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Quantum code records
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).
Ours come from quasi-twisted codes over GF(4) through quantum Construction X, from Hermitian self-dual double circulant codes, and, for qudits, from random Hermitian self-orthogonal codes.
7 sent to its maintainer and 12 waiting for our next batch.
Nineteen quantum codes
| Entry | Ours | Previous best | Status |
|---|---|---|---|
| [[33,11,7]] | 7 | 6 | next batch |
| [[34,12,7]] | 7 | 6 | next batch |
| [[39,23,5]] | 5 | 4 | sent |
| [[47,27,6]] | 6 | 5 | next batch |
| [[55,33,6]] | 6 | 5 | sent |
| [[59,37,6]] | 6 | 5 | sent |
| [[61,39,6]] | 6 | 5 | next batch |
| [[115,89,6]] | 6 | 5 | sent |
| [[120,0,22]] | 22 | 20 | next batch |
| [[122,0,20]] | 20 | 19 | sent |
| [[124,0,22]] | 22 | 20 | next batch |
| [[140,0,20]] | 20 | 18 | sent |
| [[142,0,20]] | 20 | 19 | sent |
| [[154,0,20]] | 20 | 18 | next batch |
| [[156,0,20]] | 20 | 19 | next batch |
| [[158,0,20]] | 20 | 19 | next batch |
| [[70,42,9]]_5 | 9 | 8 | next batch |
| [[80,48,10]]_5 | 10 | 9 | next batch |
| [[53,23,11]]_7 | 11 | 10 | next batch |
Questions
What does [[n,k,d]] mean?
A quantum code that encodes k qubits into n qubits with minimum distance d, so it corrects up to (d−1)/2 arbitrary errors. [[n,0,d]] codes are single quantum states with that distance.
Where are the best known quantum codes listed?
In Markus Grassl's qubit and qudit tables at codetables.de, with lower and upper bounds for each n and k.
How were the distances checked?
Each by two separate programs: for codes with k > 0 the full weight distribution, for the k = 0 codes a complete search proved twice.