Optimal Control of Flying Qubits

The transmission of flying qubits carried by itinerant photons is ubiquitous in quantum communication networks. In addition to their logical states, the temporal/frequency profiles of flying qubits must also be tailored into proper shapes to match remote receiver qubits. In this talk, we report a general framework for optimal control of flying qubits. The framework is based on quantum stochastic differential equations (QSDEs) that describe the flying qubit input-output relations actuated by a standing quantum system (e.g., a superconducting qubit or quantum dot). Under the continuous time-ordered photon-number basis, the infinite-dimensional QSDE is reduced to a system of low-dimensional deterministic ordinary differential equations for the non-unitary state evolution of the standing quantum system, and the outgoing flying qubit states can be calculated in the form of randomly occurring quantum jumps. This makes it possible to analyze general cases when the number of excitations is not reserved. The proposed framework lays the foundation for the design of flying-qubit control systems from an optimal control point of view, within which advanced optimal control techniques can be incorporated for practical applications. Some examples, such as the generation, catching and steering of flying photons by two- or three-level artificial atoms, are studied.

[1] Wenlong Li, Guofeng Zhang, and Re-bing Wu, On the control of flying qubits, Automatica, 143:110338, 2022. [2] Wenlong Li, Xue Dong, Guofeng Zhang, and Re-bing Wu, Flying-qubit control via a three-level atom with tunable waveguide, Physical Review B, 106:134305, 2022. [3] Xue Dong, Guofeng Zhang, and Re-bing Wu, Optimal control of flying-qubit generation, 2023.