https://arxiv.org/abs/2209.09267How can one learn the errors of a device and protect computations against them?

Quantum computers make errors many orders of magnitude more often than ordinary computers: Gate error rates of order one in a thousand accumulate rapidly over the many operations required for useful quantum computations.

The idea of quantum error correction is to address this problem by encoding logical information redundantly across many physical qubits. Repeated syndrome measurements (the equivalent of parity checks for classical linear codes) yield information about the errors that have occurred without revealing, and thereby destroying, the logical information itself.
A decoder then uses these syndrome data to infer (and correct) likely errors.
Decoders use knowledge of the machine's noise characteristics to decide which error patterns are more likely than others. The quality of the noise information therefore directly affects the decoding performance.

We have developed methods to extract this noise information directly from the syndrome data generated by a fault-tolerant quantum computer during operation, allowing us to characterize the device at run time and without the need for separate calibration experiments.
Our results establish conditions under which the physical error rates are identifiable from these syndrome statistics and provide methods to estimate them from these data.
We have also extended this approach to the logical level, identifying conditions under which the logical Pauli channel can be inferred from the same syndrome measurements.

We work on

complexity and realistic noise models: Studying how difficult these estimation tasks are computationally, and extending them beyond idealized noise assumptions, including circuit-level noise, correlations, and model mismatch.

This work is closely connected to the development of practical fault-tolerant quantum computing. Within the PIFTQC project (Programming Interface for Fault-Tolerant Quantum Computation), we investigate how these estimation methods can be integrated into tools for future fault-tolerant quantum computers.

Selected results

• From syndrome data to logical error information
  Syndrome measurements are usually interpreted as information about physical errors. We showed that, under suitable conditions, they contain enough information to reconstruct the logical Pauli channel - even when the underlying physical noise itself is not identifiable.
  Wagner, Kampermann, Bruß, Kliesch, “Learning logical Pauli noise in quantum error correction”, Phys. Rev. Lett. 130, 200601 (2023), [arXiv:2209.09267], presented as a talk at TQC 2023, Aveiro.
• What syndromes do and do not tell you
  We establish which physical Pauli error rates are identifiable from syndrome statistics alone, clarifying what can be learned during a running computation and what remains hidden without additional experiments.
  Wagner, Kampermann, Bruß, Kliesch, “Pauli channels can be estimated from syndrome measurements in quantum error correction”, Quantum 6, 809 (2022), [arXiv:2107.14252], presented as a talk at TQC 2023, Aveiro.