High-fidelity and Fault-tolerant Teleportation of a Logical Qubit using Transversal Gates and Lattice Surgery on a Trapped-ion Quantum Computer

TL;DR

This paper demonstrates fault-tolerant quantum state teleportation of a logical qubit on a trapped-ion quantum computer using error correction, transversal gates, and lattice surgery, achieving high process fidelities.

Contribution

First implementation of fault-tolerant logical qubit teleportation using a trapped-ion quantum processor with real-time error correction and multiple protocols.

Findings

Logical teleportation process fidelity: 0.975(2)

Lattice surgery teleportation fidelity: 0.851(9)

Knill-style error correction fidelity: 0.989(2)

Abstract

Quantum state teleportation is commonly used in designs for large-scale fault-tolerant quantum computers. Using Quantinuum's H2 trapped-ion quantum processor, we implement the first demonstration of a fault-tolerant state teleportation circuit for a quantum error correction code - in particular, the planar topological [[7,1,3]] color code, or Steane code. The circuits use up to 30 trapped ions at the physical layer qubits and employ real-time quantum error correction - decoding mid-circuit measurement of syndromes and implementing corrections during the protocol. We conduct experiments on several variations of logical teleportation circuits using both transversal gates and lattice surgery protocols. Among the many measurements we report on, we measure the logical process fidelity of the transversal teleportation circuit to be 0.975(2) and the logical process fidelity of the lattice surgery teleportation circuit to be 0.851(9). Additionally, we run a teleportation circuit that is equivalent to Knill-style quantum error correction and measure the process fidelity to be 0.989(2).