Open Quantum Neural Networks: from Fundamental Concepts to Implementations with Atoms and Photons

Project Information

QNets

Grant agreement ID: 804247

DOI

10.3030/804247

Project closed

EC signature date 4 September 2018

Start date 1 October 2019

End date 30 September 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 486 439,00

EU contribution

€ 1 486 439,00

Coordinated by

FORSCHUNGSZENTRUM JULICH GMBH
Germany

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (36)

Measurement-Free Quantum Error Correction Optimized for Biased Noise

Author(s): Katharina Brechtelsbauer, Friederike Butt, David F. Locher, Santiago Higuera Quintero, Sebastian Weber, Markus Müller, Hans Peter Büchler
Published in: PRX Quantum, Issue 6, 2025, ISSN 2691-3399
Publisher: American Physical Society (APS)
DOI: 10.1103/wsnf-prwl

Fundamental Thresholds for Computational and Erasure Errors via the Coherent Information

Author(s): Luis Colmenarez, Seyong Kim, Markus Müller
Published in: PRX Quantum, Issue 6, 2025, ISSN 2691-3399
Publisher: American Physical Society (APS)
DOI: 10.1103/d8rx-srpn

Experimental Bayesian Calibration of Trapped-Ion Entangling Operations

Author(s): Lukas Gerster, Fernando Martínez-García ,Pavel Hrmo , Martin W. van Mourik ,Benjamin Wilhelm, Davide Vodola, Markus Müller, Rainer Blatt, Philipp Schindler, and Thomas Monz
Published in: PRX Quantum, 2022, ISSN 2691-3399
Publisher: American Physical Society
DOI: 10.1103/prxquantum.3.020350

On the Interpretability of Neural Network Decoders

Author(s): Lukas Bödeker, Luc J. B. Kusters, Markus Müller
Published in: Advanced Quantum Technologies, Issue 8, 2025, ISSN 2511-9044
Publisher: Wiley
DOI: 10.1002/qute.202500158

Optimal storage capacity of quantum Hopfield neural networks

Author(s): Lukas Bödeker; Eliana Fiorelli; Markus Müller
Published in: Physical review / Physics education research, Issue 5, 2022, Page(s) 023074, ISSN 2643-1564
Publisher: American Physical Society
DOI: 10.1103/physrevresearch.5.023074

Compressed-sensing Lindbladian quantum tomography with trapped ions

Author(s): Dmitrii Dobrynin, Lorenzo Cardarelli, Markus Müller, Alejandro Bermudez
Published in: Quantum Science and Technology, Issue 10, 2025, Page(s) 045041, ISSN 2058-9565
Publisher: IOP Publishing
DOI: 10.1088/2058-9565/ae0363

Accessing the topological Mott insulator in cold atom quantum simulators with realistic Rydberg dressing

Author(s): Lorenzo Cardarelli; Sergi Julià-Farré; Maciej Lewenstein; Alexandre Dauphin; Markus Müller
Published in: Quantum science and technology, Issue 8(2), 2023, Page(s) 025018, ISSN 2058-9565
Publisher: IOP Pubishing
DOI: 10.1088/2058-9565/acbc45

Demonstration of fault-tolerant universal quantum gate operations

Author(s): Lukas Postler; Sascha Heuβen; Ivan Pogorelov; Manuel Rispler; Thomas Feldker; Michael Meth; Christian D. Marciniak; Roman Stricker; Martin Ringbauer; Rainer Blatt; Philipp Schindler; Markus Müller; Thomas Monz
Published in: Nature, Issue 605(7911), 2022, Page(s) 675 - 680, ISSN 1476-4687
Publisher: Nature Potfolio
DOI: 10.1038/s41586-022-04721-1

Characterizing Quantum Instruments: From Nondemolition Measurements to Quantum Error Correction

Author(s): Roman Stricker; Davide Vodola; Alexander Erhard; Lukas Postler; Michael Meth; Martin Ringbauer; Philipp Schindler; Rainer Blatt; Markus Müller; Thomas Monz
Published in: PRX Quantum, Issue 2, 2022, ISSN 2691-3399
Publisher: American Physical Society
DOI: 10.18154/rwth-2022-08526

Optimized measurement-free and fault-tolerant quantum error correction for neutral atoms

Author(s): Stefano Veroni, Markus Müller, Giacomo Giudice
Published in: Physical Review Research, Issue 6, 2024, ISSN 2643-1564
Publisher: American Physical Society (APS)
DOI: 10.1103/physrevresearch.6.043253

Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law

Author(s): Thomas Botzung; Thomas Botzung; Sebastian Diehl; Markus Müller; Markus Müller
Published in: Phys. Rev. B, Issue 104, 184422, 2021, ISSN 2469-9950
Publisher: American Institute of Physics
DOI: 10.1103/physrevb.104.184422

Taming Thiemann’s Hamiltonian constraint in canonical loop quantum gravity: Reversibility, eigenstates, and graph-change analysis

Author(s): T. L. M. Guedes, G. A. Mena Marugán, M. Müller, F. Vidotto
Published in: Physical Review D, Issue 112, 2025, ISSN 2470-0010
Publisher: American Physical Society (APS)
DOI: 10.1103/hjdk-kdhk

Quantum Error Correction with Quantum Autoencoders

Author(s): David F. Locher; Lorenzo Cardarelli; Markus Müller
Published in: Quantum, Issue 7, 2023, Page(s) 942, ISSN 2521-327X
Publisher: Association for the Promotion of Open Access Publishing in the Quantum Sciences
DOI: 10.22331/q-2023-03-09-942

Demonstration of Two-Dimensional Connectivity for a Scalable Error-Corrected Ion-Trap Quantum Processor Architecture

Author(s): M. Valentini, M. W. van Mourik, F. Butt, J. Wahl, M. Dietl, M. Pfeifer, F. Anmasser, Y. Colombe, C. Rössler, P. C. Holz, R. Blatt, A. Bermudez, M. Müller, T. Monz, P. Schindler
Published in: Physical Review X, Issue 15, 2025, ISSN 2160-3308
Publisher: American Physical Society
DOI: 10.1103/b9s1-6r44

Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning

Author(s): Remmy Zen, Jan Olle, Luis Colmenarez, Matteo Puviani, Markus Müller, Florian Marquardt
Published in: Physical Review X, Issue 15, 2025, ISSN 2160-3308
Publisher: American Physical Society
DOI: 10.1103/gqpr-dgz7

Fault-Tolerant Code Switching Protocols for Near-Term Quantum Processors

Author(s): Butt, Friederike; Heußen, Sascha; Rispler, Manuel; Müller, Markus
Published in: PRX QUANTUM, Issue 5, 2024, Page(s) 020345, ISSN 2691-3399
Publisher: American Physical Society
DOI: 10.1103/prxquantum.5.020345

Self-Trapped Polarons and Topological Defects in a Topological Mott Insulator

Author(s): Sergi Julià-Farré, Markus Müller, Maciej Lewenstein, Alexandre Dauphin
Published in: Physical Review Letters, Issue 125/24, 2020, Page(s) 240601, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/physrevlett.125.240601

Topological stripe state in an extended Fermi-Hubbard model

Author(s): Sergi Julià-Farré; Lorenzo Cardarelli; Maciej Lewenstein; Markus Müller; Alexandre Dauphin
Published in: Physical review B, Issue 109, 2024, Page(s) 075109, ISSN 2469-9969
Publisher: American Physical Society}
DOI: 10.1103/physrevb.109.075109

Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates

Author(s): Josias Old, Stephan Tasler, Michael J. Hartmann, Markus Müller
Published in: Physical Review Letters, Issue 135, 2025, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/sblg-fbq4

Efficient and Robust Certification of Genuine Multipartite Entanglement in Noisy Quantum Error Correction Circuits

Author(s): Andrea Rodriguez-Blanco, Alejandro Bermudez, Markus Müller, Farid Shahandeh
Published in: PRX Quantum, Issue 2/2, 2021, Page(s) 020304, ISSN 2691-3399
Publisher: American Physical Society (APS)
DOI: 10.1103/prxquantum.2.020304

"Long-Range Ising Interactions Mediated by<mml:math xmlns:mml=""http://www.w3.org/1998/Math/MathML"" display=""inline"" overflow=""scroll""><mml:mi>λ</mml:mi><mml:msup><mml:mi>ϕ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math>Fields: Probing the Renormalization of Sound in Crystals of Trapped Ions"

Author(s): G. Martín-Vázquez, G. Aarts, M. Müller, A. Bermudez
Published in: PRX Quantum, Issue 3, 2023, ISSN 2691-3399
Publisher: American Physical Society (APS)
DOI: 10.1103/prxquantum.3.020352

Strategies for a practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers

Author(s): Heußen, Sascha; Postler, Lukas; Rispler, Manuel; Pogorelov, Ivan; Marciniak, Christian D.; Monz, Thomas; Schindler, Philipp; Müller, Markus
Published in: Physical Review A, Issue 107, 2023, Page(s) 042422, ISSN 1094-1622
Publisher: American Physical Society
DOI: 10.1103/physreva.107.042422

Computing the Graph-Changing Dynamics of Loop Quantum Gravity

Author(s): Thiago L. M. Guedes, Guillermo A. Mena Marugán, Francesca Vidotto, Markus Müller
Published in: Universe, Issue 11, 2025, Page(s) 387, ISSN 2218-1997
Publisher: MDPI AG
DOI: 10.3390/universe11120387

Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application

Author(s): Eliana Fiorelli; Markus Müller; Igor Lesanovsky; Federico Carollo
Published in: New Journal of Physics, Issue 25 (8), 2023, Page(s) 083010, ISSN 1367-2630
Publisher: Institute of Physics Publishing
DOI: 10.1088/1367-2630/ace470

Automated Synthesis of Fault-Tolerant State Preparation Circuits for Quantum Error-Correction Codes

Author(s): Tom Peham, Ludwig Schmid, Lucas Berent, Markus Müller, Robert Wille
Published in: PRX Quantum, Issue 6, 2025, ISSN 2691-3399
Publisher: American Physical Society (APS)
DOI: 10.1103/prxquantum.6.020330

Lift-connected surface codes

Author(s): Josias Old, Manuel Rispler, Markus Müller
Published in: Quantum Science and Technology, Issue 9, 2024, Page(s) 045012, ISSN 2058-9565
Publisher: IOP Publishing
DOI: 10.1088/2058-9565/ad5eb6

Coherent information as a mixed-state topological order parameter of fermions

Author(s): Ze-Min Huang, Luis Colmenarez, Markus Müller, Sebastian Diehl
Published in: Physical Review Research, Issue 7, 2025, ISSN 2643-1564
Publisher: American Physical Society (APS)
DOI: 10.1103/fx56-8nvy

Two-qubit gate protocols with microwave-dressed Rydberg ions in a linear Paul trap

Author(s): Joseph W P Wilkinson, Katrin Bolsmann, Thiago L M Guedes, Markus Müller, Igor Lesanovsky
Published in: New Journal of Physics, Issue 27, 2025, Page(s) 064502, ISSN 1367-2630
Publisher: Institute of Physics Publishing
DOI: 10.1088/1367-2630/add494

Phase diagram of quantum generalized Potts-Hopfield neural networks

Author(s): Eliana Fiorelli; Igor Lesanovsky; Markus Müller
Published in: New Journal of Physics, Issue 24, 033012, 2022, ISSN 1367-2630
Publisher: Institute of Physics Publishing
DOI: 10.1088/1367-2630/ac5490

Fault-tolerant parity readout on a shuttling-based trapped-ion quantum computer

Author(s): J. Hilder; D. Pijn; O. Onishchenko; A. Stahl; M. Orth; B. Lekitsch; A. Rodriguez-Blanco; M. Müller; F. Schmidt-Kaler; U. G. Poschinger
Published in: Physical Review X, Issue 12, 011032, 2022, ISSN 2160-3308
Publisher: American Physical Society
DOI: 10.1103/physrevx.12.011032

Dynamical subset sampling of quantum error-correcting protocols

Author(s): Sascha Heußen; Don Winter; Manuel Rispler; Markus Müller
Published in: Physical Review Research, Issue 6, 2024, Page(s) 013177, ISSN 2643-1564
Publisher: American Physical Society
DOI: 10.1103/physrevresearch.6.013177

Bosonic quantum error correction with neutral atoms in optical dipole traps

Author(s): Leon H. Bohnmann, David F. Locher, Johannes Zeiher, Markus Müller
Published in: Physical Review A, Issue 111, 2025, ISSN 2469-9926
Publisher: American Physical Society (APS)
DOI: 10.1103/physreva.111.022432

Long-range Ising interactions mediated by $λϕ^4$ fields: probing the renormalisation of sound in crystals of trapped ions

Author(s): Martín-Vázquez, G.; Aarts, G.; Müller, Markus; Bermudez, A.
Published in: PRX Quantum, Issue 3(2), 2022, Page(s) 020352, ISSN 2691-3399
Publisher: American Physical Society
DOI: 10.48550/arxiv.2105.06886

Scalable characterization of localizable entanglement in noisy topological quantum codes

Author(s): David Amaro, Markus Müller, Amit Kumar Pal
Published in: New Journal of Physics, Issue 22/5, 2020, Page(s) 053038, ISSN 1367-2630
Publisher: Institute of Physics Publishing
DOI: 10.1088/1367-2630/ab84b3

Lindblad-like quantum tomography for non-Markovian quantum dynamical maps

Author(s): S. Varona, M. Müller, A. Bermudez
Published in: npj Quantum Information, Issue 11, 2025, ISSN 2056-6387
Publisher: Springer Science and Business Media LLC
DOI: 10.1038/s41534-025-01044-7

Measurement-Free Fault-Tolerant Quantum Error Correction in Near-Term Devices

Author(s): Heußen, Sascha; Locher, David; Müller, Markus
Published in: PRX Quantum, Issue 5, 2024, Page(s) 010333, ISSN 2691-3399
Publisher: American Physical Society
DOI: 10.1103/prxquantum.5.010333

Non-peer reviewed articles (3)

Demonstration of Fault-Tolerant Steane Quantum Error Correction

Author(s): Lukas Postler, Friederike Butt, Ivan Pogorelov, Christian D. Marciniak, Sascha Heußen, Rainer Blatt, Philipp Schindler, Manuel Rispler, Markus Müller, Thomas Monz
Published in: PRX Quantum, Issue 5, 2025, ISSN 2691-3399
Publisher: American Physical Society (APS)
DOI: 10.1103/prxquantum.5.030326

Robustness and measurement-induced percolation of the surface code

Author(s): T Botzung, M Buchhold, S Diehl, M Müller
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 58, 2025, Page(s) 205304, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/add2e3

Accurate optimal quantum error correction thresholds from coherent information

Author(s): Luis Colmenarez, Ze-Min Huang, Sebastian Diehl, Markus Müller
Published in: Physical Review Research, Issue 6, 2024, ISSN 2643-1564
Publisher: American Physical Society (APS)
DOI: 10.1103/physrevresearch.6.l042014

Other (5)

The random coupled-plaquette gauge model and the surface code under circuit-level noise

Author(s): Manuel Rispler, Davide Vodola, Markus Müller, Seyong Kim
Published in: 2024
Publisher: arXiv

Optical time-domain quantum state tomography on a subcycle scale

Author(s): Hubenschmid, Emanuel; Guedes, Thiago L. M.; Burkard, Guido
Published in: arXiv, Issue 2307, 2023, Page(s) 13090
Publisher: Cornell Tech
DOI: 10.48550/arxiv.2307.13090

Experimental fault-tolerant code switching

Author(s): Ivan Pogorelov, Friederike Butt, Lukas Postler, Christian D. Marciniak, Philipp Schindler, Markus Müller, Thomas Monz
Published in: 2024
Publisher: arXiv

Measurement-free, scalable and fault-tolerant universal quantum computing

Author(s): F. Butt, D. F. Locher, K. Brechtelsbauer, H. P. Büchler, and M. Müller
Published in: 2024
Publisher: arXiv

Quantum cellular automata for quantum error correction and density classification

Author(s): Guedes, Thiago L. M.; Winter, Don; Müller, Markus
Published in: https://arxiv.org/abs/2309.03608, 2023, ISSN 2331-8422
Publisher: Cornell Tech
DOI: 10.48550/arxiv.2309.03608