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The majority of quantum error detection and correction protocols assume thatthe population in a qubit does not leak outside of its computational subspace.For many existing approaches, however, the physical qubits do possess more thantwo energy levels and consequently are prone to such leakage events. Analyzingthe effects of leakage is therefore essential to devise optimal protocols forquantum gates, measurement, and error correction. In this work, we present adetailed study of leakage in a two-qubit superconducting stabilizer measurementcircuit. We simulate the repeated ancilla-assisted measurement of a single$\sigma^z$ operator for a data qubit, record the outcome at the end of eachmeasurement cycle, and explore the signature of leakage events in the obtainedreadout statistics. An analytic model is also developed that closelyapproximates the results of our numerical simulations. We find that leakageleads to destructive features in the quantum error detection scheme, makingadditional hardware and software protocols necessary.

Understanding the effects of leakage in superconducting quantum error detection circuits