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Edge-Disjoint Path Teleportation Escape

Claim/Theorem

Beverland, Kliuchnikov, and Schoute show that in a surface-code architecture one can prepare many long-range Bell pairs on qubits connected by edge-disjoint ancilla paths in constant depth, and use them to implement many parallel long-range Clifford operations in constant depth. Their edge-disjoint path compilation algorithm therefore outperforms purely SWAP-based compilation for parallel long-range operations and gives a concrete teleportation-style escape from naive routing barriers.

Dependencies

  • None.

Conflicts/Gaps

  • The result is about surface-code compilation of logical operations, not direct syndrome extraction for an expander-style QLDPC family.
  • The resource that breaks the SWAP-only barrier is explicit long-range Bell-pair generation along ancilla paths, i.e. teleportation-style nonlocality rather than nearest-neighbor SWAP routing.
  • This node is a boundary marker for Conjecture 3, not evidence against the direct static-grid lower bound.

Sources

  • 10.1103/PRXQuantum.3.020342
  • 10.48550/arXiv.2110.11493