DOI: 10.5281/zenodo.15008486
title: Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories

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).