Understanding the effects of leakage in superconducting quantum error detection circuits

TL;DR

This paper investigates how leakage outside the computational subspace affects superconducting quantum error detection circuits, revealing that leakage causes destructive errors and highlighting the need for improved protocols.

Contribution

It provides a detailed simulation and analytic model of leakage effects in superconducting qubit error detection, emphasizing the importance of addressing leakage for optimal quantum error correction.

Findings

Leakage causes destructive errors in error detection schemes

Simulation and analytic models closely match, validating the analysis

Leakage signatures can be identified in readout statistics

Abstract

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