DOI: 10.22002/4m9sp-yzr58
title: Supporting data for "A tweezer array with 6100 highly coherent atomic qubits"

description: The following datasets are provided to support the findings published in the main text of "A tweezer array with 6100 highly coherent atomic qubits" (arXiv:2403.12021). Additional data, codes, and information are available from the authors upon request.
Fig 1 and 2: array imaging
Files: fig1-2_part01.npy to fig1-2_part08.npy
This dataset consists of raw qCMOS camera images (in units of photons collected per pixel, with type float16) acquired during sequences of 4-time repeated atomic imaging. It served as a basis for Fig1a, Fig1b, Fig1d, the quoted imaging fidelity and survival results (apart from many-time repeated imaging survival results), and Fig2.
Structure: this is a series of 8 4-dimensional arrays in NPY format.

1st dimension: experiment iteration. The 8 files may be concatenated along this dimension.
2nd dimension: image index within the four images. As explained in the paper, the first image is omitted for the 3-image analysis procedure.
3rd and 4th dimensions: height and width of the images.
 
Fig 3a: vacuum-limited lifetime
Files: fig3_vacuum_lifetime_pulsedPGC.npy, fig3_vacuum_lifetime_contiPGC.npy, fig3_vacuum_lifetime_noPGC.npy
This dataset consists of processed data (describing the detected presence or absence of an atom at a given site, with boolean type) resulting from atomic lifetime measurements in different conditions. It serves as a basis for Fig3a and the quoted vacuum-limited lifetime.
Structure: each file contains a 4-dimensional array in NPY format.

1st dimension: index of delay between 1st and 2nd image. The delays are 0.019s + {0s, 30s, 60s, 90s, 120s, 150s, 180s}.
2nd dimension: experiment iteration. Note that for the continuous PGC case, the experiment with indexed 0 was incorrectly programmed, and therefore was removed from the data analysis procedure.
3rd dimension: index of image in the sequence (1st and 2nd image).
4th dimension: site index in the array.
The filenames refer to the Fig3a caption.
 
Fig 3b: 1000-time repeated imaging
File: fig3_repeated_imaging.npy
This dataset consists of raw qCMOS camera images (in units of photons collected per pixel, with type float16) resulting from 1000-time repeated imaging. It served as a basis for Fig 3b and the quoted steady-state imaging survival probability.
Structure: this is a 4-dimensional array in NPY format.

1st dimension: experiment iteration.
2nd dimension: image index within the 1001 images.
3rd and 4th dimensions: height and width of the images.
 
Fig 4a: Rabi oscillations
Files: fig4a_rabi_duration.npy, fig4a_rabi_pop_1.npy, fig4a_rabi_pop_1_std.npy
This dataset consists of processed population numbers in state |1> after a Rabi oscillation. It served as a basis for Fig4a and to extract the microwave Rabi frequency.
Structure: these 3 files contain 1-dimensional arrays in NPY format.

1st file: duration of Rabi oscillation in seconds.
2nd file: population in |1> after the Rabi oscillation.
3rd file: estimated 1sigma uncertainty of population after the Rabi oscillation.
 
Fig 4b: Ramsey oscillations
Files: fig4b_ramsey_evolution_time.npy and fig4b_ramsey_presence.npy
This dataset consists of processed data (describing the detected presence or absence of an atom at a given site, with boolean type) resulting from a Ramsey oscillation experiment with various free-evolution times. It serves as a basis for Fig4b and T2*.
Structure:

1st file: 1D NPY array with the free-evolution times in seconds
2nd file: 4D NPY array

1st dimension: experiment iteration.
2nd dimension: index of free-evolution time.
3rd dimension: index of image (1st image before the Ramsey oscillation, 2nd image after the Ramsey oscillation).
4th dimension: site index in the array.
 
Fig4c: T2 with dynamical decoupling
Files: fig4c_t2_time.npy, fig4c_t2_pop.npy, fig4c_t2_pop_std.npy
This dataset consists of measurements of population in |0> after probing T2 with dynamical decoupling (further details are provided in the paper). It serves as a basis for Fig4c and T2.
Structure:

1st file: 1D NPY array with the total duration of the microwave sequence (from first pi/2 pulse to last pi/2 pulse) in seconds.
2nd and 3rd files: population in |0> and estimated 1sigma uncertainty after the T2 measurement. Each file is a 2D NPY array.

1st dimension: index of the total duration of the microwave sequence.
2nd dimension: phase of the final pi/2 pulse (0 or pi).
 
Fig4d: 1Q global randomized benchmarking
Files: fig4d_rb_length.npy, fig4d_rb_return_prob.npy, fig4d_rb_return_prob_std.npy
This dataset consists of return probabilities in state |1> after 1Q Clifford global randomized benchmarking (further details are provided in the paper). It serves as a basis for Fig4d and the single-qubit fidelity.
Structure:

1st file: 1D NPY array containing the number of applied gates.
2nd and 3rd files: 2D NPY array containing the return probability and the estimated 1sigma uncertainty.

1st dimension: index of the number of applied gates.
2nd dimension: index of the randomly selected gates (each different index corresponds to a different string of random Clifford gates with a total number of gates given by the 1st dimension).
 
Fig5a: atom survival for straight and diagonal moves
Files: fig5a_duration.npy, fig5a_survival.npy
This dataset consists of measured atom survival probabilities after transporting atoms in a straight move or in a diagonal move (further details are provided in the paper). It serves as a basis for Fig5a.
Structure:

1st file: 2D NPY array containing the duration of the move in seconds.

1st dimension: index of duration.
2nd dimension: index of move type (0: straight, 1: diagonal).
 
2nd file: 2D NPY array containing the estimated survival probabilities and confidence interval.

1st dimension: index of duration.
2nd dimension: data type.

0: lower bound of 68% confidence interval for atomic survival after straight moves.
1: central estimate for atomic survival after straight moves.
2: upper bound of 68% confidence interval for atomic survival after straight moves.
3: lower bound of 68% confidence interval for atomic survival after diagonal moves.
4: central estimate for atomic survival after diagonal moves.
5: upper bound of 68% confidence interval for atomic survival after diagonal moves.
 
Fig5b: Ramsey oscillations for static and transported atoms
Files: fig5b_phases.npy, fig5b_pop_0.npy
This dataset consists of measurements of population in state |0> after transporting or not atoms (futher details are provided in the paper). It serves as a basis for Fig5b.
Structure:

1st file: 1D NPY array containing the analyzer phase (i.e. the phase of the final pi/2 pulse) in radians.
2nd file: 2D NPY array containing the estimated population in |0> after the experiment and the confidence interval.

1st dimension: index of analyzer phase.
2nd dimension:

0: lower bound of 68% confidence interval for static case.
1: central estimate  for static case.
2: upper bound of 68% confidence interval  for static case.
3: lower bound of 68% confidence interval for transported case.
4: central estimate for transport case.
5: upper bound of 68% confidence interval for transported case.
 
Fig5d: atomic survival after IRB of coherent transport
File: fig5d_survival.npy
This datasets consists of measurements of atomic survival after IRB of coherent transport along 610um for various move durations and numbers of moves (further details are provided in the paper). It serves as a basis for Fig5d, top panel.
Structure: 3D NPY array containing the estimated atomic survival and corresponding confidence interval.

1st dimension: index of move duration {0.8, 1, 1.2, 1.4, 1.6, 1.8} ms.
2nd dimension: index of number of moves {8, 16, 24, 32, 40, 48, 56, 64, 72, 80}.
3rd dimension: data type.

0: lower bound of the 68% confidence interval.
1: central estimate.
2: upper bound of the 68% confidence interval.
 
Fig5d: return probability after IRB of coherent transport
File: fig5d_rb_return_prob.npy
This dataset consists of measurements of the return probability after IRB of coherent transport for various numbers of moves (further details are provided in the paper). It serves as basis for Fig5d, middle and bottom panel, and the quoted early-time coherent transport fidelity.
Structure: 2D NPY array containing the estimated return probability and the 1sigma uncertainty.

1st dimension: index of number of moves {8, 16, 24, 32, 40, 48, 56, 64, 72, 80}.
2nd dimension: data type.

0: return probability for static case.
1: 1sigma uncertainty on return probability for static case.
2: return probability for transported case.
3: 1sigma uncertainty on return probability for transported case.
 
Fig6d: atomic survival after IRB of coherent atom transfer
File: fig6d_survival.npy
This datasets consists of measurements of atomic survival after IRB of coherent atom transfer between static and dynamic tweezers (further details are provided in the paper). It serves as a basis for Fig6d, top panel.
Structure: 3D NPY array containing the estimated return probability and the 1sigma uncertainty.

1st dimension: index move duration and trajectory {[0.2, 0.4, 0.6] ms, hand optimized; 0.4 ms, ML-optimized).
2nd dimension : index of number of one-way moves {2, 4, 8, 12, 16, 20, 30, 40, 50, 60}.
3rd dimension: data type.

0: estimated survival.
1: 1sigma uncertainty on survival.
 
Fig6d: return probability after IRB of coherent atom transfer
File: fig6d_rb_return_prob.npy
This datasets consists of measurements of the return probability after IRB of coherent atom transfer between static and dynamic tweezers (further details are provided in the paper). It serves as a basis for Fig6d, middle and bottom panel, and the quoted early-time coherent atom transfer fidelity.
Structure: 2D NPY array containing the estimated return probability and the 1sigma uncertainty.

1st dimension: index of number of moves {2, 4, 8, 12, 16, 20, 30, 40, 50, 60}.
2nd dimension: data type.

0: estimated return probability for static case.
1: 1sigma uncertainty on return probability for static case.
2: estimated return probability for transported case.
3: 1sigma uncertainty on return probability for transported case.