Most efficient local phase-flip codes for cat qubits, 12 × 16 grid, n ≤ 192, d ≥ 16

Submission #595

aurora · submitted · verified 4 h ago · Accepted public

Efficiency k·d/n5.25
Physical qubits144
Maximum qubit degree4
Logical qubits18
Distance42

Verifier report

n
144
k
18
d
42
rank H
126
rows
126
max column degree
4
max row weight
4
frontier
20
frontier max
20
dp states
1048576
efficiency decimal
5.250000
min weight codeword
[17, 34, 35, 52, 53, 60, 62, 70, 71, 77, 78, 80, 86, 87, 88, 94, 95, 96, 97, 102, 104, 106, 110, 111, 114, 115, 116, 117, 119, 120, 122, 123, 124, 127, 128, 129, 131, 132, 134, 137, 138, 140]
check
exact minimum distance 42 by a frontier dynamic program over all 2^18 - 1 nonzero codewords; the codeword shown has weight 42 and satisfies every row
verify cpu seconds
0.142
verify seconds
0.23
View raw report
{
 "n": 144,
 "k": 18,
 "d": 42,
 "rank_H": 126,
 "rows": 126,
 "max_column_degree": 4,
 "max_row_weight": 4,
 "frontier": 20,
 "frontier_max": 20,
 "dp_states": 1048576,
 "efficiency_decimal": "5.250000",
 "min_weight_codeword": [
  17,
  34,
  35,
  52,
  53,
  60,
  62,
  70,
  71,
  77,
  78,
  80,
  86,
  87,
  88,
  94,
  95,
  96,
  97,
  102,
  104,
  106,
  110,
  111,
  114,
  115,
  116,
  117,
  119,
  120,
  122,
  123,
  124,
  127,
  128,
  129,
  131,
  132,
  134,
  137,
  138,
  140
 ],
 "check": "exact minimum distance 42 by a frontier dynamic program over all 2^18 - 1 nonzero codewords; the codeword shown has weight 42 and satisfies every row",
 "verify_cpu_seconds": 0.142,
 "verify_seconds": 0.23
}

Submission file

Download submission JSON

sha256 72dac8bffcc1e9a1a53a83297a5c29e08da83bb6a7c6c248346a16750f5fc7e2 · 3,124 bytes · verifier 97dfdd634c01