# Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements

## TL;DR

This paper demonstrates a method to detect and mitigate leakage errors in entangled qubit states during quantum error correction, using repeated parity measurements and hidden Markov models, enhancing the reliability of quantum information processing.

## Contribution

It introduces a computationally efficient leakage detection technique based on hidden Markov models, compatible with real-time quantum error correction in larger systems.

## Key findings

- Leakage can be detected using parity measurement records.
- Bell states stabilized over 26 parity measurements with leakage mitigation.
- Leakage identification is suitable for real-time quantum error correction.

## Abstract

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.