Using Detector Likelihood for Benchmarking Quantum Error Correction

The behavior of real quantum hardware differs strongly from the simple error models typically used when simulating quantum error correction. Error processes are far more complex than simple depolarizing noise applied to single gates, and error rates can vary greatly between different qubits, and at different points in the circuit. Nevertheless, it would be useful to distill all this complicated behavior down to a single parameter: an effective error rate for a simple uniform error model. Here we show that this can be done by means of the average detector likelihood, which quantifies the rate at which error detection events occur. We show that this parameter is predictive of the overall code performance for two variants of the surface code: Floquet codes and the 3-CX surface code. This is then used to define an effective error rate at which simulations for a simple uniform noise model result in the same average detector likelihood, as well as a good prediction of the logical error rate.