Leakage and Paralysis in Ancilla-assisted Qubit Measurement: Consequences for Topological Error Correction in Superconducting Architectures

Abstract : Although topological error-correcting codes offer a promising paradigm for fault- tolerant quantum computation, their robustness in the presence of leakage to non- computational states is unclear. Here we explore the signature and consequences of leakage errors on ancilla-assisted Pauli operator measurement in superconducting devices. We consider a realistic coupled-qutrit model and simulate the repeated measurement of a single sigma z operator. Typically, a data-qubit leakage event manifests itself by producing a noisy ancilla qubit that randomly reads /0/ or /1/ from cycle to cycle. Although the measurement operation is compromised, the presence of the leakage event is apparent and detectable. However, there is also the possibility of a less typical but more dangerous type of leakage event, where the ancilla becomes paralyzed rendering it oblivious to data-qubit errors for many consecutive measurement cycles and compromising the fault-tolerance. Certain dynamical phases associated with the entangling gate determine which type of leakage event will occur in practice. Leakage errors occur in most qubit realizations and our model and results are relevant for many stabilizer-based error correction protocols.