Self-organized error correction in random unitary circuits with measurement
By Ruihua Fan, S. Vijay, Ashvin Vishwanath, Yi-Zhuang You. 2020
140 citations recorded by the source corpus.
Random measurements have been shown to induce a phase transition in an extended quantum system evolving under chaotic unitary dynamics, when the strength of measurements exceeds a threshold value. Below this threshold, a steady state with a sub-thermal volume law entanglement emerges, which is resistant to the disentangling action of measurements, suggesting a connection to quantum error-correcting codes. Here we quantify these notions by identifying a universal, subleading logarithmic contribution to the volume law entanglement entropy: $S^{(2)}(A)=\kappa L_A+\frac{3}{2}\log L_A$ which bounds the mutual information between a qudit inside region $A$ and the rest of the system. Specifically, we find the power law decay of the mutual information $I(\{x\}:\bar{A})\propto x^{-3/2}$ with distance $x$ from the region's boundary, which implies that measuring a qudit deep inside $A$ will have negligible effect on the entanglement of $A$. We obtain these results by mapping the entanglement dynamics to the imaginary time evolution of an Ising model, to which we can apply field-theoretic and matrix-product-state techniques. Finally, exploiting the error-correction viewpoint, we assume that the volume-law state is an encoding of a Page state in a quantum error-correcting code to obtain a bound on the critical measurement strength $p_{c}$ as a function of the qudit dimension $d$: $p_{c}\log[(d^{2}-1)({p_{c}^{-1}-1})]\le \log[(1-p_{c})d]$. The bound is saturated at $p_c(d\rightarrow\infty)=1/2$ and provides a reasonable estimate for the qubit transition: $p_c(d=2) \le 0.1893$.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/bd991fc02c09fa4b0a49a494a9ac5d3fde8cf1d8
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions (2021, background): “[23] Ruihua Fan, Sagar Vijay, Ashvin Vishwanath, and Yi-Zhuang You, “Self-organized error correction in random unitary circuits with measurement,” Physical Review B 103 (2021), 10.”
- Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits (2021, background): “[18] Ruihua Fan, Sagar Vijay, Ashvin Vishwanath, and Yi-Zhuang You, “Self-Organized Error Correction in Random Unitary Circuits with Measurement,” arXiv:2002.”
- Measurement-protected quantum phases (2020, background): “[22] Ruihua Fan, Sagar Vijay, Ashvin Vishwanath, and Yi-Zhuang You, “Self-organized error correction in random unitary circuits with measurement,” (2020), arXiv:2002.”
- Random Quantum Circuits (2022, methodology): “The code rate vanishes upon approaching the “pure” phase – the purification transition thus corresponding to a transition in the encodability of the quantum code (61, 56, 107, 108).”
- Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, methodology): “Viewing the circuit as a quantum information processor, the MPT is a transition in the properties of a randomly generated error-correcting code [11, 24, 28], the structure of which has been argued to be optimal in some senses [12].”
- Statistical mechanics of quantum error correcting codes (2020, background): “Finally, we mention that QECCs can also be dynamically generated for circuits with a pure initial state in the volume law entangled phase when p < pc [17, 23], if we”