Develop active error correction for distributed dynamic-circuit primitives

Develop a systematic active-error-correction treatment for the distribute–collapse framework, including correction strategies for non-Clifford controlled-U operations, rather than discarding shots flagged by the error-detection checks.

Background

The framework developed in the paper detects fusion-measurement, readout, and ancilla bit-flip errors by postselecting on consistent check outcomes. Its current implementation discards flagged measurement shots, converting some physical infidelity into a sampling overhead.

The conclusion identifies active correction as the next unresolved direction. Potential approaches include majority voting among redundant checks and more complete decoding of the underlying error. Although correction is straightforward at the circuit-structure level for Clifford controlled-U operations, a systematic treatment—especially for non-Clifford controlled-U—has not been provided.