Introduction

numerical sumulation for subsystem product code and higher dimensional hypergraph product code

progress

[ ] parameter in mind: use small codes with large distance, typically k need to be small
[x] write a function to search for 'good' CSS codes first, then use it for product code/chain complex
- cannot find good CSS codes with both distance greater than 1, after 10000 trials
  - this was a small bug.
- try to remove all zero columns, not working yet
  - not necessary
- I tried an alternate approach: add a filter to remove distance 1 entrances. This works well

TODO:

[ ] run more test for subsystem product code
[ ] add chain complex product for two CSS codes.

Weilei Zeng Nov 26, 2018 main program:concatenation.c, run_result.sh, run_limited_process.sh

From two CSS code, construct a new code in two ways: concatenatoin and reducing. See hypergraph_product_code002.pdf Check their distance and verify d_c=d_a * d_b for both construction. They relation is verified.

Weilei Zeng Jul 20, 2018

main program:concatenation.c, hypergraph.c, run_result.sh, run_limited_process.sh

Generate small random matrix, save in Matrix Market format, named by P [index for random matrix] .mm

From Pi Pj Pk ... Pm construct chain complex C1 - Cm, save each matrix as C [index for m] [index for Bj] Use another file to save name for P matrix

copy directary from ../hypercubic

Weilei Zeng, April 2018 These programs generate toric codes in 2D, 3D(cubic code) and 4D(hypercubic code). It taste the parameters for the qubit code and the syndrome code. Those matrix are saved: G_x G_z C_x C_z G_sx G_sz C_sx C_sz It turns out that C_s and G^T are kind of equivalent. For more results, look at research note.pdf Wed May 9 12:05:48 PDT 2018

toric codes are generated by circulant repetition generating matrix a. Try more codes with generating matrix of [7,3,4] code and [7,4,3] code