High-fidelity teleportation of a logical qubit using transversal gates and lattice surgery.

Quantum state teleportation is commonly used in designs for large-scale quantum computers. Using Quantinuum's H2 trapped-ion quantum processor, we demonstrate fault-tolerant state teleportation circuits for a quantum error correction code-specifically the Steane code. The circuits use up to 30 qubits at the physical level and employ real-time quantum error correction. We conducted experiments on several variations of logical teleportation circuits using both transversal gates and lattice surgery. We measured the logical process fidelity to be 0.975 ± 0.002 for the transversal teleportation implementation and 0.851 ± 0.009 for the lattice surgery teleportation implementation as well as 0.989 ± 0.002 for an implementation of Knill-style quantum error correction.