Decoding across transversal Clifford gates in the surface code

Understand

Transversal logical gates offer the opportunity for fast and low-noise logic, particularly when interspersed by a single round of parity check measurements of the underlying code.

• Using such circuits for the surface code requires decoding across logical gates, complicating the decoding task.
• We show how one can decode across an arbitrary sequence of transversal gates for the unrotated surface code, using a fast "logical observable" minimum-weight-perfect-matching (MWPM) based decoder, and benchmark its performance in Clifford circuits under circuit-level noise.
• We propose windowed logical observable matching decoders to address the problem of fully efficient decoding: our basic windowed decoder is computationally efficient under the restriction of quiescent (slow) resets.