Scrambling in Random Unitary Circuits: Exact Results
Authors: Bruno Bertini, Lorenzo Piroli
Abstract
We study the scrambling of quantum information in local random unitary circuits by focusing on the tripartite information proposed by Hosur et al. We provide exact results for the averaged R\'enyi-$2$ tripartite information in two cases: (i) the local gates are Haar random and (ii) the local gates are dual-unitary and randomly sampled from a single-site Haar-invariant measure. We show that the latter case defines a one-parameter family of circuits, and prove that for a "maximally chaotic" subset of this family quantum information is scrambled faster than in the Haar-random case. Our approach is based on a standard mapping onto an averaged folded tensor network, that can be studied by means of appropriate recurrence relations. By means of the same method, we also revisit the computation of out-of-time-ordered correlation functions, re-deriving known formulae for Haar-random unitary circuits, and presenting an exact result for maximally chaotic random dual-unitary gates.
The papers around it, by date and closeness
Higher is closer to this paper; left is older. Lines join papers close to each other: groups of lines are sub-topics. Select a point to see why it is there. Back to the summary of this paper
Papers around this one
Ranked by how close their title and abstract are to this paper’s. Select some to read them together.
Closest papers
-
Large deviation full counting statistics in adiabatic open quantum dynamicsPaulo J. Paulino, Igor Lesanovsky, Federico Carollo · 2024 · Statistical Mechanics · AI summary available
Abstract
The state of an open quantum system undergoing an adiabatic process evolves by following the instantaneous stationary state of its time-dependent generator. This observation allows one to characterize, for a generic adiabatic evolution, the average dynamics of the open system. However, information about fluctuations of dynamical observables, such as the number of photons emitted or the time-integrated stochastic entropy production in single experimental runs, requires controlling the whole spectrum of the generator and not only the stationary state. Here, we show how such information can be obtained in adiabatic open quantum dynamics by exploiting tools from large deviation theory. We prove …
-
Topology protects chiral edge currents in stochastic systemsEvelyn Tang, Jaime Agudo-Canalejo, Ramin Golestanian · 2020 · Phys. Rev. X 11, 031015 (2021) · AI summary available
Abstract
Constructing systems that exhibit time-scales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly. Inspiration often comes from living systems, in which robust global behavior prevails despite the stochasticity of the underlying processes. Here, we present two-dimensional stochastic networks that consist of minimal motifs representing out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. These currents arise in the topological phase due to the bulk-boundary correspondence and dominate the system dynamics in t…
-
First-order transition and marginal critical behavior in a novel 2D frustrated Ising modelChristophe Chatelain · 2024 · Phys. Rev. E 111, 024109 (2024) · AI summary available
Abstract
The phase diagram of a novel two-dimensional frustrated Ising model with both anti-ferromagnetic and ferromagnetic couplings is studied using Tensor-Network Renormalization-Group techniques. This model can be seen as two anti-ferromagnetic Ising replicas coupled by non-local spin-spin interactions, designed in such a way that the continuum limit matches that of the still debated J1 -J2 model and induces a marginal critical behavior. Our model has the advantage of having more symmetries than the J1 -J2 model and of allowing a more straightforward implementation of Tensor-Network Renormalization-Group algorithms We demonstrate the existence of two transition lines, featuring both first and sec…
-
Maximum Kolmogorov-Sinai entropy vs minimum mixing time in Markov chainsMartin Mihelich, Berengere Dubrulle, Didier Paillard et al. · 2015 · Statistical Mechanics · AI summary available
Abstract
Many modern techniques employed in physics, such a computation of path integrals, rely on random walks on graphs that can be represented as Markov chains. Traditionally, estimates of running times of such sampling algorithms are computed using the number of steps in the chain needed to reach the stationary distribution. This quantity is generally defined as mixing time and is often difficult to compute. In this paper, we suggest an alternative estimate based on the Kolmogorov-Sinai entropy, by establishing a link between the maximization of KSE and the minimization of the mixing time. Since KSE are easier to compute in general than mixing time, this link provides a new faster method to appro…
-
Understanding quantum entanglement by thermo field dynamicsYoichiro Hashizume, Masuo Suzuki · 2013 · Statistical Mechanics · AI summary available
Abstract
We propose a new method to understand quantum entanglement using the thermo field dynamics (TFD) described by a double Hilbert space. The entanglement states show a quantum-mechanically complicated behavior. Our new method using TFD makes it easy to understand the entanglement states, because the states in the tilde space in TFD play a role of tracer of the initial states. For our new treatment, we define an extended density matrix on the double Hilbert space. From this study, we make a general formulation of this extended density matrix and examine some simple cases using this formulation. Consequently, we have found that we can distinguish intrinsic quantum entanglement from the thermal fl…
-
Continuously varying exponents in the distribution of waiting times in the symmetric exclusion process on a percolation clusterArpan Chatterjee, Kabir Ramola, Deepak Dhar · 2026 · Statistical Mechanics · Not summarized yet
Abstract
We study the waiting-time distribution of hard-core interacting particles in the symmetric exclusion process on one- and two-dimensional lattices with side branches attached to each lattice site in the steady state. We use numerical simulations together with an approximate analytical treatment of particles trapped in side branches in the steady state. Such a two-dimensional carpet serves as a simplified model for trapping of a supercritical percolation cluster. At high particle densities, the system exhibits strong dynamical heterogeneity, with the distribution of logarithms of waiting times developing well-separated peaks corresponding to particles trapped at different depths from the backb…
-
Classical limit of measurement-induced transition in many-body chaos in integrable and non-integrable oscillator chainsSibaram Ruidas, Sumilan Banerjee · 2022 · Statistical Mechanics · AI summary available
Abstract
We discuss the dynamics of integrable and non-integrable chains of coupled oscillators under continuous weak position measurements in the semiclassical limit. We show that, in this limit, the dynamics is described by a standard stochastic Langevin equation, and a measurement-induced transition appears as a noise- and dissipation-induced chaotic-to-non-chaotic transition akin to stochastic synchronization. In the non-integrable chain of anharmonically coupled oscillators, we show that the temporal growth and the ballistic light-cone spread of a classical out-of-time correlator characterized by the Lyapunov exponent and the butterfly velocity, are halted above a noise or below an interaction s…
-
Comment on Bramwell et al, "Universal Fluctuations in Correlated Systems"N. W. Watkins, S. C. Chapman, G. Rowlands · 2002 · Phys. Rev. Lett 89, 208901 (2002) · Not summarized yet
Abstract
This is a comment on "Universal Fluctuations in Correlated Systems", by Bramwell et al, Phys. Rev. Lett., 84, 3744 (2000.
Go further
How are these papers found?
We compare the title and abstract of this paper with those of every paper summarized on this site, and with the papers Semantic Scholar recommends, those it cites and those citing it (for a much-cited paper, its most recent citations and, from OpenAlex, the most cited ones). Among the prior work and the follow-ups, the papers that use each other in depth, a method it uses and the much-cited follow-ups come a little higher. The levels (very close, close, related) come from the similarity of the texts, not from a judgment of quality; * marks a paper without an abstract, compared by its title. The sentence under a paper is written by an AI from the two abstracts: check it in the papers. A paper marked not relevant by three readers leaves the list.
For now only among the papers summarized on this site: search again to add the prior work, the follow-ups and Semantic Scholar’s recommendations.