running statistics

• parameters
  • general: size na, nb=[6,15],k=[1,3]
  • more frequent: size na, nb=[7,12],k=[1,2]
• set-up
  • sysmetric code A and B, where B is obtained by flip X and Z in code A
  • identical code A and B
  • random code A and B
• what is calculated in each test?
  • generate code A B with a filter of distance > 1
  • subsystem product code
  • higher-dimensional hypergraph product code from the product of these two CSS codes.
  • both left (X) and right (Z) are calculated for all those codes.
• a million tests have been running for each set-up
• estimeted total running time: 256 cores x 7 x 24 hours = 43008 cpu hours

result

• dozens of cases has been found with the set-up of symmetric code A B or identical code A B
• no cases has been found with random code A and B
• observations
  • symmetry plays a role here, which tends to give smaller distance. This is consistent with the numericas of homological product code in (Bravyi & Hastings 2013)

files

• each test has a unique trial number, the log files is in this folder, and the matrices are saved in MatrixMarket format in /matrices
• the shell script to generate those file is ../check_random_concatenation.sh

result on Jul 2, enumerate all codes up to size 6

• no case found for size 3-6.
• size 7 would take one month to finish