Quantum codes
[[158,0,20]]
A [[158,0]] qubit code with minimum distance 20, one more than the 19 listed at codetables.de, where the upper bound is 47. Quantavane found it on 25 October 2026.
Checked; it goes to codetables.de with our next batch of results.
The record
| Ours | d = 20 |
|---|---|
| Previous best | d = 19 (upper bound 47) |
| 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 | The distance was proved by a complete search, then proved again on an equivalent code. |
A single entangled state of 158 qubits whose distance is 20.
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 [[158,0]] 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?
Checked; it goes to codetables.de with our next batch of results.