Abstract
Quantum state teleportation is commonly used in designs for large scale fault-tolerant quantum computers such as for teleporting states across modules, code switching, and to implement certain forms of QEC. Using the Quantinuum H2 quantum processor, we implement the first demonstration of a fully fault-tolerant state teleportation circuit. Encoding the circuit in the [[7,1,3]] Steane quantum error correction code (or 2D topological color code), we examine different circuit designs for implementing different fault-tolerant protocols, including the use of a QEC gadget (i.e., syndrome extraction), and investigate different methods for implementing logical operations within this logical teleportation circuit - utilizing as many as 30 physical qubits. Further, these implementations utilize both real-time decoding and adaptive syndrome extraction, important ingredients for running general logical algorithms in future large-scale fault-tolerant devices. By teleporting the six eigenstates of the three single-qubit logical Pauli operators, we estimate the process fidelity.