Teleporting two-qubit entanglement across 19 qubits on a superconducting
  quantum computer
Quantum teleportation is not merely a fascinating corollary of quantum
entanglement, it also finds utility in quantum processing and circuit
compilation. In this paper, we measure and track the entanglement and fidelity
of two-qubit states prepared on a 127-qubit IBM Quantum device, as one of the
qubits is teleported across 19 qubits. We design, evaluate and compare two
distinct approaches to teleportation: post-selected measurement categorisation
and dynamic circuit corrections based on mid-circuit measurements, and compare
with direct state transportation using SWAP gates. By optimally choosing the
teleportation path which exhibits the highest total negativity entanglement
measure across nearest-neighbour pairs, we show the entanglement of a two-qubit
graph state is sustained after at least 19 hops in teleportation using the
post-selection approach and 17 hops using the dynamic circuit approach. We
observe a higher level of teleported entanglement in paths determined from
two-qubit negativities compared to those obtained from gate errors,
demonstrating an advantage in using the negativity map over the gate error map
for compiling quantum circuits.
Haiyue Kang John F. Kam Gary J. Mooney Lloyd C. L. Hollenberg