Fault-tolerant demonstration of single-round walking-qubit motion

Demonstrate that a single-round walking-qubit schedule, moving a surface-code patch by one patch width per logical round, constitutes a fault-tolerant protocol.

Background

Walking qubits enable surface-code patches to slide across a lattice by shifting the stabilizer-measurement schedule. The paper distinguishes between a two-round-per-patch-width rate established by McEwen et al. and a faster one-round rate suggested by a construction based on the Y basis. RushHour assumes the faster rate for its primary evaluation, while also reporting sensitivity results at the proven two-round rate.

The unresolved issue is whether the single-round schedule can be implemented as a fault-tolerant protocol. Establishing this would validate the principal motion-rate assumption underlying RushHour’s most efficient dynamic lattice reconfigurations.

References

McEwen et al. establish walking at one patch width per two logical rounds, while a single-round schedule is conjectured from the $Y$-basis construction of but not yet demonstrated as a fault-tolerant protocol.

— RushHour: A Dynamically Reconfigurable Lattice-Surgery Architecture  (2608.18985 - Tornow et al., 19 Aug 2026) in Section 2, subsection “Walking Qubits” (Section 2.3)