DOI: 10.5061/dryad.0cfxpnw80
title: Data from: Flat-band localization and interaction-induced delocalization of photons

description: Lattices with dispersionless, or flat, energy bands have attracted
 significant interest in part due to the strong dependence of particle
 dynamics on interactions. Using superconducting circuits, we
 experimentally study the dynamics of one and two particles in a single
 plaquette of a lattice whose band structure consists entirely of flat
 bands. We first observe strictly localized dynamics of a single particle,
 the hallmark of all-bands-flat physics. Upon initializing two particles on
 the same site, we see an interaction-enabled delocalized walk across the
 plaquette. We further find localization in Fock space for two particles
 initialized on opposite sides of the plaquette. These results mark the
 first experimental observation of a quantum walk that becomes delocalized
 due to interactions and establishes a key building block in
 superconducting circuits for studying flat-band dynamics with strong
 interactions.
description: This data was collected by averaging 3000 single shot data points
 at each time evolution point. Data is bounded by 0 and 1 and was corrected
 for measurement errors using readout mitigation from the qiskit python
 library. The error bars for the data are 95% Clopper-Pearson confidence
 intervals. 
description: # Data from: Flat-band localization and interaction-induced delocalization
 of photons
 [https://doi.org/10.5061/dryad.0cfxpnw80](https://doi.org/10.5061/dryad.0cfxpnw80) The data included here was used to generate Figures 2, 3, and 4 in the main body of the text. Figure 2 characterizes single particle dynamics in the plaquette with zero and pi flux. In the pi flux device, we see localized dynamics where an initial excitation is localized to three of the four lattice sites. Figure 3 characterizes the dynamics of two particles initialized on the same site. Due to interactions, these particles hop as a pair and we find delocalized dynamics for the bound pair across the plaquette in both zero and pi flux devices. Figure 4 characterizes the dynamics of two particles initialized on opposite sides of the plaquette. Here, we find that when particles are initialized on the left and right sites (LR state), transfer to the TB state is prohibited in the pi flux plaquette. ## Description of the data and file structure There are three different CSV files for the three figures: * Figure2_Data.csv * Figure3_Data.csv * Figure4_Data.csv For the data in Fig. 2 and Fig. 3, the columns include "Time (us)" which provides the time axis from 0 to approximately 2.3 us in units of microseconds. Additionally, there are columns for each qubit, each device, experiment, and simulation. For example, the experimental data for the bottom qubit on the pi flux device is labeled "Qubit 3 PiF Exp". Qubit indeces 1, 2, 3, 4 correspond to labels "left", "top", "bottom", "right" in the paper. Simulation data uses the descriptor "Sim" rather than "Exp" and the zero flux device uses "0F" rather than "PiF". Error bars are included for all experimental data. These error bars are 95% Clopper-Pearson confidence intervals and there are individual columns for the lower and upper intervals. Data was corrected for measurement errors using readout mitigation from qiskit python library. There are a few data entries in the lower bound column of the datasets labeled as "n/a". This comes from how the Clopper-Pearson confidence intervals are generated: because the data is bounded below by zero, if the population is very low or zero, the lower bound will be invalid and therefore is registered as "n/a" or NaN in the data. The data in Fig. 4 has the same columns and structure as for Fig. 2 and 3 with the exception of how qubits are designated. All measurements here were correlation measurements where the data from two qubits was simultaneously measured. The columns for the correlated data from the left (1) and right (4) qubit is labeled as Qubit 14. The column for experimental data in the zero flux device for the top (2) and bottom (3) qubits is "Qubit 23 0F Exp".