Efficient Pauli noise learning in fault-tolerant Clifford circuits.

Device characterization is crucial in quantum computing. While there are many protocols for benchmarking devices before operating on actual algorithms, there is also a need for online benchmarking for both physical and logical errors on fault-tolerant circuits. We map general fault-tolerant Clifford circuits to spacetime codes and present a scheme of characterizing Pauli noise in Clifford circuits using syndrome data during active error correction. Moreover, we estimate both physical and logical fidelity in a general logical Clifford circuits and show that the logical fidelity can be efficiently estimated using the syndrome data only under the assumption of local Pauli noise. This provides a way of characterizing physical components of the device to help gate tune up, improve decoding, and verify logical circuits with no extra cost but only efficient classical processing of the syndrome data.