Gross Code Sandbox
Explore the [[144,12,12]] gross code — a bivariate bicycle (BB) qLDPC code that stores 12 logical qubits in 144 physical ones. Inject Pauli errors and watch the weight-6 stabilizers fire. Hover any stabilizer to trace its six qubits: 4 local couplings (solid) plus 2 long-range ones (dashed) — the degree-3 x³/y³ terms that let this qLDPC code beat the surface code's overhead.
Bivariate Bicycle Code
Code Parameters
Qubits n
144
Logical k
12
Distance d
12
Check weight
6
Polynomials over the torus ℤℓ × ℤm:
HX = [A | B], HZ = [Bᵀ | Aᵀ]
A = x³ + y + y²B = y³ + x + x²HX = [A | B], HZ = [Bᵀ | Aᵀ]
Error Injection Mode
Pick an error type, then click the circular data qubits. Hover any qubit or stabilizer to trace its connections.
Syndrome
Errors
0
Defects
0
X-checks fired
0
Z-checks fired
0
Actions
Noise p
3%
Legend
Data qubit, L sublattice
Data qubit, R sublattice
Z-stabilizer (detects X errors)
X-stabilizer (detects Z errors)
Each check couples to 4 local qubits (solid) and 2 long-range qubits (dashed, glowing) — the degree-3
x³ and y³ terms. Every check touches 6 qubits; every qubit sits in 3 X- and 3 Z-checks.