Trapped Ion Quantum Repeaters with Entanglement Distillation based on Quantum LDPC Codes

Quantum repeaters are essential to realizing long-range entanglement distribution networks. To achieve enhanced rates of high-fidelity entanglement distribution, we investigate how entanglement distillation can be used on trapped-ion-based quantum repeater networks. Entanglement distillation is the process of distilling from a large number of copies of low-fidelity entangled qubits a fewer number of copies of higher-fidelity entangled qubits. It has been shown that quantum error-correcting codes (QECCs) can be used to devise protocols for entanglement distillation. In this paper, we consider entanglement distillation based on three lifted-product (LP) quantum low density parity check (QLPDC) codes ([[544, 80, 12], [[714, 100, 16]], and [20, 10, 136, 20]) on trapped-ion repeater networks with spatial and time multiplexing over various total distances with different inter-repeater spacing to calculate the end-to-end entanglement rates that they enable. The reported rates assume entanglement over each elementary link succeeds synchronously and do not assume any constraint on the number of ions present in each trap. We furthermore assume that distillation occurs at every elementary link and that the entanglement swaps are ideal. Our findings can be considered as groundwork for implementing more efficient distillation and communication protocols on trapped ion networks.