Datasets for "A superconducting dual-rail cavity qubit with erasure-detected logical measurements"

Title of Dataset: Demonstrating a superconducting dual-rail cavity qubit with erasure-detected logical measurements---

Included are data shown in Figures 1-4 of the main text and Extended Data Figures 2 and 3 in the Methods.Data was collected by running quantum programs on hardware deployed at Quantum Circuits, Inc. The results of these experiments are decoded and assigned an appropriate label (discussed below and in the manuscript). We provide various levels of processing: number of counts, fraction of counts, and the logical assignment. Full labeled shot-by-shot outcomes can be provided upon request.

## Description of the data and file structure

Description of column labels- xs: sweep variable (if applicable)- Counts:  - 00_counts, 01_counts, 10_counts, 11_counts: Number of runs with outcome labeled "00", "01", "10", "11", respectively  - A_counts: Number of runs with outcome labeled as ambiguous outcome  - FSP_counts: Number of runs with outcome labeled as a failed state preparation  - all_shots: Total number of runs  - total_counts: Number of runs with a successful state preparation (e.g. all_shots - B_counts)- Outcome fraction  - 00, 01, 10, 11, A, FSP: Fraction of counts normalized by total_counts  - 00_err, 01_err, 10_err, 11_err, A_err, FSP_err: Standard error for all above- Logical outcomes  - 0L, 1L, erasures, Z_L: Computed logical dual-rail outcome for "0_L", "1_L", erasures, and expectation value of logical sigma_z , respectively  - 0L_err, 1L_err, erasures_err, Z_L_err: Standard error for all above

State assignment datasets:- Fig2_state_assignment_1msmts.csv: Data for Figure 2- ExtendedDataFig2_state_assignment_2msmts.csv: Data for Extended Data Figure 2

Bit-flip datasets: - Each row corresponds to a different delay specified in the xs column in units of microseconds- Counts and Outcome fraction are plotted in Figure 3A- Logical outcomes are plotted in Figure 3B- Detail on datasets:  - Fig3_bit_flip_0L_1ms.csv: Data for Figure 3, left panel  - Fig3_bit_flip_0L_20us.csv: Data for Figure 3, left panel inset  - Fig3_bit_flip_1L_1ms.csv: Data for Figure 3, right panel  - Fig3_bit_flip_1L_20us.csv: Data for Figure 3, right panel inset

Phase error datasets: - Each row corresponds to a different delay specified in the xs column in units of microseconds- Counts and Outcome fraction are plotted in the top panels for Figure 4A and 4B- Logical outcomes are plotted in the bottom panel for Figure 4A and 4B- Short time data are shown in the inset of bottom panel for Figure 4A and 4B. - We provide additional detail for the short time data in Extended Data Figure 3 for short-time Ramsey- Detail on ramsey_short_time.csv: Data includes an additional dimension where the Ramsey phase angle is swept  - values in radians are enumerated in ExtendedDataFig3_ramsey_short_time_phases.csv- Detail on datasets:  - Fig4_ramsey_long_time.csv: Data for Figure 4A  - ExtendedDataFig3_ramsey_short_time.csv, ExtendedDataFig3_ramsey_short_time_phases.csv: Data for Figure 4A, inset (bottom panel); Data for Extended Data Figure 3  - Fig4_echo_long_time.csv: Data for Figure 4B  - Fig4_echo_short_time.csv: Data for Figure 4B, inset (bottom panel)