  Protecting quantum information from errors is essential for large-scale
quantum computation. Quantum error correction (QEC) encodes information in
entangled states of many qubits, and performs parity measurements to identify
errors without destroying the encoded information. However, traditional QEC
cannot handle leakage from the qubit computational space. Leakage affects
leading experimental platforms, based on trapped ions and superconducting
circuits, which use effective qubits within many-level physical systems. We
investigate how two-transmon entangled states evolve under repeated parity
measurements, and demonstrate the use of hidden Markov models to detect leakage
using only the record of parity measurement outcomes required for QEC. We show
the stabilization of Bell states over up to 26 parity measurements by
mitigating leakage using postselection, and correcting qubit errors using
Pauli-frame transformations. Our leakage identification method is
computationally efficient and thus compatible with real-time leakage tracking
and correction in larger quantum processors.

Quantum Physics