aiqbench analysis
This paper presents a significant theoretical counterexample in quantum many-body physics, demonstrating that operator entanglement in integrable brickwork circuits can grow with the square root of time rather than logarithmically. The findings directly impact the efficiency of matrix product operator simulations by establishing new lower bounds on bond dimension growth for specific error tolerances. This work advances the fundamental understanding of entanglement dynamics in exactly solvable quantum systems, a core area of research within quantum computing and statistical mechanics.
Square-root growth of operator entanglement in an integrable brickwork circuit
arXiv:2609.39401v1 Announce Type: cross Abstract: It is widely expected that the von Neumann entanglement of a local operator grows at most logarithmically in integrable many-body systems in infinite volume. We give a counterexample in a four-state brickwork circuit whose gate is a permutation matrix solving the constant Yang--Baxter equation. The von Neumann operator entropy grows as $(\log2)\sqrt{t/\pi}+O(\log t)$, whereas fixed-index R\'enyi entropies grow linearly below index one and logarithmically above it. At fixed relative Hilbert--Schmidt error below one, matrix product operator simulations require a bond dimension growing at least as $\exp(c\sqrt t)$ for some $c>0$.
Abstract:It is widely expected that the von Neumann entanglement of a local operator grows at most logarithmically in integrable many-body systems in infinite volume. We give a counterexample in a four-state brickwork circuit whose gate is a permutation matrix solving the constant Yang--Baxter equation. The von Neumann operator entropy grows as $(\log2)\sqrt{t/\pi}+O(\log t)$, whereas fixed-index Rényi entropies grow linearly below index one and logarithmically above it. At fixed relative Hilbert--Schmidt error below one, matrix product operator simulations require a bond dimension growing at least as $\exp(c\sqrt t)$ for some $c>0$.
4.5 pages and 17 pages of Supplemental Material
Statistical Mechanics (cond-mat.stat-mech); Exactly Solvable and Integrable Systems (nlin.SI); Quantum Physics (quant-ph)
arXiv:2609.39401 [cond-mat.stat-mech]
(or arXiv:2609.39401v1 [cond-mat.stat-mech] for this version)
https://doi.org/10.48550/arXiv.2609.39401 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 201 words
