Exp_BivariateBicycleCode

In our work Demonstration of low-overhead quantum error correction codes, we report the demonstration of two low-overhead quantum low-density parity-check (qLDPC) codes, a distance-4 bivariate bicycle code and a distance-3 punctured bivariate bicycle code code, on our latest superconducting processor, Kunlun, featuring 32 long-range-coupled transmon qubits.

Utilizing a two-dimensional architecture with overlapping long-range couplers, we demonstrate simultaneous measurements of all nonlocal weight-6 stabilizers via periodic execution of an efficient syndrome extraction circuit. We achieve a logical error rate per logical qubit per cycle of (8.91 ± 0.17)% for the distance-4 bivariate bicycle code with four logical qubits and (7.77 ± 0.12)% for the distance-3 punctured bivariate bicycle code with six logical qubits. Our results establish the feasibility of implementing various qLDPC codes with long-range coupled superconducting processors, marking a crucial step towards large-scale low-overhead quantum error correction.

Here, we provide the codes for exprimental data analysis and classical simulation and the data for experimental results and simulation results.

The numerical simulations are built With

• Python - Version 3.10.14 ;
• Stim -Version 1.13.0, a tool for high performance simulation and analysis of quantum error correction circuits ;
• LDPC - Version 0.1.53, a package for decoding quantum error correction codes in Python language ;
• bposd - Version 1.6, a decoder for quantum LDPC codes ;
• leaky - Version 0.2.2, an implementation of Google's Pauli+ simulator ;

Key folders/files and descriptions

• functions_BB_code.py
  contains functions used in both experimental data analysis and classical simulation.

• component_error_rates.py
  contains physical error rate data for quantum operations on our Kunlun processor.

• 18_4_4/Experimental_data/
  experimental data for the [[18,4,4]] code

• 18_6_3/Experimental_data/ experimental data for the [[18,6,3]] code

• 18_4_4/Pauli_plus_simulation/ Pauli+ simualtion and error budget analysis of the [[18,4,4]] code

• 18_6_3/Pauli_plus_sim/ Pauli+ simualtion of the [[18,6,3]] code

• Performance_projection/ Pauli simualtion for BB code performance projection

Reproducing experimental results

To reproduce experimental results:

• Run:

  • 18_4_4/Plot_figures_experiment_18_4_4.ipynb

  • 18_6_3/Plot_figures_experiment_18_6_3.ipynb

These notebooks:

• Decode the experimental measured error syndromes
• Plot:
  • Fig.3a,b
  • Extended Data Fig.3
  • Fig.2b, Extended Data Fig.2

We note that this decoding step takes several hours to complete. If you wish to speed up the decoding, you may open the file "18_4_4/ErrorCorrection_for_experiment_18_4_4.py" or "18_6_3/ErrorCorrection_for_experiment_18_6_3.py" and reduce the value of "my_max_iter = 10000" to a smaller number.

Pauli+ simulation

To simulate the experiment using the Pauli+ framework:

• Run:
  • 18_4_4/Pauli_plus_simulation/Run_PauliPlus.ipynb
  • 18_6_3/Pauli_plus_sim/run_PauliPlus.ipynb

These notebooks produce the Pauli+ simulation results in:

• Fig.2c, Extended Data Fig.2
• Fig.3a,b
• Extended Data Fig.3

To conduct error budget analysis:

• Run:
  • 18_4_4/Pauli_plus_simulation/Logical_error_budget/main_logical_error_budget.ipynb
  • 18_4_4/Pauli_plus_simulation/Detection_error_budget/main_detect_budget.ipynb

These notebooks produce the results in:

• Fig.2d,
• Fig.3c

Performance Projection

To estimate the logical performance of BB codes in future devices with improved performance, we simulate the BB codes with distances ranging from 4 to 12 under varying physical error rates. For efficiency, only Pauli errors are included in the simulation.

• Run:

  • Performance_projection/18_4_4/run_18_4_4.ipynb
  • Performance_projection/36_4_6/run_36_4_6.ipynb
  • Performance_projection/54_4_8/run_54_4_8.ipynb
  • Performance_projection/90_8_10/run_90_8_10.ipynb
  • Performance_projection/144_12_12/run_144_12_12.ipynb

• Run:

  • Performance_projection/Prediction.ipynb

These notebooks produce the results in:

• **Fig.3c,d **

Acknowledgments

This project includes substantial portions of code derived from [BivariateBicycleCodes] (https://github.com/sbravyi/BivariateBicycleCodes/tree/main) which is licensed under the Apache License 2.0.