Assessing Teleportation of Logical Qubits in a Distributed Quantum Architecture under Error Correction

Abstract

Quantum computing is facing challenges in terms of scaling to thousands of qubits and implementing quantum error correction (QEC). Scaling efforts focus on connecting multiple smaller quantum devices (nodes) in a distributed manner. Non-local CNOTs and teleportation of quantum states become important operations as they enable computation between different nodes in a distributed architecture. For physical qubits, today's high quantum network noise rates prevent the execution of distributed operations with useful accuracy. By employing QEC, we show that non-local operations and teleportation of logical qubits between nodes are feasible under Surface Code and qLDPC encodings with very low logical error rates (LER), even with network noise in near-term regimes. We use circuit-level simulations to assess physical and network noise regimes ranging from $10^{-1}$ to $10^{-6}$. This is a wider range than typically studied in circuit level simulations, understanding the behavior of QEC codes in these regimes is necessary for achieving accurate computation. Our simulations give evidence that transversal distributed operations may carry significantly lower LER than lattice surgery. Importantly, we also find that the LER of our distributed operations decreases exponentially as QEC code distance increases, proving the feasibility of executing large algorithms on distributed quantum computers. Our results indicate that non-local CNOTs can be carried out with a logical error rate of $10^{-12}$ for a physical error rate of $10^{-3}$ and ebit noise of $10^{-2}$. Teleportations realized with the same logical error rate under a physical error rate of $3 \times 10^{-4}$ and ebit noise of $3 \times 10^{-3}$.