The last years have seen significant advances in the field of quantum technologies, consolidating the development of basic requirements for quantum computation. Protecting the quantum computation from noise and decoherence has become more topical than ever, challenging and bringing quantum error correction fairly close to the integration into practical quantum computers. However, to make such an integration viable, further innovations and advances are required in both theoretical research and engineering practice. This Dagstuhl Seminar is intended to be an interaction forum for senior and talented junior researchers, crossing boundaries between classical and quantum coding theory, and related areas of quantum technology and engineering problems. The aim is to exchange on the challenges and the toolsets that emerged in the different areas, towards creating a diverse and inclusive research network, where researchers from different domains can share ideas and knowledge, and inspire each other. Topics to be covered include:

Quantum error correction and fault tolerant quantum computation:

• Connections and interactions between classical and quantum coding theory,
• Theory and practice of topological quantum codes, quantum LDPC, and quantum Polar codes,
• Decoding aspects of topological and quantum LDPC codes,
• Non-qubit based quantum error-correcting codes, in particular variety of oscillator-based codes and Gottesman-Kitaev-Preskill codes and their concatenation with quantum stabilizer codes,
• Variety of Pauli error channels, including those derived from Clifford circuits with gate error models customized for specific hardware,
• Related unification of decoding protocols for qubit-based codes,
• Decoding using soft syndrome information, decoding in the presence of leakage errors,
• Codes and decoding algorithms for single-shot error correction,
• Subsystem codes (both on their own right and as part of fault tolerant gadgets).

From noisy intermediate scale quantum era to large-scale fault tolerance:

• Low-qubit overhead fault-tolerant schemes and demonstration of small quantum error correcting codes in noisy intermediate-scale quantum devices,
• Software implementation of quality decoders,
• Quantum hardware architectures for quantum error correction and large-scale fault tolerance,
• Optimization of quantum error correction for specific technology constraints or noise models,
• Hardware implementations and prototyping of quantum error correction decoders,
• Challenges of the integration of quantum error correction and control systems.

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Carmen Garcia Almudéver, Leonid Pryadko, Valentin Savin, and Bane Vasic