Quantum circuits are inherently noisy: every component, from state preparation to two-qubit gates and measurements, can fail. The circuit-level noise model captures how such faults propagate through the circuit, producing correlated and time-dependent errors that simpler models cannot represent. These faults also corrupt the syndrome measurements, which require additional protection.

A common strategy to protect syndrome bits is to perform multiple rounds of measurements and build the Detector Error Model (DEM). The DEM is a new Tanner graph where variable nodes represent fault mechanisms and check nodes (or detectors) represent inconsistencies in measurement outcomes. An edge connects a fault to a detector if the fault flips that detector’s parity. The DEM’s structure is therefore determined jointly by the stabilizers of the quantum code and the circuit realizing them.

However, the DEM’s graph typically contains short cycles and low-degree nodes, making generic iterative decoders ineffective. In this seminar, I will demystify the connection between quantum stabilizers, circuit-level noise, and the resulting DEM, showing how the latter can be systematically constructed from a QLDPC code’s stabilizer matrix. I will discuss how different fault mechanisms alter the measured syndrome, how these effects are modeled within the DEM, and finally present an iterative decoder that achieves state-of-the-art performance with significantly reduced complexity compared to existing approaches.