Swap Across a Gap

On a linear three-qubit chip the outer qubits cannot talk directly, and the device has no native SWAP. Exchange them anyway, and leave the middle qubit exactly as you found it.

Objective

Return a three-qubit circuit whose unitary equals SWAP(q0, q2) with q1 unchanged.

Constraints

• Allowed gates: cx.
• CX only between (0, 1) or (1, 2).
• At most 9 CX gates.

Entry Point

Checks

• Exports swap_ends().
• Uses at most 9 nearest-neighbour CX gates.
• The unitary equals SWAP(q0, q2).