Quantum Optimal Control Theory for the Shaping of Flying Qubits

TL;DR

This work addresses shaping flying qubits carried by itinerant photons in quantum networks when emitters and couplers are non-ideal. It develops a quantum optimal control framework that jointly optimizes incoherent and coherent controls ($\gamma(t)$ and $u(t)$) to tailor the photon waveform $\xi(t)$ and the vacuum amplitude $\xi^{(0)}$, using three objective functionals for standing-qubit preparation, direct generation, and emitter-to-qubit state transfer. Numerical results show that gradient-based optimization can reduce photon leakage and level leakage, with substantial gains when a tunable coupler is combined with coherent control; in particular, fidelities around 99.4% are achieved in standing-state preparation, and joint optimization with a tunable coupler can push shaping errors down from roughly 0.11 to 0.03. This framework provides a systematic, device-realist approach to high-quality flying-qubit control and can be extended to more complex emitters, multi-channel setups, and robust optimization strategies for practical quantum networks.

Abstract

The control of flying qubits carried by itinerant photons is ubiquitous in quantum networks. Beside their logical states, the shape of flying qubits must also be tailored for high-efficiency information transmission. In this paper, we introduce quantum optimal control theory to the shaping of flying qubits. Building on the flying-qubit control model established in our previous work, we design objective functionals for the generation of shaped flying qubits under practical constraints on the emitters and couplers. Numerical simulations employing gradient-descent algorithms demonstrate that the optimized control can effectively mitigate unwanted level and photon leakage caused by these non-idealities. Notably, while coherent control offers limited shaping capacity with a fixed coupler, it can significantly enhance the shaping performance when combined with a tunable coupler that has restricted tunability. The proposed optimal control framework provides a systematic approach to achieving high-quality control of flying qubits using realistic quantum devices.

Figures (8)

• Figure 1: Schematics of a microwave flying-qubit emitter implemented by a transmon qubit. The emitter is inductively coupled to a transmission-line waveguide through a tunable gmon coupler. The transmon-qubit is frequency tunable by the $Z$ control and its state can be coherently manipulated by the microwave $XY$ driving field.
• Figure 2: (a) The amplitude of the Gaussian $\pi$-pulse, the DRAG pulse and the optimized control pulses subject to objective functionals $J_1^{\rm ME}$and$J_1^{\rm QSDE}$; (b) the fidelity of the transmon-qubit being in the target state $\ket{1}$ during the control process.
• Figure 3: (a) The photon leakage $1-|\xi^{(0)}|^2$ and (b) the level leakage (total population $P_2+P_3+P_4$ of non-computational states $\ket{2}$, $\ket{3}$ and $\ket{4}$) during the state preparation.
• Figure 4: The optimized shapes of single-photon components under coherent driving control and fixed coupling strength $\gamma_c=2\pi\times 6$MHz, where the target single-photon shapes are exponentially decaying, symmetric and exponentially rising, respectively, with $\alpha=2\pi\times 6$MHz.
• Figure 5: The best performance achieved by coherent control for different types of single-photon shapes under different values of $\alpha$ ranging from $0.4\gamma_c$ to $1.6\gamma_c$