Dagstuhl-Seminar 25382
Quantum Error Correction Meets ZX-Calculus
( 14. Sep – 19. Sep, 2025 )
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Organisatoren
- Miriam Backens (INRIA Nancy - Grand-Est Research Center, FR)
- Aleks Kissinger (University of Oxford, GB)
- John van de Wetering (University of Amsterdam, NL)
- Michael Vasmer (INRIA - Paris, FR)
Kontakt
- Marsha Kleinbauer (für wissenschaftliche Fragen)
- Susanne Bach-Bernhard (für administrative Fragen)
Gemeinsame Dokumente
- Dagstuhl Materials Page (Use personal credentials as created in DOOR to log in)
Impacts
- SpiderCat : Optimal Fault-Tolerant Cat State Preparation - Khesin, Andrey Boris; Li, Sarah Meng; Poor, Boldizsar; Rodatz, Benjamin; Wetering, John van de; Yeung, Richie - Cornell University : arXiv.org, 2026. - 45 pp..
- Fault Tolerance by Construction - Rodatz, Benjamin; Poór, Boldizsár; Kissinger, Aleks - Cornell University : arXiv.org, 2026. - 59 S..
Seminar Topics
To achieve the transformational use cases of quantum computers, quantum error correction (QEC) must be used to protect delicate quantum information by encoding logical quantum bits across many physical qubits. Fault-tolerant logical gates are then used to process the encoded information reliably and execute quantum algorithms. This, however, comes with a large resource overhead. To this end, extensive research has been carried out to study QEC and optimise fault-tolerant quantum computation.
The ZX-calculus is a graphical language for reasoning about quantum computations. It can express computations in different models, such as quantum circuits or the one-way model. It is complete, in the sense that any true equality between diagrams can be derived entirely graphically. Over the past decade, the ZX-calculus has been used to optimise quantum computations and map logical circuits to hardware architectures.
Initial steps have already been taken in applying ZX-calculus to quantum error correction and fault tolerance, but the two communities thus far have remained mostly separate. In this Dagstuhl Seminar 25382 “Quantum Error Correction Meets ZX-Calculus”, we share knowledge and foster collaboration between experts from both communities. Below lists the main topics that have been discussed.
The ZX-calculus and mainstream fault-tolerant quantum computation: How do ZXbased methods compare to and/or complement the techniques and representations used in the larger community to study diverse quantum error-correcting codes such as colour codes, Floquet codes, bicycle codes, and quantum low-density parity check codes? How can the ZX-calculus be used to improve fault-tolerant quantum compilation and help solve open problems in developing quantum error-correcting codes? For example, can we use the ZX-calculus to analyze various fault-tolerant protocols, design more efficient fault-tolerant compilation strategies, and connect different frameworks for dynamical codes?
Quantum error correction beyond static codes: Building on recent work about Floquet codes and the spacetime frameworks for QEC, as well as insights from measurement-based quantum computing, what dynamical protocols can we develop that go beyond the state-of-the-art? For example, can we optimise Floquetification procedures with respect to qubit and gate count, qubit connectivity, and number of measurement cycles?
The ZX-calculus and error correction beyond qubits: Error-correcting codes based on qudits or bosons have advantages over standard qubit-based codes. What new protocols for quantum error-correcting codes can we develop by leveraging the ZX-calculi for qudits or bosonic modes as a unified language? For example, can we use the ZX-calculus for bosonic modes to derive improved protocols for preparing resource states such as Gottesman-Kitaev-Preskill states and cluster state fragments?
By bringing together researchers and industry practitioners to discuss these challenges in small groups, our aim was to bridge the ZX-calculus and QEC communities and foster collaborative efforts toward advancing fault-tolerant quantum computation. Several groups generated promising insights and ideas with the potential to develop into strong projects, and we look forward to seeing how these unfold in the coming years.
Seminar Program
This Dagstuhl Seminar 25382 “Quantum Error Correction Meets ZX-Calculus” brought together researchers from quantum error correction, ZX calculus, and fault-tolerant quantum computing (FTQC) to explore new synergies between graph-theoretical methods and emerging FTQC frameworks. Over the course of five days, the program combined tutorials, structured discussions, and collaborative breakout sessions to develop shared understanding and identify promising research directions.
The seminar opened with in-depth tutorials on quantum error correction through the lens of ZX-calculus and on error detection in Clifford protocols, establishing a common technical foundation for participants. Subsequent sessions expanded the scope to higher-dimensional quantum systems, fault-tolerance-by-construction techniques, and decoding approaches for qLDPC codes. These tutorials sparked active discussions and shaped the formation of working groups.
A central component of the seminar was the daily cycle of brainstorming, progress reporting, and regrouping. Participants identified key open questions, self-organized into focused teams, and iteratively refined problem statements across the week. This structure fostered cross-disciplinary collaboration, allowing ideas developed in earlier tutorials to inform concrete research tasks. Group activities, including a mid-week hike, further strengthened informal communication and collaboration within the community.
By the end of the seminar, the working groups had narrowed down several directions for ongoing research, including improved interfaces between ZX-based reasoning and errorcorrection formalisms, as well as methodologies for constructing fault-tolerant protocols via compositional or automated tools. The momentum built during the seminar is expected to carry forward, fostering collaboration between previously separate research areas and supporting the development of future joint projects.
Creative Commons BY 4.0
Miriam Backens, Aleks Kissinger, John van de Wetering, and Michael Vasmer
To achieve the transformational use-cases of quantum computers, quantum error correction (QEC) must be used to protect delicate quantum information by encoding logical quantum bits across many physical qubits. Fault-tolerant logical gates are then used to process the encoded information reliably and execute quantum algorithms. This, however, comes with a large resource overhead. To this end, extensive research has been carried out to study QEC and optimise fault-tolerant quantum computation.
The ZX-calculus is a graphical language for reasoning about quantum computations. It can express computations in different models, such as quantum circuits or the one-way model. It is complete, in the sense that any true equality between diagrams can be derived entirely graphically. Over the past decade, the ZX-calculus has been used to optimise quantum computations and map logical circuits to hardware architectures.
Initial steps have already been taken in applying ZX-calculus to quantum error correction and fault tolerance, but the two communities thus far have remained mostly separate. The aim of this seminar is to share knowledge and foster collaboration between experts from both communities. Topics to be discussed include (but are not limited to):
- The ZX-calculus and mainstream fault-tolerant quantum computation: How do ZX-based methods compare to and/or complement the techniques and representations used in the larger community to study diverse quantum error-correcting codes such as colour codes, Floquet codes, bicycle codes, and quantum low-density parity check codes? How can the ZX-calculus be used to improve fault-tolerant quantum compilation and help solve open problems in developing quantum error-correcting codes? For example, can we use the ZX-calculus to analyze various fault-tolerant protocols, design more efficient code-deformation-based compilation strategies, and connect different frameworks for dynamical codes?
- Quantum error correction beyond static codes: Building on recent work about Floquet codes and the spacetime frameworks for QEC, as well as insights from measurement-based quantum computing, what dynamical protocols can we develop that go beyond the state-of-the-art? For example, can we optimise Floquetification procedures with respect to qubit and gate count, qubit connectivity, and number of measurement cycles?
- The ZX-calculus and error correction beyond qubits: Error-correcting codes based on qudits or bosons have advantages over standard qubit-based codes. What new protocols for quantum error-correcting codes can we develop by leveraging the ZX-calculi for qudits or bosonic modes as a unified language? For example, can we use the ZX-calculus for bosonic modes to derive improved protocols for preparing resource states such as Gottesman-Kitaev-Preskill states and cluster state fragments?
By bringing together researchers and industry practitioners, we aim to bridge the ZX-calculus and QEC communities, building a shared language to tackle key challenges in fault-tolerant quantum computation.
Miriam Backens, Aleks Kissinger, John van de Wetering, and Michael Vasmer
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- Miriam Backens (INRIA Nancy - Grand-Est Research Center, FR) [dblp]
- Simon Burton (Quantinuum - Cambridge, GB)
- Ophelia Crawford (Riverlane - Cambridge, GB)
- Alexander Frei (University of Waterloo, CA)
- Linnea Grans-Samuelsson (University of Oxford, GB)
- Mackenzie Hooper Shaw (TU Delft, NL)
- Jiaxin Huang (University of Hong Kong, HK) [dblp]
- Andrey Khesin (University of Oxford, GB) [dblp]
- Aleks Kissinger (University of Oxford, GB) [dblp]
- Sarah Meng Li (University of Amsterdam, NL) [dblp]
- Julio Carlos Magdalena de la Fuente (FU Berlin, DE) [dblp]
- Alexandra Moylett (Nu Quantum - Cambridge, GB)
- Ewan Murphy (University of Waterloo, CA) [dblp]
- Hironari Nagayoshi (University of Tokyo, JP)
- Armanda O. Quintavalle (FU Berlin, DE) [dblp]
- Simon Perdrix (LORIA - Nancy, FR) [dblp]
- Arthur Pesah (University College London, GB) [dblp]
- Clément Poirson (INRIA - Paris, FR)
- Benjamin Rodatz (University of Oxford, GB)
- Joschka Roffe (University of Edinburgh, GB) [dblp]
- Thomas Scruby (Okinawa Institute of Science and Technology, JP) [dblp]
- Peter Selinger (Dalhousie University - Halifax, CA) [dblp]
- Alex Townsend-Teague (FU Berlin, DE) [dblp]
- John van de Wetering (University of Amsterdam, NL) [dblp]
- Michael Vasmer (INRIA - Paris, FR) [dblp]
- Christophe Vuillot (Alice & Bob - Paris, FR) [dblp]
- Lia Yeh (University of Oxford, GB) [dblp]
- Sascha Zakaib-Bernier (University of Waterloo, CA)
Klassifikation
- Emerging Technologies
- Information Theory
- Logic in Computer Science
Schlagworte
- Quantum Computing
- Quantum Error Correction
- Fault-tolerance
- ZX-calculus
