DOI: 10.5061/dryad.s7h44j1n3
title: Generation of reconfigurable hypercubic graph states in 1-4 dimensions in a simple optical system

description: Entangled graph states can be used for quantum sensing and computing
 applications. In some measurement-based quantum computing schemes, error
 correction will require the construction of cluster states in at least 3
 dimensions. Here, we generate 1-, 2-, 3-, and 4-dimensional optical
 frequency-mode graph states, which become cluster states at sufficiently
 high squeezing levels, by sending broadband 2-mode vacuum-squeezed light
 through an electro-optical modulator (EOM) driven with multiple
 frequencies. We create the squeezed light using 4-wave mixing in Rb atomic
 vapor and mix the sideband frequencies (qumodes) using an EOM, as proposed
 by Zhu et al. [Optica 8, 281 (2021)], producing a pattern of entanglement
 correlations that constitute continuous-variable graph states containing
 up to several hundred qumodes. We verify the entanglement structure by
 using homodyne measurements to construct the covariance matrices and
 evaluate the nullifiers. This technique enables scaling of optical cluster
 states to multiple dimensions without increasing loss.
description: # Generation of reconfigurable hypercubic graph states in 1-4 dimensions
 in a simple optical system Dryad
 DOI: https://doi.org/10.5061/dryad.s7h44j1n3 ## General description The
 data are stored as comma-delimited text files (CSV). Each file contains
 digitized homodyne signals as a function of time. The various files of
 simultaneously-recorded data are organized by the recorded quadratures:
 XX, XP, and PP, with a given drive voltage and frequency on the EOM. For
 instance, “2D100k500k_60V” is a folder containing 2-dimensional graph data
 for an EOM driven with 60V/2 = 30V per “dimension” or drive waveform; the
 waveforms are sine waves at 100kHz and 500kHz frequencies. Each of the
 files is recorded for the full drive voltage, as well as a baseline of 0V
 (representing 2-mode squeezing) and for shot noise denoted SNL (vacuum
 input instead of squeezing). The various data runs are denoted as:
 scope_XP_2D100k500k_SNL_1.3 scope_PP_2D100k500k_60V_1.6
 scope_XX_2D100k500k_0V_1.6 etc. These names encode: 1. the measured
 homodyne quadratures (XX, XP, PP), 2. the dimensionality (1D, 2D, 3D, 4D),
 3. the EOM drive frequencies, 4. the drive condition (SNL, 0V, or the full
 drive voltage), and 5. a shot identifier (e.g. \_1.3, \_1.6). The files
 (see details in section 3) contain a few lines of general information
 about the data and 2 columns of data recorded, which are the probe and
 conjugate homodyne signals. Optionally, we had the third column as a
 trigger pulse we used to trigger data-taking, which is not used later for
 data processing. --- ## Data folders for 1-4 dimensional graph states 1D
 folder: (6 shots) 2023-05-08: 1D_200k_30V_CSV.zip 2D folder: (6 shots)
 2024-04-07 2D scaling: 2D100k500k_60V_CSV.zip 3D folder: (there are 24
 shots; there are 12 in each of V1 and V2) 2024-05-13 #D 90V:
 3D100k300k900k_90V1_CSV.zip 3D100k300k900k_90V2_CSV.zip 4D folder: (the V1
 and V2 folders have 6 shots in each of them)
 4D33k99k297k891k_120V1_CSV.zip 4D33k99k297k891k_120V2_CSV.zip --- ##
 File-by-File Description of Auxiliary Metadata Files (for buff_size,
 data_len, scope_, temp_, save_traces_, and the single-value files)* This
 folder contains raw oscilloscope traces together with a set of metadata
 helper files used to reconstruct sampling parameters, vertical scaling,
 and acquisition settings. Many of these CSV files contain a single numeric
 value (one cell), corresponding to a specific instrument configuration
 parameter. #### 3.1 Single-value metadata files *aa.csv Content: A single
 numeric value. Meaning: Internal flag used by the acquisition script.
 Equivalent to a boolean/identifier for this dataset. Unit: Unitless.
 Usage: Does not affect the analysis; included for completeness.
 *scope_ch1.csv, scope_ch2.csv, scope_ch3.csv Content: A single numeric
 value (voltage scalar). Meaning: Channel-dependent vertical scaling factor
 applied by the oscilloscope (Ch1, Ch2, CH3). Units: Volts per division
 (V/div). Usage: When reconstructing voltage values from raw binary or
 scaled data arrays, this factor defines the amplitude calibration.
 *scope_recordlength.csv Content: Single integer. Meaning: Total number of
 sample points recorded per trace at the oscilloscope level. Usage: Helps
 validate consistency between buff_size, data_len, and the exported trace
 lengths. *scope_sample_rate_set.csv Content: Single floating-point number.
 Meaning: Nominal oscilloscope sampling rate set by the acquisition script
 (samples per second). Usage: Parameter used for acquisition
 reproducibility; sometimes differs slightly from the effective sample
 rate. *scope_samplerate.csv Content: Single floating-point number.
 Meaning: Actual sampling rate used by the oscilloscope in this capture
 (samples per second). Usage: Used to compute the time axis
 𝑡_𝑛=𝑛/sample_ratet. *scope_vertscale1.csv, scope_vertscale2.csv Content:
 Single floating-point number. Meaning: Vertical scale (V/div) applied to
 oscilloscope channels 1 and 2. Usage: Used for converting digitizer values
 into calibrated voltages. *num_shots.csv Content: Single integer (e.g.,
 number of repeated traces). Meaning: Total number of independent
 oscilloscope acquisitions (shots). Usage: Determines how many individual
 traces are available for averaging, covariance calculation, noise
 estimation, etc. #### 3.2 Time-axis and acquisition-config helper files
 *buff_size.csv Content: Single integer. Meaning: Oscilloscope acquisition
 buffer size (number of sample points). Usage: Defines maximum trace
 length. *data_len.csv Content: Single integer. Meaning: Number of sample
 points used per trace in analysis. Usage: Defines how many data points are
 read from each waveform. *scope_data_time.csv Content: Single
 floating-point value. Meaning: Time step Δt between adjacent points
 (seconds). Usage: Time axis defined by t_n=n×Δt. *scope_horzscale.csv
 Content: Single floating-point value. Meaning: Horizontal scale setting
 (s/div) used in the oscilloscope front panel. Usage: Metadata consistency
 check; not required for numerical reproduction. #### 3.3 Raw traces and
 saved oscilloscope data *save_traces_1.csv, save_traces_2.csv,
 save_traces_3.csv Content: Large CSV files containing raw oscilloscope
 voltage data for Channels 1–3 (CH1, CH2, CH3).  Structure: - 2 columns of
 data (CH1, CH2) recorded, which are the probe and conjugate homodyne
 signals. Optionally, we had the third column (Ch3) as a trigger pulse we
 used to trigger data-taking, which is not used later for data processing.
 Usage: Primary dataset used for producing the figures and covariance
 matrices in the manuscript. *temp_trace_1.csv, temp_trace_2.csv,
 temp_trace_3.csv Content: Intermediate per-trace files generated during
 acquisition. Meaning: Temporary buffers saved by the acquisition script
 (redundant but included for completeness). Usage: Not required for
 reproducing final results; kept for transparency. *scope_obj.csv Content:
 Encoded oscilloscope configuration object (scalar identification value).
 Usage: Internal object ID used by the acquisition software. #### 3.4 Notes
 / human-readable descriptors *filename_NOTE.txt *scope_name_NOTE.txt
 *temp_NOTE.txt *VScale_NOTE.txt Content: Short reference notes generated
 during acquisition. Meaning: Provide context such as scope name, file
 naming conventions, or scale settings. Usage: Human-readable aids; not
 used in numerical analysis.