Entanglement-assisted quantum-code bounds
How far can an entanglement-assisted quantum error-correcting code protect information when its length, encoded information and shared entanglement are fixed? Its distance measures the errors it can correct under ideal decoding. For a code written [[n,k,d;c]], n is the number of transmitted units, k the number encoded, d the distance and c the number of shared entangled pairs.
Why it matters and what counts as progress
Why it matters: Better distance at the same resource budget strengthens the code’s guaranteed error protection. Exact constructions also show which bounds in published code tables can be improved.
What counts as progress: Construct a code with larger verified distance at fixed n, k and c; prove a family of such codes under stated field and length conditions; or certify that no better code exists in the specified class. Compare with a dated table and keep ideal-code guarantees separate from hardware performance.
How the problem developed
- 2006 · Entanglement-assisted codes [1]
Todd Brun, Igor Devetak and Min-Hsiu Hsieh Showed that preshared entanglement relaxes the compatibility constraint on quantum error-correcting codes, establishing the setting for these resource and distance comparisons.
- 15 Oct 2020 · Earlier bounds and constructions [2]
Markus Grassl, Felix Huber and Andreas Winter Published a length-reduction rule used for an earlier listed binary code. Their result helps date one comparison bound; it does not give the later evolved constructions.
- 12 Jul 2022 · Earlier entanglement bounds [3]
Gaojun Luo, Martianus Frederic Ezerman, Markus Grassl and San Ling Reported constructions and resource bounds that supply several of the prior table entries compared with the new codes.
AlphaEvolve with Jae-Hyun Baek, Byung-Sun Won and Jon-Lark Kim The model evolved programs that found finite qubit codes under researcher-designed targets and exact evaluation. The researchers identified and proved a broader prime-power family. The paper reports independent exact parameter checks for the finite codes.
Selected milestones for entanglement-assisted code bounds. The 2026 comparison uses table entries accessed on 17 July 2026, not a complete history of all possible improvements.
AI contribution
Researcher--Loop Evolutionary Discovery of Entanglement-Assisted Quantum Code Families
Under researcher-defined targets and an exact evaluator, AlphaEvolve evolved programs that produced finite entanglement-assisted stabilizer quantum codes. One binary code has parameters [[12,1,11;8]], raising the listed distance from 9 to 11 at the same length, encoded-qubit count and entanglement cost. Researchers then identified a pattern, generalized it and proved a separate prime-power family; the family and entanglement lifting together close 54 gaps in the archived tables.
Sources
- Brun, Devetak and Hsieh: Correcting quantum errors with entanglement
- Grassl, Huber and Winter: Entropic proofs of Singleton bounds
- Luo and colleagues: How much entanglement does a quantum code need?
- Baek, Won and Kim: Researcher--Loop Evolutionary Discovery of Entanglement-Assisted Quantum Code Families
- Code matrices, saved programs and verification artifact
Publication history
AlphaEvolve finds finite quantum codes behind a broader family
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