1. ABOUT THE DATASET -------------------- Title: Data supporting "Quantum many-body mixed phase space revealed by hybrid feedback control" Creator(s): Jie Ren Organisation(s): University of Leeds Rights-holder(s): Copyright 2026 University of Leeds Publication Year: 2026 Description: This dataset contains source data and regeneration code for the quantitative main-text figures of a study of mixed phase-space dynamics and hybrid feedback control in an interacting Su-Schrieffer-Heeger (SSH) ladder. The work combines time-dependent variational-principle (TDVP) calculations, exact diagonalization, and measurements from a 24-qubit superconducting processor. The deposited files are the final source-data tables behind every quantitative figure panel: TDVP trajectories and Poincare-section crossings, first-revival and co-moving imbalance maps, hybrid-feedback trajectories, and subsystem-fidelity measurements. Only data and documentation are deposited; no plotting or processing code is included, because the deposited tables are exactly the data from which the figures are drawn. Note: the figure shown as Fig. 4 in early versions of the manuscript appears as Extended Data Fig. 1 in the final version; the corresponding files are stored under ExtendedDataFigure1/ (file names retain their original figure4 prefixes). Cite as: Jie Ren (2026): Data supporting "Quantum many-body mixed phase space revealed by hybrid feedback control". University of Leeds. [Dataset] https://doi.org/10.5518/1890 Related publication: Dong, H., Ren, J., Hallam, A. et al. "Quantum many-body mixed phase space revealed by hybrid feedback control". Nature Physics (accepted). Article DOI to be added after publication. Contact: Jie Ren, J.Ren@leeds.ac.uk 2. TERMS OF USE --------------- Copyright 2026 University of Leeds. Unless otherwise stated, this dataset is licensed under a Creative Commons Attribution 4.0 International Licence: https://creativecommons.org/licenses/by/4.0/. 3. PROJECT AND FUNDING INFORMATION ---------------------------------- Title: Quantum many-body mixed phase space revealed by hybrid feedback control Dates: 2024-2026 Funding organisation: Leverhulme Trust; Engineering and Physical Sciences Research Council (EPSRC); US National Science Foundation (NSF) Grant no.: RL-2019-015, EP/Z533634/1, UKRI1337, PHY-2309135 4. CONTENTS ----------- File listing Data/ Final source-data tables (CSV) for the quantitative main-text figures and the Extended Data figure, organised by figure: - Figure1/figure1c_tdvp_trajectories.csv - Figure1/figure1d_poincare_section.csv - Figure2/figure2b_imbalance_timeseries_experimental.csv - Figure2/figure2c_first_revival_imbalance_numerical.csv - Figure2/figure2d_first_revival_imbalance_experimental.csv - Figure2/figure2e_comoving_imbalance_numerical.csv - Figure2/figure2f_comoving_imbalance_experimental.csv - Figure3/figure3b_feedback_trajectory_experimental.csv - Figure3/figure3b_stable_orbit_numerical.csv - Figure3/figure3c_imbalance_by_feedback_step.csv - Figure3/figure3d_stable_orbits_experimental_and_numerical.csv - ExtendedDataFigure1/figure4a_subsystem_fidelity_experimental.csv - ExtendedDataFigure1/figure4b_first_revival_fidelity_experimental.csv - ExtendedDataFigure1/figure4b_first_revival_global_fidelity_numerical.csv - ExtendedDataFigure1/figure4b_first_revival_global_fidelity_numerical_full_grid.csv Documentation/ - dataset_inventory.csv: panel-by-panel description of the source data. - file_manifest_sha256.csv: SHA-256 manifest of the deposited files. Files are deposited uncompressed: every CSV can be previewed and downloaded individually from the repository record. The completed Leeds metadata spreadsheet (data_deposit_jie_ren_DOI-1890_filled.xlsx) is provided to the Research Data team alongside the deposit. All CSV files use UTF-8 encoding with comma separators and header rows. Angles are given as fractions of pi (theta_pi, phi1_pi, phi2_pi). Time is in nanoseconds for experimental data and in units with hbar*abs(J_o)=1 for TDVP output. 5. METHODS ---------- Theoretical methods Numerical data were generated using exact diagonalization (ED) of the 1D SSH ladder Hamiltonian and time-dependent variational-principle (TDVP) evolution on the shallow-circuit variational manifold. TDVP trajectories were integrated with the equations of motion derived in the manuscript and used to construct the Poincare section shown in Figure 1d. ED was used for the first-revival imbalance maps (Figure 2c,e) and the global fidelity map in Figure 4b-right. The TDVP equations of motion are given explicitly in the Methods section of the manuscript, and all parameters are stated there and in the Supplementary Information. The Figure 1c trajectories were obtained by integrating these equations with Jo = 1, Je = 0.6, J3 = 0.05 (in units of hbar*|Jo| = 1) from the initial conditions (theta, phi1, phi2) = (0.053 pi, 0, pi/2) [periodic orbit], (0, 0, pi/2) [nearby regular trajectory], and (0.21 pi, 0.8 pi, 0.13 pi) [chaotic trajectory]; the deposited table lists the integrated time series. Experimental methods Experimental data were obtained from a 24-qubit superconducting processor. The device was initialised in product states parameterised by (theta, phi1, phi2) using a shallow digital circuit, evolved under the analog SSH ladder Hamiltonian, and measured after an inverse rotation. Imbalance and subsystem-fidelity observables were extracted from projective bitstring measurements. Feedback-control trajectories were obtained by classically optimising the post-evolution variational parameters at each feedback step. Further experimental details, including calibration, gate fidelities and readout, are described in the manuscript and Supplementary Information. Data processing Experimental imbalance and fidelity maps were computed from measured bitstrings. First-revival peaks were identified from the time series; co-moving imbalance was evaluated at a fixed reference time. The Extended Data Fig. 1 experimental subsystem-fidelity map was derived from 4-qubit fidelity revivals across a 7-by-21 parameter grid. The deposited CSVs are the final processed values underlying the published figures and require no further processing. SHA-256 manifests are included in Documentation.zip. Software No software is required to use the deposit: all files are plain-text CSV tables. Numerical data were generated with the equations and methods described in the manuscript and Supplementary Information (TDVP integration and exact diagonalization).