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.

Creative Commons BY 4.0

Miriam Backens, Aleks Kissinger, John van de Wetering, and Michael Vasmer