Path Optimization in Quantum Networks Using Surface Codes

Surface codes have emerged as a promising approach for protecting quantum information against decoherence in quantum computation and communication. In this paper, we investigate the fundamental problem of path computation in quantum networks where surface codes are systematically employed in quantum information transmission. Specifically, we formulate the problem of finding a min-cost path subject to end-to-end fidelity constraint. The problem is non-trivial as only a subset of nodes in the network can perform coding and decoding operations due to its high cost, adding a combinatorial flavor to it. Our problem being NP-hard, we design an approximation path optimization algorithm by technically employing a discretization scheme allowing to bound the time and space complexity of the algorithm to be polynomial. We also demonstrate the effectiveness of our algorithm via extensive numerical analysis.