Distributional property testing in a quantum world
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing closeness between unknown distributions, testing independence between two distributions, and estimating the Shannon / von Neumann entropy of distributions. The distributions can be either classical or quantum, however our quantum algorithms require coherent quantum access to a process preparing the samples. Our results build on the recent technique of quantum singular value transformation, combined with more standard tricks such as divide-and-conquer. The presented approach is a natural fit for distributional property testing both in the classical and the quantum case, demonstrating the first speed-ups for testing properties of density operators that can be accessed coherently rather than only via sampling; for classical distributions our algorithms significantly improve the precision dependence of some earlier results.
Code (0)
등록된 구현이 없습니다.
Tasks
Learning TheorySimilar Papers 제목 키워드 기반
Attesting Distributional Properties of Training Data for Machine Learning
The success of machine learning (ML) has been accompanied by increased concerns about its trustworthiness. Several jurisdictions are preparing ML regulatory frameworks. One such concern is ensuring that model training da…
DiversityHamiltonian Property Testing
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 …
A Hierarchy for Replica Quantum Advantage
We prove that given the ability to make entangled measurements on at most $k$ replicas of an $n$-qubit state $\rho$ simultaneously, there is a property of $\rho$ which requires at least order $2^n$ measurements to learn.…
Analysis of Atom-level pretraining with Quantum Mechanics (QM) data for Graph Neural Networks Molecular property models
Despite the rapid and significant advancements in deep learning for Quantitative Structure-Activity Relationship (QSAR) models, the challenge of learning robust molecular representations that effectively generalize in re…
Therapeutics Data CommonsSecurity Concerns in Quantum Machine Learning as a Service
Quantum machine learning (QML) is a category of algorithms that employ variational quantum circuits (VQCs) to tackle machine learning tasks. Recent discoveries have shown that QML models can effectively generalize from l…
Quantum Machine Learning