Related papers: Nearly optimal algorithms to learn sparse quantum …
We study how parallelism can speed up quantum simulation. A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including…
Sparse coding is a class of unsupervised methods for learning a sparse representation of the input data in the form of a linear combination of a dictionary and a sparse code. This learning framework has led to state-of-the-art results in…
The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…
Hamiltonian learning is crucial to the certification of quantum devices and quantum simulators. In this paper, we propose a hybrid quantum-classical Hamiltonian learning algorithm to find the coefficients of the Pauli operator components of…
We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…
Learning quantum Hamiltonians with high precision is important for quantum physics and quantum information science. We propose a multi-stage neural network framework that significantly enhances Hamiltonian learning precision through…
Imitation learning algorithms have been interpreted as variants of divergence minimization problems. The ability to compare occupancy measures between experts and learners is crucial in their effectiveness in learning from demonstrations.…
Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with…
In recent years, the crucial importance of metrics in machine learning algorithms has led to an increasing interest for optimizing distance and similarity functions. Most of the state of the art focus on learning Mahalanobis distances…
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. For this task, there is a well-studied quantum algorithm that performs quantum phase estimation on an initial trial state that…
Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix…
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…
We develop new stochastic gradient methods for efficiently solving sparse linear regression in a partial attribute observation setting, where learners are only allowed to observe a fixed number of actively chosen attributes per example at…
We present a fairly general framework for reducing $(\varepsilon, \delta)$ differentially private (DP) statistical estimation to its non-private counterpart. As the main application of this framework, we give a polynomial time and…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…