Measurement-induced criticality in random quantum circuits

By Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, A. Ludwig. Physical review B, 2019

388 citations recorded by the source corpus.

We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two-dimensional statistical mechanics model. In this language, the area- to volume-law entanglement transition can be interpreted as an ordering transition in the statistical mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. We analyze in detail the limit of infinite on-site Hilbert space dimension in which the statistical mechanics model maps onto percolation. In particular, we compute the exact value of the universal coefficient of the logarithm of subsystem size in the $n$th R\'enyi entropies for $n \geq 1$ in this limit using relatively recent results for conformal field theory describing the critical theory of 2D percolation, and we discuss how to access the generic transition at finite on-site Hilbert space dimension from this limit, which is in a universality class different from 2D percolation. We also comment on the relation to the entanglement transition in Random Tensor Networks, studied previously in Ref. 1.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3667ac0d53ea550581bb4ca269e31460837bd8df

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. D. Huse
5. B. Skinner
6. S. Vijay
7. Michael J. Gullans
8. Yaodong Li

In Atomic and Molecular Physics, and Optics

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

Citations in the corpus

• Statistical mechanics of quantum error correcting codes (2020, methodology): “As for random Haar circuits [19, 20] and random tensor networks [32], the identification in Eq.”
• Entanglement Membrane in Chaotic Many-Body Systems (2019, neutral): “[81] Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, and Andreas WW Ludwig.”
• Measurement-protected quantum phases (2020, background): “[16] Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, and Andreas W.”
• Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, methodology): “In the many-body case this random dynamics admits a “measurement phase transition” (MPT) between two qualitatively different, stable dynamical phases, with distinct entanglement properties [6–27].”
• Random Quantum Circuits (2022, methodology): “Numerical evidence for this transition has by now been found in a wide range of microscopic models (52, 53, 58, 68, 65, 66, 61, 62, 54, 63, 64, 77, 67).”
• Measurement-induced quantum phases realized in a trapped-ion quantum computer (2021, background): “5, 1) and L = (4, 6, 8), and observe the first experimental evidence of the phases of a dynamical purification phase transition.”