Floquet codes measure stabilizers not all at once but in periodic sequences — a temporal decomposition that converts high-weight checks into sequences of low-weight measurements. Stairway codes apply this principle to bivariate bicycle codes, using foliated ZX-calculus to decompose weight-w stabilizers into scheduled two-qubit parity measurements. The construction reduces the problem to choosing periodic boundary conditions in a space-time lattice, and the resulting codes achieve competitive logical error rates with fewer than 300 physical qubits — matching what semi-hyperbolic Floquet codes require over 1,300 qubits to achieve.
The compression factor is striking, but the mechanism matters more than the ratio. By spreading a stabilizer measurement across time steps rather than executing it in a single round, the code trades spatial resources for temporal ones. Each individual measurement is simpler, involving only two qubits, and the information about the full stabilizer accumulates through the periodic schedule. Time becomes a dimension of the code, not just the medium through which the code operates.
The principle extends beyond quantum error correction: any system that cannot afford to verify a complex constraint all at once can decompose verification into a temporal rhythm of simpler checks, accumulating certainty through periodicity rather than demanding it in a single snapshot.
(arXiv:2603.00228)