Related papers: Nearly optimal algorithms to learn sparse quantum …
This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient…
We give an improved algorithm for learning a quantum Hamiltonian given copies of its Gibbs state, that can succeed at any temperature. Specifically, we improve over the work of Bakshi, Liu, Moitra, and Tang [BLMT24], by reducing the sample…
Locality is a fundamental feature of many physical time evolutions. Assumptions on locality and related structural properties also underlie recently proposed procedures for learning an unknown Hamiltonian from access to the induced time…
This paper presents a structure-preserving Bayesian approach for learning nonseparable Hamiltonian systems using stochastic dynamic models allowing for statistically-dependent, vector-valued additive and multiplicative measurement noise.…
Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available…
We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular…
Learning a Gaussian mixture model (GMM) is a fundamental problem in machine learning, learning theory, and statistics. One notion of learning a GMM is proper learning: here, the goal is to find a mixture of $k$ Gaussians $\mathcal{M}$ that…
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…
This paper proposes Hamiltonian Learning, a novel unified framework for learning with neural networks "over time", i.e., from a possibly infinite stream of data, in an online manner, without having access to future information. Existing…
We study efficient PAC learning of homogeneous halfspaces in $\mathbb{R}^d$ in the presence of malicious noise of Valiant (1985). This is a challenging noise model and only until recently has near-optimal noise tolerance bound been…
The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy) has been demonstrated to offer coarse-graining capabilities in the context of interacting particle systems (https://doi.org/10.1016/j.physd.2022.133406). In this…
Hamiltonian parameter estimation is crucial in condensed matter physics, but time and cost consuming in terms of resources used. With advances in observation techniques, high-resolution images with more detailed information are obtained,…
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…
We study the problem of learning to partition users into groups, where one must learn the compatibilities between the users to achieve optimal groupings. We define four natural objectives that optimize for average and worst case…
This paper considers the distributed sparse identification problem over wireless sensor networks such that all sensors cooperatively estimate the unknown sparse parameter vector of stochastic dynamic systems by using the local information…
We ask whether the Hamiltonian, interaction geometry, and symmetries of a quantum many-body system can be inferred from a few low-lying eigenstates without knowing which sites interact with each other. Directly solving the eigenvalue…