arXiv subjects

Yichen Huang

Publications and source records attributed to Yichen Huang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Long-time properties of generic Floquet systems are approximately periodic with the driving period

A Floquet quantum system is governed by a Hamiltonian that is periodic in time. Consider the space of piecewise time-independent Floquet systems with (geometrically) local interactions. We prove that for all but a measure zero set of systems in this space, starting from a random product state, many properties (including expectation values of observables and the entanglement entropy of a macroscopically large subsystem) at long times are approximately periodic with the same period as the Hamiltonian. Thus, in almost every Floquet system of arbitrarily large but finite size, discrete time-crystalline behavior does not persist to strictly infinite time.

quant-ph↗

arXiv2024

High-precision simulation of finite-size thermalizing systems at long times

To simulate thermalizing systems at long times, the most straightforward approach is to calculate the thermal properties at the corresponding energy. In a quantum many-body system of size $N$, for local observables and many initial states, this approach has an error of $O(1/N)$, which is reminiscent of the finite-size error of the equivalence of ensembles. In this paper, we propose a simple and efficient numerical method so that the simulation error is of higher order in $1/N$. This finite-size error scaling is proved by assuming the eigenstate thermalization hypothesis.

cond-mat.stat-mech↗

arXiv2024

REFeREE: A REference-FREE Model-Based Metric for Text Simplification

Text simplification lacks a universal standard of quality, and annotated reference simplifications are scarce and costly. We propose to alleviate such limitations by introducing REFeREE, a reference-free model-based metric with a 3-stage curriculum. REFeREE leverages an arbitrarily scalable pretraining stage and can be applied to any quality standard as long as a small number of human annotations are available. Our experiments show that our metric outperforms existing reference-based metrics in predicting overall ratings and reaches competitive and consistent performance in predicting specific ratings while requiring no reference simplifications at inference time.

cs.CL↗

arXiv2024

Learning Interpretable Low-dimensional Representation via Physical Symmetry

We have recently seen great progress in learning interpretable music representations, ranging from basic factors, such as pitch and timbre, to high-level concepts, such as chord and texture. However, most methods rely heavily on music domain knowledge. It remains an open question what general computational principles give rise to interpretable representations, especially low-dim factors that agree with human perception. In this study, we take inspiration from modern physics and use physical symmetry as a self consistency constraint for the latent space of time-series data. Specifically, it requires the prior model that characterises the dynamics of the latent states to be equivariant with respect to certain group transformations. We show that physical symmetry leads the model to learn a linear pitch factor from unlabelled monophonic music audio in a self-supervised fashion. In addition, the same methodology can be applied to computer vision, learning a 3D Cartesian space from videos of a simple moving object without labels. Furthermore, physical symmetry naturally leads to counterfactual representation augmentation, a new technique which improves sample efficiency.

cs.LG↗

arXiv2023

Thermalization without eigenstate thermalization

In an isolated quantum many-body system undergoing unitary evolution, we study the thermalization of a subsystem, treating the rest of the system as a bath. In this setting, the eigenstate thermalization hypothesis (ETH) was proposed to explain thermalization. Consider a nearly integrable Sachdev-Ye-Kitaev model obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model. When the subsystem size is larger than the square root of but is still a vanishing fraction of the system size, we prove thermalization if the system is initialized in a random product state, while almost all eigenstates violate the ETH. In this sense, the ETH is not a necessary condition for thermalization.

cond-mat.stat-mech↗

arXiv2023

Improved concentration of Laguerre and Jacobi ensembles

We consider the asymptotic limits where certain parameters in the definitions of the Laguerre and Jacobi ensembles diverge. In these limits, Dette, Imhof, and Nagel proved that up to a linear transformation, the joint probability distributions of the ensembles become more and more concentrated around the zeros of the Laguerre and Jacobi polynomials, respectively. In this paper, we improve the concentration bounds. Our proofs are similar to those in the original references, but the error analysis is improved and arguably simpler. For the first and second moments of the Jacobi ensemble, we further improve the concentration bounds implied by our aforementioned results.

math.PR↗

arXiv2023

Robustness Tests for Automatic Machine Translation Metrics with Adversarial Attacks

We investigate MT evaluation metric performance on adversarially-synthesized texts, to shed light on metric robustness. We experiment with word- and character-level attacks on three popular machine translation metrics: BERTScore, BLEURT, and COMET. Our human experiments validate that automatic metrics tend to overpenalize adversarially-degraded translations. We also identify inconsistencies in BERTScore ratings, where it judges the original sentence and the adversarially-degraded one as similar, while judging the degraded translation as notably worse than the original with respect to the reference. We identify patterns of brittleness that motivate more robust metric development.

cs.CL↗

arXiv2023

Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement

It is well known that in Anderson localized systems, starting from a random product state the entanglement entropy remains bounded at all times. However, we show that adding a single boundary term to an Anderson localized Hamiltonian leads to unbounded growth of entanglement. Our results imply that Anderson localization is not a local property. One cannot conclude that a subsystem has Anderson localized behavior without looking at the whole system, as a term that is arbitrarily far from the subsystem can affect the dynamics of the subsystem in such a way that the features of Anderson localization are lost.

cond-mat.dis-nn↗

arXiv2022

Convergence of eigenstate expectation values with system size

Understanding the asymptotic behavior of physical quantities in the thermodynamic limit is a fundamental problem in statistical mechanics. In this paper, we study how fast the eigenstate expectation values of a local operator converge to a smooth function of energy density as the system size diverges. In translation-invariant quantum lattice systems in any spatial dimension, we prove that for all but a measure zero set of local operators, the deviations of finite-size eigenstate expectation values from the aforementioned smooth function are lower bounded by $1/O(N)$, where $N$ is the system size. The lower bound holds regardless of the integrability or chaoticity of the model, and is saturated in systems satisfying the eigenstate thermalization hypothesis.

math-ph↗

arXiv2022

Finite-size scaling analysis of eigenstate thermalization

We study the fluctuations of eigenstate expectation values in a microcanonical ensemble. Assuming the eigenstate thermalization hypothesis, an analytical formula for the finite-size scaling of the fluctuations is derived. The same problem was studied by Beugeling et al. [Phys. Rev. E 89, 042112 (2014)]. We compare our results with theirs.

cond-mat.stat-mech↗

arXiv2022

Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement

We study the entanglement dynamics of quantum many-body systems and prove the following: (I) For any geometrically local Hamiltonian on a lattice, starting from a random product state the entanglement entropy is bounded away from the maximum entropy at all times with high probability. (II) In a spin-glass model with random all-to-all interactions, starting from any product state the average entanglement entropy is bounded away from the maximum entropy at all times. We also extend these results to any unitary evolution with charge conservation and to the Sachdev-Ye-Kitaev model. Our results highlight the difference between the entanglement generated by (chaotic) Hamiltonian dynamics and that of random states, for the latter is nearly maximal.

quant-ph↗

arXiv2021

UNITER-Based Situated Coreference Resolution with Rich Multimodal Input

We present our work on the multimodal coreference resolution task of the Situated and Interactive Multimodal Conversation 2.0 (SIMMC 2.0) dataset as a part of the tenth Dialog System Technology Challenge (DSTC10). We propose a UNITER-based model utilizing rich multimodal context such as textual dialog history, object knowledge base and visual dialog scenes to determine whether each object in the current scene is mentioned in the current dialog turn. Results show that the proposed approach outperforms the official DSTC10 baseline substantially, with the object F1 score boosted from 36.6% to 77.3% on the development set, demonstrating the effectiveness of the proposed object representations from rich multimodal input. Our model ranks second in the official evaluation on the object coreference resolution task with an F1 score of 73.3% after model ensembling.

cs.CL↗

arXiv2021

Neural network representation of tensor network and chiral states

We study the representational power of Boltzmann machines (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network representation. Despite the difficulty of representing (gapped) chiral topological states with local tensor networks, we construct a quasi-local neural network representation for a chiral $p$-wave superconductor. These results demonstrate the power of Boltzmann machines.

cond-mat.dis-nn↗

arXiv2021

Locally accurate matrix product approximation to thermal states

In one-dimensional quantum systems with short-range interactions, a set of leading numerical methods is based on matrix product states, whose bond dimension determines the amount of computational resources required by these methods. We prove that a thermal state at constant inverse temperature $β$ has a matrix product representation with bond dimension $e^{\tilde O(\sqrt{β\log(1/ε)})}$ such that all local properties are approximated to accuracy $ε$. This justifies the common practice of using a constant bond dimension in the numerical simulation of thermal properties.

quant-ph↗

arXiv2021

Entropic uncertainty relations in multidimensional position and momentum spaces

Commutator-based entropic uncertainty relations in multidimensional position and momentum spaces are derived, twofold generalizing previous entropic uncertainty relations for one-mode states. They provide optimal lower bounds and imply the multidimensional variance-based uncertainty principle. The article concludes with an open conjecture.

quant-ph↗

arXiv2021

Variance-based uncertainty relations

Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide near-optimal lower bounds in some typical examples, and are useful for entanglement detection.

quant-ph↗

arXiv2021

Universal eigenstate entanglement of chaotic local Hamiltonians

This arXiv repository is a bundle of two closely related papers. Abstract of the first paper: In systems governed by "chaotic" local Hamiltonians, we conjecture the universality of eigenstate entanglement (defined as the average entanglement entropy of all eigenstates) by proposing an exact formula for its dependence on the subsystem size. This formula is derived from an analytical argument based on a plausible assumption, and is supported by numerical simulations. Abstract of the second paper: In systems governed by chaotic local Hamiltonians, the first paper conjectured the universality of the average entanglement entropy of all eigenstates by proposing an exact formula for its dependence on the subsystem size. In this note, I extend this result to the average entanglement entropy of a constant fraction of eigenstates in the middle of the energy spectrum. The generalized formula is supported by numerical simulations of various chaotic spin chains.

quant-ph↗

arXiv2021

Two-dimensional local Hamiltonian problem with area laws is QMA-complete

We show that the two-dimensional (2D) local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete. We also prove similar results in 2D translation-invariant systems and for the 3D Heisenberg and Hubbard models with local magnetic fields. Consequently, unless MA = QMA, not all ground states of 2D local Hamiltonians with area laws have efficient classical representations that support efficient computation of local expectation values. In the future, even if area laws are proved for ground states of 2D gapped systems, the computational complexity of these systems remains unclear.

cond-mat.str-el↗