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
e6/6 · finding.asserted · reviewer:will-blair · 2026-06-02 · null→56c6
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Signals
Finding types
5 findings- computational4
- open_question1
Review state
5 findings- unreviewed5
Flow
Top findings
all stateThe [[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.
0.97vf_916a76afc89cce11asserted4892· 9dThe 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.
0.97vf_b6c315bb1ecb182dasserted4892· 9dThe 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.
0.97vf_d5782594d6fabd80asserted4892· 9dThe 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.
0.97vf_f682d49c4214bdbcasserted4892· 9dThe 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.
0.50vf_00940b13c44c9822asserted4892· 9dShowing 5 of 5