Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Concept

Hilbert cube

Related publications (27)

Quantum circuits for solving local fermion-to-qubit map- pings

Giuseppe Carleo, Jannes Willy E. Nys

Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the lo-cality of the operators comes at the ex-pense of increasing the Hilbert space with auxiliary degrees of freedom. In order to retrieve the l ...

VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF2023

Self-correcting quantum many-body control using reinforcement learning with tensor networks

Friederike Metz

Quantum many-body control is a central milestone en route to harnessing quantum technologies. However, the exponential growth of the Hilbert space dimension with the number of qubits makes it challenging to classically simulate quantum many-body systems an ...

NATURE PORTFOLIO2023

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

Many-body localization in a fragmented Hilbert space

Loïc Jean Pierre Herviou

We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than t ...

2021

A kernel‐based change detection method to map shifts in phytoplankton communities measured by flow cytometry

Automated, ship-board flow cytometers provide high-resolution maps of phytoplankton composition over large swaths of the world's oceans. They therefore pave the way for understanding how environmental conditions shape community structure. Identification of ...

2021

Electromagnetic waves under nonstationary conditions, the connection with parity-time symmetry and studies on resonant systems

Theodoros Koutserimpas

In this thesis, the electromagnetic wave propagation is studied in nonstationary-medium scenarios. The electromagnetic fields under material time-modulation are shown to conserve their momentum but not their energy. The mathematical foundations and analysi ...

EPFL2021

Convergences of Regularized Algorithms and Stochastic Gradient Methods with Random Projections

Volkan Cevher, Junhong Lin

We study the least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space as a special case. We rst investigate regularized algorithms adapted to a projection operator on a closed subspace ...

2020

Frequency domain theory for functional time series: Variance decomposition and an invariance principle

Neda Mohammadi Jouzdani

This paper is concerned with frequency domain theory for functional time series, which are temporally dependent sequences of functions in a Hilbert space. We consider a variance decomposition, which is more suitable for such a data structure than the varia ...

INT STATISTICAL INST2020

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Georges Samarine

The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups. In this Part II, we prove that a disjoint union ...

2019

A Generalized Representer Theorem for Hilbert Space - Valued Functions

Colin Neil Jones, Sanket Sanjay Diwale

The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space - valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a common occurrence ...

2019

DMRG investigation of constrained models: from quantum dimer and quantum loop ladders to hard-boson and Fibonacci anyon chains

Frédéric Mila, Natalia Chepiga

Motivated by the presence of Ising transitions that take place entirely in the singlet sector of frustrated spin-1/2 ladders and spin-1 chains, we study two types of effective dimer models on ladders, a quantum dimer model and a quantum loop model. Buildin ...

2019

Learning Positive Functions with Pseudo Mirror Descent

Negar Kiyavash

The nonparametric learning of positive-valued functions appears widely in machine learning, especially in the context of estimating intensity functions of point processes. Yet, existing approaches either require computing expensive projections or semidefin ...

Curran Associates, Inc.2019

Kernel methods and Model predictive approaches for Learning and Control

Sanket Sanjay Diwale

Data-driven modeling and feedback control play a vital role in several application areas ranging from robotics, control theory, manufacturing to management of assets, financial portfolios and supply chains. Many such problems in one way or another are rela ...

EPFL2019

Optimal Rates of Sketched-regularized Algorithms for Least-Squares Regression over Hilbert Spaces

Volkan Cevher, Junhong Lin

We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect to variants of n ...

ICML2018

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Volkan Cevher, Junhong Lin

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regressi ...

2020

Methodology And Convergence Rates For Functional Time Series Regression

Victor Panaretos, Tung Huy Pham

The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite-dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose inverse is by defi ...

STATISTICA SINICA2018

Fixed Points For Bounded Orbits In Hilbert Spaces

Nicolas Monod, Maxime Gheysens

Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact a-compact groups (e.g., countabl ...

2017

Representing groups against all odds

Maxime Gheysens

We investigate how probability tools can be useful to study representations of non-amenable groups. A suitable notion of "probabilistic subgroup" is proposed for locally compact groups, and is valuable to induction of representations. Nonamenable groups ad ...

EPFL2017

A generalized mountain-pass theorem: the existence of multiple critical points

Hans-Jörg Ruppen

We analyse the existence of multiple critical points for an even functional J : H -> R in the following context: the Hilbert space H can be split into an orthogonal sum H = Y circle plus Z in such a way that inf{J(u) : u is an element of Z and parallel to ...

Springer Heidelberg2016

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Daniel Kressner, André Uschmajew

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue p ...

Elsevier Science Inc2016