no code implementations • 5 Mar 2024 • Andreas Bluhm, Matthias C. Caro, Aadil Oufkir
Our work initiates the study of property testing for quantum Hamiltonians, demonstrating that a broad class of Hamiltonian properties is efficiently testable even with limited quantum capabilities, and positioning Hamiltonian testing as an independent area of research alongside Hamiltonian learning.
no code implementations • 30 Oct 2023 • Haimeng Zhao, Laura Lewis, Ishaan Kannan, Yihui Quek, Hsin-Yuan Huang, Matthias C. Caro
While quantum state tomography is notoriously hard, most states hold little interest to practically-minded tomographers.
no code implementations • 8 Jun 2023 • Matthias C. Caro, Marcel Hinsche, Marios Ioannou, Alexander Nietner, Ryan Sweke
Finally, we showcase two general scenarios in learning and verification in which quantum mixture-of-superpositions examples do not lead to sample complexity improvements over classical data.
no code implementations • 22 Mar 2023 • Sofiene Jerbi, Joe Gibbs, Manuel S. Rudolph, Matthias C. Caro, Patrick J. Coles, Hsin-Yuan Huang, Zoë Holmes
Quantum process learning is emerging as an important tool to study quantum systems.
no code implementations • 8 Dec 2022 • Matthias C. Caro
We show that a quantum memory allows to efficiently solve the following tasks: (a) learning the Pauli transfer matrix of an arbitrary $\mathcal{N}$, (b) predicting expectation values of bounded Pauli-sparse observables measured on the output of an arbitrary $\mathcal{N}$ upon input of a Pauli-sparse state, and (c) predicting expectation values of arbitrary bounded observables measured on the output of an unknown $\mathcal{N}$ with sparse Pauli transfer matrix upon input of an arbitrary state.
no code implementations • 21 Apr 2022 • Joe Gibbs, Zoë Holmes, Matthias C. Caro, Nicholas Ezzell, Hsin-Yuan Huang, Lukasz Cincio, Andrew T. Sornborger, Patrick J. Coles
Much attention has been paid to dynamical simulation and quantum machine learning (QML) independently as applications for quantum advantage, while the possibility of using QML to enhance dynamical simulations has not been thoroughly investigated.
no code implementations • 21 Apr 2022 • Matthias C. Caro, Hsin-Yuan Huang, Nicholas Ezzell, Joe Gibbs, Andrew T. Sornborger, Lukasz Cincio, Patrick J. Coles, Zoë Holmes
However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution.
no code implementations • 9 Nov 2021 • Matthias C. Caro, Hsin-Yuan Huang, M. Cerezo, Kunal Sharma, Andrew Sornborger, Lukasz Cincio, Patrick J. Coles
Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i. e., generalizing).
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 • Matthias C. Caro
Our work shows that undecidability appears in the theoretical foundations of artificial intelligence: There is no one-size-fits-all algorithm for deciding whether a machine learning model can be successful.
no code implementations • 10 Jun 2020 • Matthias C. Caro
In particular, we see that the sample complexity is the same as in the classical binary classification task w. r. t.
no code implementations • 4 Feb 2020 • Matthias C. Caro, Ishaun Datta
We characterize the expressive power of quantum circuits with the pseudo-dimension, a measure of complexity for probabilistic concept classes.
no code implementations • 23 Feb 2019 • Matthias C. Caro
With our analysis we contribute to a more quantitative understanding of the power and limitations of quantum training data for learning classical functions.