Quantum codes
[[122,0,20]]
A [[122,0]] qubit code with minimum distance 20, one more than the 19 listed at codetables.de, where the upper bound is 42. Quantavane found it on 24 October 2026.
Sent to Markus Grassl for codetables.de on 25 October 2026; the table shows it once he adds it.
The record
| Ours | d = 20 |
|---|---|
| Previous best | d = 19 (upper bound 42) |
| Previous source | the lower bound listed at codetables.de |
| Found | 24 October 2026 |
| Status | Sent to Markus Grassl for codetables.de on 25 October 2026; the table shows it once he adds it. |
| Check | The distance was proved by a complete search, then proved again on an equivalent code. |
A single entangled state of 122 qubits whose distance is 20. It also improves [[121,0,19]] (the table lists 18), by the standard propagation rules.
How it was found and checked
A Hermitian self-dual double circulant code over GF(4). The distance was proved by a complete search, then proved again on an equivalent code.
A quantum error-correcting code protects qubits the way a linear code protects symbols. An [[n,k]] code spreads k qubits over n, and with minimum distance d it corrects up to (d−1)/2 errors. Codes with k = 0, single entangled states of n qubits, are listed too. Markus Grassl's tables at codetables.de keep the largest d known for each n and k, for qubits and for larger dimensions q (qudits).
Questions
What is the best known [[122,0]] qubit code?
Ours, with minimum distance 20; codetables.de listed 19 (read 26 October 2026).
How was it built?
A Hermitian self-dual double circulant code over GF(4).
Is it on codetables.de yet?
Sent to Markus Grassl for codetables.de on 25 October 2026; the table shows it once he adds it.