuits [13, 19, 20, 22, 56] or other “generic” models of non-unitary dynamics [57–66], or circuit models with measurements only [40, 67–69].”
• Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, background): “[16]), though many features of the stable phases are similar.”
• Measurement-protected quantum phases (2020, background): “[19] Aidan Zabalo, Michael J.”
• Random Quantum Circuits (2022, background): “Simulations with Haar-random gates or in general Hamiltonian models are restricted to much smaller sizes but are also consistent with a continuous transition with z = 1 (65, 66).”
• Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits (2021, methodology): “(10) clearly differ from those at the measurement induced transition without a conservation law [28].”