Universal distributions of overlaps from unitary dynamics in generic quantum many-body systems
- URL: http://arxiv.org/abs/2404.10057v1
- Date: Mon, 15 Apr 2024 18:01:13 GMT
- Title: Universal distributions of overlaps from unitary dynamics in generic quantum many-body systems
- Authors: Alexios Christopoulos, Amos Chan, Andrea De Luca,
- Abstract summary: We study the preparation of a quantum state using a circuit of depth $t$ from a factorized state of $N$ sites.
We argue that in the appropriate scaling limit of large $t$ and $N$, the overlap between states evolved under generic many-body chaotic dynamics.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study the preparation of a quantum state using a circuit of depth $t$ from a factorized state of $N$ sites. We argue that in the appropriate scaling limit of large $t$ and $N$, the overlap between states evolved under generic many-body chaotic dynamics belongs to a family of universal distribution that generalizes the celebrated Porter-Thomas distribution. This is a consequence of a mapping in the space of replicas to a model of dilute domain walls. Our result provides a rare example in which analysis at an arbitrary number of replicas is possible, giving rise to the complete overlap distribution. Our general picture is derived and corroborated by the exact solution of the random phase model and of an emergent random matrix model given by the Ginibre ensemble. Finally, numerical simulations of two distinct random circuits show excellent agreement, thereby demonstrating universality.
Related papers
- Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces [0.0]
We derive an analytical expression for the time-averaged quantum Fisher information (QFI) that applies to all quantum chaotic systems governed by Dyson's ensembles.
Our approach integrates concepts of randomness, multipartite entanglement and quantum chaos.
arXiv Detail & Related papers (2024-07-16T15:11:20Z) - Projected state ensemble of a generic model of many-body quantum chaos [0.0]
The projected ensemble is based on the study of the quantum state of a subsystem $A$ conditioned on projective measurements in its complement.
Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design.
arXiv Detail & Related papers (2024-02-26T19:00:00Z) - Conformal inference for regression on Riemannian Manifolds [49.7719149179179]
We investigate prediction sets for regression scenarios when the response variable, denoted by $Y$, resides in a manifold, and the covariable, denoted by X, lies in Euclidean space.
We prove the almost sure convergence of the empirical version of these regions on the manifold to their population counterparts.
arXiv Detail & Related papers (2023-10-12T10:56:25Z) - DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained
Diffusion [66.21290235237808]
We introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states.
We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs.
Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks.
arXiv Detail & Related papers (2023-01-23T15:18:54Z) - Super-model ecosystem: A domain-adaptation perspective [101.76769818069072]
This paper attempts to establish the theoretical foundation for the emerging super-model paradigm via domain adaptation.
Super-model paradigms help reduce computational and data cost and carbon emission, which is critical to AI industry.
arXiv Detail & Related papers (2022-08-30T09:09:43Z) - Many-Body Quantum Chaos and Space-time Translational Invariance [0.0]
We study the consequences of having translational invariance in space and in time in many-body quantum chaotic systems.
We consider an ensemble of random quantum circuits, composed of single-site random unitaries and nearest neighbour couplings.
We numerically demonstrate, with simulations of two distinct circuit models, that in such a scaling limit, most microscopic details become unimportant.
arXiv Detail & Related papers (2021-09-09T18:00:00Z) - Exact Recovery in the General Hypergraph Stochastic Block Model [92.28929858529679]
This paper investigates fundamental limits of exact recovery in the general d-uniform hypergraph block model (d-HSBM)
We show that there exists a sharp threshold such that exact recovery is achievable above the threshold and impossible below it.
arXiv Detail & Related papers (2021-05-11T03:39:08Z) - Generic aspects of the resource theory of quantum coherence [0.0]
We prove that if two $n$-dimensional pure states are chosen independently according to the natural uniform distribution, then the probability that they are comparable as $nrightarrowinfty$.
We also study the maximal success probability of incoherent conversions and find an explicit formula for its large-$n$ distribution.
arXiv Detail & Related papers (2020-10-13T16:38:52Z) - GANs with Variational Entropy Regularizers: Applications in Mitigating
the Mode-Collapse Issue [95.23775347605923]
Building on the success of deep learning, Generative Adversarial Networks (GANs) provide a modern approach to learn a probability distribution from observed samples.
GANs often suffer from the mode collapse issue where the generator fails to capture all existing modes of the input distribution.
We take an information-theoretic approach and maximize a variational lower bound on the entropy of the generated samples to increase their diversity.
arXiv Detail & Related papers (2020-09-24T19:34:37Z) - Maximum Multiscale Entropy and Neural Network Regularization [28.00914218615924]
A well-known result shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution.
This paper investigates a generalization of these results to a multiscale setting.
arXiv Detail & Related papers (2020-06-25T17:56:11Z) - Contextuality scenarios arising from networks of stochastic processes [68.8204255655161]
An empirical model is said contextual if its distributions cannot be obtained marginalizing a joint distribution over X.
We present a different and classical source of contextual empirical models: the interaction among many processes.
The statistical behavior of the network in the long run makes the empirical model generically contextual and even strongly contextual.
arXiv Detail & Related papers (2020-06-22T16:57:52Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.