no code implementations • 25 Sep 2023 • Elies Gil-Fuster, Jens Eisert, Vedran Dunjko
After proving the universality of embedding quantum kernels for both shift-invariant and composition kernels, we identify the directions towards new, more exotic, and unexplored quantum kernel families, for which it still remains open whether they correspond to efficient embedding quantum kernels.
no code implementations • 20 Sep 2023 • Ryan Sweke, Erik Recio, Sofiene Jerbi, Elies Gil-Fuster, Bryce Fuller, Jens Eisert, Johannes Jakob Meyer
We build on these insights to make concrete suggestions for PQC architecture design, and to identify structures which are necessary for a regression problem to admit a potential quantum advantage via PQC based optimization.
1 code implementation • 23 Jun 2023 • Elies Gil-Fuster, Jens Eisert, Carlos Bravo-Prieto
In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models.
no code implementations • 9 May 2023 • Alexander Nietner, Marios Ioannou, Ryan Sweke, Richard Kueng, Jens Eisert, Marcel Hinsche, Jonas Haferkamp
In this work, we show that learning the output distributions of brickwork random quantum circuits is average-case hard in the statistical query model.
no code implementations • 6 Mar 2023 • Junyu Liu, Minzhao Liu, Jin-Peng Liu, Ziyu Ye, Yunfei Wang, Yuri Alexeev, Jens Eisert, Liang Jiang
Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process.
no code implementations • 26 Oct 2022 • Niklas Pirnay, Ryan Sweke, Jens Eisert, Jean-Pierre Seifert
Specifically, we (a) provide an overview of the relationships between hardness results in supervised learning and distribution learning, and (b) show that any weak pseudo-random function can be used to construct a classically hard density modelling problem.
no code implementations • 13 Oct 2022 • Junyu Liu, Frederik Wilde, Antonio Anna Mele, Liang Jiang, Jens Eisert
Saddle points constitute a crucial challenge for first-order gradient descent algorithms.
1 code implementation • 28 Sep 2022 • Frederik Wilde, Augustine Kshetrimayum, Ingo Roth, Dominik Hangleiter, Ryan Sweke, Jens Eisert
The physics of a closed quantum mechanical system is governed by its Hamiltonian.
no code implementations • 7 Jul 2022 • Marcel Hinsche, Marios Ioannou, Alexander Nietner, Jonas Haferkamp, Yihui Quek, Dominik Hangleiter, Jean-Pierre Seifert, Jens Eisert, Ryan Sweke
We first show that the generative modelling problem associated with depth $d=n^{\Omega(1)}$ local quantum circuits is hard for any learning algorithm, classical or quantum.
no code implementations • 23 Jun 2022 • Franz J. Schreiber, Jens Eisert, Johannes Jakob Meyer
In this work, we introduce the concept of a classical surrogate, a classical model which can be efficiently obtained from a trained quantum learning model and reproduces its input-output relations.
no code implementations • 12 May 2022 • Johannes Jakob Meyer, Marian Mularski, Elies Gil-Fuster, Antonio Anna Mele, Francesco Arzani, Alissa Wilms, Jens Eisert
The success of variational quantum learning models crucially depends on finding a suitable parametrization of the model that encodes an inductive bias relevant to the learning task.
no code implementations • 11 Oct 2021 • Marcel Hinsche, Marios Ioannou, Alexander Nietner, Jonas Haferkamp, Yihui Quek, Dominik Hangleiter, Jean-Pierre Seifert, Jens Eisert, Ryan Sweke
As many practical generative modelling algorithms use statistical queries -- including those for training quantum circuit Born machines -- our result is broadly applicable and strongly limits the possibility of a meaningful quantum advantage for learning the output distributions of local quantum circuits.
no code implementations • 7 Jun 2021 • Matthias C. Caro, Elies Gil-Fuster, Johannes Jakob Meyer, Jens Eisert, Ryan Sweke
However, none of these generalization bounds depend explicitly on how the classical input data is encoded into the PQC.
no code implementations • 2 Jun 2021 • Thomas Hubregtsen, Frederik Wilde, Shozab Qasim, Jens Eisert
A popular set of optimization methods work on the estimate of the gradient, obtained by means of circuit evaluations.
no code implementations • 24 Feb 2021 • Abhinav Deshpande, Arthur Mehta, Trevor Vincent, Nicolas Quesada, Marcel Hinsche, Marios Ioannou, Lars Madsen, Jonathan Lavoie, Haoyu Qi, Jens Eisert, Dominik Hangleiter, Bill Fefferman, Ish Dhand
Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS.
Quantum Physics
no code implementations • 4 Feb 2021 • Alexander Jahn, Jens Eisert
Recent progress in studies of holographic dualities, originally motivated by insights from string theory, has led to a confluence with concepts and techniques from quantum information theory.
Tensor Networks Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory
no code implementations • 28 Jul 2020 • Ryan Sweke, Jean-Pierre Seifert, Dominik Hangleiter, Jens Eisert
Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework.
no code implementations • 8 Apr 2020 • Alexander Jahn, Zoltán Zimborás, Jens Eisert
Based on these symmetries, we introduce the notion of a quasiperiodic conformal field theory (qCFT), a critical theory less restrictive than a full CFT and with characteristic multi-scale quasiperiodicity.
Tensor Networks Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory
1 code implementation • NeurIPS 2019 • Ivan Glasser, Ryan Sweke, Nicola Pancotti, Jens Eisert, Ignacio Cirac
Inspired by these developments, and the natural correspondence between tensor networks and probabilistic graphical models, we provide a rigorous analysis of the expressive power of various tensor-network factorizations of discrete multivariate probability distributions.
no code implementations • 2 Oct 2019 • Ryan Sweke, Frederik Wilde, Johannes Meyer, Maria Schuld, Paul K. Faehrmann, Barthélémy Meynard-Piganeau, Jens Eisert
We formalize this notion, which allows us to show that in many relevant cases, including VQE, QAOA and certain quantum classifiers, estimating expectation values with $k$ measurement outcomes results in optimization algorithms whose convergence properties can be rigorously well understood, for any value of $k$.
1 code implementation • 8 Jul 2019 • Ivan Glasser, Ryan Sweke, Nicola Pancotti, Jens Eisert, J. Ignacio Cirac
Inspired by these developments, and the natural correspondence between tensor networks and probabilistic graphical models, we provide a rigorous analysis of the expressive power of various tensor-network factorizations of discrete multivariate probability distributions.
1 code implementation • 16 Oct 2018 • Ryan Sweke, Markus S. Kesselring, Evert P. L. van Nieuwenburg, Jens Eisert
Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation.
1 code implementation • 1 Mar 2018 • Ingo Roth, Richard Kueng, Shelby Kimmel, Yi-Kai Liu, David Gross, Jens Eisert, Martin Kliesch
For the important case of characterising multi-qubit unitary gates, we provide a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured respect to random Clifford unitaries.
Quantum Physics Information Theory Information Theory