GuillaumeLessard QECTOR Glossary and Notation
Source of authority: v1.0.0 reference manual, Appendices A and B.
Notation (Appendix A)
| Symbol | Meaning |
|---|---|
| F2 | Binary field {0, 1} |
| H | Parity-check matrix in F2^(m x n) |
| Hx, Hz | CSS sector check matrices |
| s | Syndrome vector s = H e (mod 2) |
| e | True physical error vector |
| c | Decoder correction vector |
| ker(H) | Right kernel of H |
| im(H^T) | Row space of H (stabilizer span) |
| L | Logical-observable matrix |
| gamma_q | Posterior LLR of qubit q |
| phi(x) | Box-plus kernel -ln(tanh(x/2)) |
| pi(C) | Parity of fired detectors in cluster C |
| alpha(n) | Inverse Ackermann function |
| w_uv | Edge weight log((1-p)/p) |
| d_{c,t} | Detector difference s_{c,t} xor s_{c,t-1} |
| lambda | Decay factor of the sliding window (0 <= lambda < 1) |
| W | OSD sweep width max(2 * osd_order, 6) |
Glossary (Appendix B)
Syndrome faithfulness. The property H c = s (mod 2) for
reachable syndromes; the universal correctness gate of the
engine. Theorem 1.
MWPM. Minimum-weight perfect matching; the exact optimization solved by the blossom decoder.
Blossom. An odd cycle of tight edges contracted during Edmonds' algorithm.
Graphlike code. A code in which every qubit participates in at most two checks; matching decoders apply.
Hyperedge / non-graphlike. A mechanism touching three or more detectors; requires BP-OSD.
BP-OSD. Belief propagation followed by ordered-statistics decoding over GF(2).
OSD-0 / OSD-W. Basis solve with free bits from BP hard decisions / plus a combination sweep of width W.
Union-Find decoding. Cluster-growth decoding with spanning-forest peeling.
DEM. Detector error model: the standard description of a decoding problem.
Collapse to graph. Merging parallel mechanisms between the same detector pair into one edge.
Logical operator. An element of ker(H) \ im(H^T); flipping
it changes the logical state undetectably.
Wilson interval. A binomial confidence interval with correct coverage at small k.
Bit identity. GPU batch output equal to CPU reference output, bit for bit, on tested configurations.
Cascade. A cheap faithful pre-filter with an exact fallback.
MCP. Model Context Protocol; the JSON-RPC stdio server surface.
CSS code. Calderbank-Shor-Steane code with separate X and Z
sectors. The condition Hx Hz^T = 0 (mod 2) is the commutation
guarantee.
Steane code. The [[7,1,3]] CSS code, the smallest CSS example on which every sector-level statement of chapters 3, 8, 9, and 12 can be verified by hand (manual 2.7, appendix E.1).
Steane syndrome [1,1,0]. The syndrome of the error
e = [0,0,0,0,0,1,0] (qubit 5) on the Steane X-checks. A
canonical reference example.
Rotated surface code. A 2D surface code on a d x d grid with weight-4 plaquette checks plus weight-2 boundary checks so that each interior qubit is shared by two checks; one logical qubit (the horizontal top-row string). Graphlike.
Unrotated surface code. A 2D surface code on a d x d vertex
lattice; the canonical Z-stabilizer construction. The single-
sector matching graph in the v1.0.0 library has k = 0, so
logicals_matrix() is None; LER cannot be defined.
Toric code. A 2D code on an L x L torus with 2 L^2 qubits on the edges and L^2 vertex checks; two logical qubits.
Heavy-hex code. A heavy-hex lattice interleaving data and flag qubits on a brick-wall pattern; the v1.0.0 helper builds the graphlike Z-sector.
Color code. Triangular 6.6.6 (C2) color code with k = 2 logicals (planar) or k = 4 (toric).
Hamming weight. The number of 1s in a binary vector.
Logical coset. The equivalence class of a correction in
ker(H) / im(H^T). Two corrections in the same coset produce
the same logical outcome.
Logical failure. A non-trivial logical operator applied to
the state; the decoder returned a correction whose residual with
the true error lies in ker(H) \ im(H^T).
AutoDecoder. The 7-tier self-debugging fallback chain in the
Python layer; native_auto is the Rust routing primitive.
NativeAutoDecoder. The Rust class for native routing with
license enforcement. The Python AutoDecoder is the 7-tier
self-debugging controller.
Planted error. A known error used in correctness tests; the
syndrome is computed as s = H e (mod 2) and the decoder is
expected to return a correction c with H c = s (Theorem 1)
and the same logical coset as e (Theorem 2).
Stale test-count policy. The shipped 0.5 validation report
(832 Python tests, 87 Rust tests) is marked stale for post-0.5
builds; the reader is pointed at the decoder tree's
docs/CORRECTNESS_AUDIT.md and its live suite. No current pass /
fail count is claimed.
Withdrawn benchmark policy. The competitive and throughput tables published for earlier cores were withdrawn in the frozen tree because the measured figures did not survive a core fingerprint change. No performance number in the manual is intended to replace a regenerated artifact.
License tiers. Community d<=7 (free, source-available), Pro d<=19 (Ed25519-signed token), Enterprise d<=63 (Ed25519- signed token, GPU/GNN paths).
Token formats. v2 (generic), QECT-PRO-* (Pro prefix),
QECT-ENT-* (Enterprise prefix). All verified offline in the
Rust core.
Resolution order. QECTOR_LICENSE_KEY ->
QECTOR_LICENSE_FILE -> ~/.qector/license.key. A set-but-
unreadable QECTOR_LICENSE_FILE is invalid, not a silent
Community downgrade.
Zero egress. All compute stays local via the MCP server. No
.stim / .npy / parity matrices leave the machine.