Quantum codes
[[34,12,7]]
A [[34,12]] qubit code with minimum distance 7, one more than the 6 listed at codetables.de, where the upper bound is 8. Quantavane found it on 25 October 2026.
Checked; it goes to codetables.de with our next batch of results.
The record
| Ours | d = 7 |
|---|---|
| Previous best | d = 6 (upper bound 8) |
| Previous source | the lower bound listed at codetables.de |
| Found | 25 October 2026 |
| Status | Checked; it goes to codetables.de with our next batch of results. |
| Check | Two separate programs computed the full weight distribution. |
It encodes 12 qubits into 34 and corrects up to 3 arbitrary errors.
How it was found and checked
A Hermitian self-orthogonal quasi-cyclic code over GF(4). Two separate programs computed the full weight distribution.
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 [[34,12]] qubit code?
Ours, with minimum distance 7; codetables.de listed 6 (read 26 October 2026).
How was it built?
A Hermitian self-orthogonal quasi-cyclic code over GF(4).
Is it on codetables.de yet?
Checked; it goes to codetables.de with our next batch of results.