Multiplexed Toric Codes on Erasure Channel

This is a C++ implementation of multiplexed toric codes simulator.

Simulation Flow

You can simulate the multiplexed quantum communication with surface code by g++ -O2 -std=c++20 *.cpp -o main && "your_path/multiplexed_toric/src/"main; and then you get result.json.

Simulation flows are:

• Multiplexing (assign qubits to photons)
• Erasure error on a photon -> erasure errrors on multiple qubits
• Replace erased qubits with mixed state -> erasure can be regarded as a random Pauli error.
• X stabilizer measurement
• Run peeling decoder
• Determines if any Z logical errors remain after decoding.

The default error model is erasure with main_with_loss_error();. Combined error model (random Z + Erasure + random Z) is also available in main_with_combined_error().

You can visualize the result of the simulation as .png file with python python draw_toric.py LATTICE_SIZE_V LATTICE_SIZE_H "result.json"; with lattice sizes (python draw_toric.py 10 10 "result.json"; works for the default case).

You will get something like this: python draw_toric.py LATTICE_SIZE_V LATTICE_SIZE_H "result.json";

Requirements

• nlohmann/json
  • JSON library for C++

Citation

ArXiv submission is available at HERE. For the citation of this work, please use this bibtex file.

@misc{nishio2024multiplexed,
      title={Multiplexed Quantum Communication with Surface and Hypergraph Product Codes}, 
      author={Shin Nishio and Nicholas Connolly and Nicolò Lo Piparo and William John Munro and Thomas Rowan Scruby and Kae Nemoto},
      year={2024},
      eprint={2406.08832},
      archivePrefix={arXiv},
      primaryClass={id='quant-ph' full_name='Quantum Physics' is_active=True alt_name=None in_archive='quant-ph' is_general=False description=None}
}