Strictly Local Tile-Code Architectures on Two-Dimensional Planar Lattices

• URL: http://arxiv.org/abs/2607.05897v1
• Date: Tue, 07 Jul 2026 06:50:27 GMT
• Title: Strictly Local Tile-Code Architectures on Two-Dimensional Planar Lattices
• Abstract summary: Tile codes are a family of planar quantum low-density parity-check (qLDPC) codes with weight-6 stabilizers and open boundary conditions.<n>We show that routed tile codes require fewer physical qubits per logical qubit than the surface code at sufficiently low physical error rates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Tile codes are a family of planar quantum low-density parity-check (qLDPC) codes with weight-6 stabilizers and open boundary conditions, offering an encoding efficiency $kd^2/n$ of up to four times that of the surface code. In this work, we develop an exhaustive search algorithm for finding SWAP-based routing schemes that implement syndrome extraction for four tile-code families using only nearest-neighbor interactions on a two-dimensional square lattice, matching the connectivity of the surface code. Using explicitly constructed routed syndrome-extraction circuits decoded with BP+OSD, we estimate the circuit-level thresholds of these code families. For the SI1000 noise model, the threshold without such a connectivity constraint is obtained in a range 0.23%-0.31%, while it decreases to 0.11%-0.13% with routing, representing a reduction factor of around two to three. Despite this threshold penalty, our resource-footprint analysis shows that routed tile codes require fewer physical qubits per logical qubit than the surface code at sufficiently low physical error rates: Under the SI1000 noise model, we find a crossover near $p^*\approx 0.08\%$, below which routed tile codes become more qubit-efficient, with an advantage that grows monotonically as the physical error rate decreases.

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