Published June 4, 2025 | Version v1
Dataset Open

Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories

Creators

  • 1. ROR icon QuEra Computing (United States)

Description

The datasets contained herein correspond to the raw data from the quantum processor and displayed results of the main figures of Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories, published in Nature. For details of the classical numerical results, refer to the ReCirq.

Experimental results are reported in pandas dataframes as base-ten integers. The bitstrings on the device can be recovered from the included values using:

bitstrings = (np.floor(np.outer(base_ten_values,1/2**np.arange(number_of_qubits)))%2).astype(int)

where base_ten_values are what is included in the pandas dataframe and the number_of_qubits depends on the experiment. This means that the first bit is the least significant bit and the last bit is the most significant bit. When parsing bitstrings, the mapping from the bitstrings generated as above to the physical layout is achieved by comparing the `qubit_order` column of the pandas dataframe to the included image title qubit_mapping.png.

The datasets are organized into four .zip files corresponding to each figure. Each compressed file contains a number or pickle files (.pkl). The contents of each compressed file are listed below.

Fig2.zip

Fig2c_raw_bitstrings.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter. NaN if the initial state is 'toric_code' or 'polarized'.
lambda Hamiltonian parameter
initial state The initial state prepared.
theta The single qubit rotation angle for the WALA ansatz.
Loschmidt echo A boolean to determine if the circuit corresponds to the Loschmidt echo.
qubit_order Mapping from qubit index to physical qubit defined in qubit_mapping.png.
values The results.

Fig2c_plotted_data.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
lambda Hamiltonian parameter
initial state The initial state prepared.
theta The single qubit rotation angle for the WALA ansatz.
Loschmidt echo A boolean to determine if the circuit corresponds to the Loschmidt echo.
he List of he values.
Energy_values The absolute values of the energy for our full system.
Energy_uncertainties The error of the Energy_values.
Energy_error_per_unit_cell_values The difference between the energy measured and the energy of the ground state determined by exact diagonization.
Energy_error_per_unit_cell_uncertainties The error of the Energy_error_per_unit_cell_uncertainties.

Fig2d_plotted_data.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
initial state The initial state prepared.
theta The single qubit rotation angle for the WALA ansatz.
A_values The expectation values of the A_v party values for all electric sites.
A_uncertainties The uncertainty values of A_values.
B_values The expectation values of the B_p parity values for all magnetic sites.
B_uncertainties The uncertainty values of B_values.
Z_values The expectation values of Z for all qubits.
Z_uncertainties The uncertainty values of Z_values.
X_values The expectation values of X for all qubits.
X_uncertainties The uncertainty values of X_values.

Fig3.zip

fig3a_raw_bitstrings_he_0_lambda0.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial state The initial state prepared.
qubit_order Mapping from qubit index to physical qubit defined in qubit_mapping.png.
steps The number of Trotter steps.
results The results.

fig3a_raw_bitstrings_he_0.25_lambda0.pkl

See above

fig3a_raw_bitstrings_he_0.25_lambda0.3.pkl

See above

fig3a_raw_bitstrings_he_0.25_lambda0.6.pkl

See above

fig3a_raw_bitstrings_he_0.25_lambda0.8.pkl

See above

fig3a_raw_bitstrings_he_0.25_lambda2.0.pkl

See above

fig3a_raw_data_results.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial state The initial state prepared.
qubit_order Mapping from qubit index to physical qubit defined in qubit_mapping.png.
results List of dictionaries with 'step', 'value", and 'error' keys for each data point.

fig3a_mitigated_results.pkl

See above.

fig3b_heatmap_data.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial_state The initial state prepared.
steps The number of Trotter steps.
A_v results The values of the A_v parity values in the heatmap.

fig3d_raw_data.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial_state The initial state prepared.
qubit_order Mapping from qubit index to physical qubit defined in qubit_mapping.png.
steps The number of Trotter steps.
A_v results The results.

fig3d_plotted_results.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial_state The initial state prepared.
steps The list of Trotter steps.
Results The values of the separation.

fig3e_heatmap_results.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial_state The initial state prepared.
step The number of Trotter steps.
site_conditions_upon The electric site determined by i,j in the conditional probaility.
Results The conditional probability plotted in the heatmaps.

Fig4.zip

fig4_raw_data_he_{HE}_qubit_{QUBIT}.pkl

There are 70 files with the above naming structure, corresponding to different values of HE and QUBIT. These files include the results of the measurements used to determine the expectation value of the Z(0)Z(t) correlator. The expectation values of Z(0) can be extracted from fig2c_raw_bitstrings.pkl or fig5bc_raw_bitstrings_no_initial_string.pkl in Fig5.zip. HE is the Hamiltonian parameter he and QUBIT is the qubit number that the Z(0)Z(t) correlator was measured, as determined from the mapping defined in qubit_mapping.png.

HE runs over [0,0.1,0.2,0.4,0.6,0.8,1.4]

QUBIT runs over [15,21,23,25,27,29,31,33]

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial_state The initial state prepared.
qubit_order Mapping from qubit index to physical qubit defined in qubit_mapping.png.
qubit The qubit whose expectation value of Z(0)Z(t) these results correspond to.
steps The number of Trotter steps.
Results The results.

fig4_results.pkl

By including values of S_ZZ(t), ZZ(t), and Z(0) for all qubits and all timesteps, the plotted data for the heatmaps in Fig 4c and the plots in Fig 4d are included.

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial_state The initial state prepared.
step The Trotter step.
qubit_index Qubit mapping qubit position (qubit_mapping.png) to the ordering of S_ZZ, ZZ, and Z.
S_ZZ The results for the string correlation function.
ZZ The results of the two-time correlator Z(t)Z(0).
Z The results of the expectation value of Z(0).

Fig5.zip

fig5bc_raw_bitstrings_initial_string.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial_state The initial state prepared.
step The Trotter step.
qubit_order Mapping from qubit index to physical qubit defined in qubit_mapping.png.
results The results.

fig5bc_raw_bitstrings_no_initial_string.pkl

See above.

fig5d_raw_bitstrings_lambda_0.pkl

See above.

fig5d_raw_bitstrings_lambda_0.25.pkl

See above.

fig5d_raw_bitstrings_lambda_0.5.pkl

See above.

fig5b_heatmap_results.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial_state The initial state prepared.
steps The Trotter step.
A_v differences The difference of the expectation values of A_v between the evolution of initial states with and without a string.

fig5c_results.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
he Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial_state The initial state prepared.
steps The list of Trotter steps.
site_label The label of the electric site, as defined in Fig 5a.
results The results of the expectation value of A_v.

fig5d_results.pkl

Column name Description
Je Hamiltonian parameter
Jm Hamiltonian parameter
lambda Hamiltonian parameter
dt Trotter step size.
initial_state The initial state prepared.
steps The Trotter step.
site_label The label of the electric site, as defined in Fig 5a.
he The list of Hamiltonian parameters
results The results of P(A_v).

Files

Fig2.zip

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Additional details

Related works

Has metadata
Preprint: arXiv:2409.17142 (arXiv)
Is published in
Journal article: 10.1038/s41586-025-08999-9 (DOI)

Software

Repository URL
https://github.com/quantumlib/ReCirq/blob/master/docs/lattice_gauge/lattice_gauge.ipynb
Programming language
Python
Development Status
Unsupported