Spooky action nearby: Entangling logical qubits without physical operations

Logical entangling gates on quantum computers are expensive, requiring many noisy physical operations. Phantom codes are a new class of quantum error-correcting codes that enable logical entanglement between qubits through physical qubit permutations alone, achieving zero overhead and perfect fidelity. These codes can be implemented by simply relabeling measurement outcomes rather than executing physical gates. Research identifies hundreds of thousands of phantom codes and demonstrates they can outperform surface codes by one to two orders of magnitude for entanglement-heavy tasks like GHZ-state preparation and many-body simulation, though with tradeoffs in stabilizer weight and qubit count.