frontiers / frontier

Quantum codes: stabilizer [[n,k,d]] certificates

id: vfr_001f148c07eebecb
license: CC-BY-4.0
findings: 5
accepted core: 0
contested: 0
links: 0
sources: 5
evidence: 5
avg conf: 0.88

used by 0 · replayed by 1 producer · second seat open

e6/6 · finding.asserted · reviewer:will-blair · 2026-06-02 · null→56c6

State

by type

computational4
open_question1

by review state

unreviewed5

bundle anatomy

finding statement

The largest distance of a single-logical-qubit stabilizer code at length 10, [[10,1,d]], is open within the band d in [3,4]; whether a [[10,1,4]] stabilizer code exists is undetermined here.

open_question

evidence

computational · ScienceClaw-shaped artifact packet import · agent artifact packet

5 atoms

provenance

cap_a1b2c3d4e5f60718 · vc_qcopen000000001

review state

The example finding is unreviewed. Frontier changes still pass through reviewable changes and accepted events.

6 accepted events

derived signals

Links, candidate gaps, bridges, citation stance, nearby papers, and generated summaries route review. They do not rewrite the record by themselves.

0 linked findings6 reviewable changes

5 findings · 0 machine-sealed

verifiedreplayedsupersededbankedleasedcontesteddeprecated

Quantum codes: stabilizer [[n,k,d]] certificates

State

bundle anatomy

The largest distance of a single-logical-qubit stabilizer code at length 10, [[10,1,d]], is open within the band d in [3,4]; whether a [[10,1,4]] stabilizer code exists is undetermined here.

The [[4,2,2]] code with stabilizers XXXX, ZZZZ encodes 2 logical qubits in 4 physical qubits with distance 2, verified by exact recomputation of k and d.

The Steane code [[7,1,3]] (CSS from the [7,4,3] Hamming code) encodes 1 logical qubit in 7 physical qubits with distance 3, verified from its six stabilizer generators.

The perfect five-qubit code [[5,1,3]] (cyclic stabilizers XZZXI and rotations) encodes 1 logical qubit in 5 physical qubits with distance 3, and is optimal at its length.

The Shor code [[9,1,3]] (concatenated bit- and phase-flip repetition) encodes 1 logical qubit in 9 physical qubits with distance 3, verified from its eight stabilizer generators.

The largest distance of a single-logical-qubit stabilizer code at length 10, [[10,1,d]], is open within the band d in [3,4]; whether a [[10,1,4]] stabilizer code exists is undetermined here.

The [[4,2,2]] code with stabilizers XXXX, ZZZZ encodes 2 logical qubits in 4 physical qubits with distance 2, verified by exact recomputation of k and d.

The Steane code [[7,1,3]] (CSS from the [7,4,3] Hamming code) encodes 1 logical qubit in 7 physical qubits with distance 3, verified from its six stabilizer generators.

The perfect five-qubit code [[5,1,3]] (cyclic stabilizers XZZXI and rotations) encodes 1 logical qubit in 5 physical qubits with distance 3, and is optimal at its length.

The Shor code [[9,1,3]] (concatenated bit- and phase-flip repetition) encodes 1 logical qubit in 9 physical qubits with distance 3, verified from its eight stabilizer generators.

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