Modeling of decoherence and fidelity enhancement during transport of entangled qubits

Entangled qubits transported through space is a key element in many prospective quantum information systems, from long-distance quantum communication to large modular quantum processors. The moving qubits are decohered by time- and space-dependent noises with finite extent of correlations. Since the qubit paths are interrelated, the phase fluctuations experienced by the qubits exhibit peculiar correlations, which are difficult to analyze with the conventional theory of random processes. We propose an approach to this problem based on the concept of trajectories on random sheets. We establish its efficacy with a specific example of the electron spins shuttled in semiconductor structures, and derive explicit solutions, revealing the role of unusual noise correlations. We also demonstrate how the analysis of noise correlations can enhance the shuttling fidelity, by studying transport of two entangled spins encoding a logical qubit. The proposed approach enabled us to specify the favorable conditions for this encoding, and find a particularly beneficial shuttling regime. We also describe application of this approach to other shuttling scenarios, and explain its utility for analysis of other types of systems, such as atomic qubits and photons in quantum networks.