Superconducting qubits, while promising for scalability and long coherencetimes, contain more than two energy levels, and therefore are susceptible toerrors generated by the leakage of population outside of the computationalsubspace. Such leakage errors constitute a prominent roadblock towardsfault-tolerant quantum computing (FTQC) with superconducting qubits. FTQC usingtopological codes is based on sequential measurements of multiqubit stabilizeroperators. Here, we first propose a leakage-resilient procedure to performrepetitive measurements of multiqubit stabilizer operators, and then use thisscheme as an ingredient to develop a leakage-resilient approach for surfacecode quantum error correction with superconducting circuits. Our protocol isbased on swap operations between data and ancilla qubits at the end of everycycle, requiring read-out and reset operations on every physical qubit in thesystem, and thereby preventing persistent leakage errors from occurring.
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