*** A hardware-efficient leakage-reduction scheme for quantum error correction with superconducting transmon qubits *** 

Authors: Francesco Battistel, Boris M. Varbanov, Barbara M. Terhal
 QuTech, Delft University of Technology; JARA Institute for Quantum Information
Corresponding author: Francesco Battistel
Contact Information: battistel.fra@protonmail.com

***General Introduction***
[Additional data after peer review] This collection of datasets contains data generated in simulation for the paper at https://arxiv.org/abs/2102.08336, as well as the code used for the analysis. The code used to generate the data is available upon request to the corresponding author. This research project was made possible by the ERC grant EQEC No. 682726

***Abstract*** Leakage outside of the qubit computational subspace poses a threatening challenge to quantum error correction (QEC). We propose a scheme using two leakage-reduction units (LRUs) that mitigate these issues for a transmon-based surface code, without requiring an overhead in terms of hardware or QEC-cycle time as in previous proposals. For data qubits we consider a microwave drive to transfer leakage to the readout resonator, where it quickly decays, ensuring that this negligibly disturbs the computational states for realistic system parameters. For ancilla qubits we apply a |1⟩ ↔ |2⟩ π pulse conditioned on the measurement outcome. Using density-matrix simulations of the distance- 3 surface code we show that the average leakage lifetime is reduced to almost 1 QEC cycle, even when the LRUs are implemented with limited fidelity. Furthermore, we show that this leads to a significant reduction of the logical error rate. This LRU scheme opens the prospect for near-term scalable QEC demonstrations.

***Description of the data in this data set*** All data is provided in the netCDF format. We refer to the paper for the variable names.
The notebooks for the analysis are written in Python 3.6

- S17_raw_data_additional: results of the density-matrix simulations. Each different choice of parameters is saved in a different archive file. The title provides the essential information about the parameters changing. See coordinates of the netCDF files for the full information.
- S17_decoded_data_additional: it contains the weight matrices used for decoding, as well as the results of decoding itself. The name of the files are in direct correspondence to S17_raw_data
- Lindblad_raw_data_additional: results of the Lindblad simulations of the res-LRU. All points in the heatmaps are saved including the time evolution of the quantities of interest (some examples of which are shown in the paper). [This entirely substitutes Lindblad_raw_data]
- data_code_figures_additional: minimal data shown in the figures of the paper for quick access, as well as the code generating the figures from that.

The code for data analysis is provided in data_analysis




