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arXiv:2404.09487 · Physical Review Applied

Quantum optimal control theory for the shaping of flying qubits

Xue Dong, Xi Cao, Wenlong Li, Guofeng Zhang, Zhihui Peng, Re-Bing Wu

Published Apr 21, 2025• 4 citations
arXivHTMLPDF

Abstract

The control of flying qubits carried by itinerant photons is ubiquitous in quantum networks. In addition to their logical states, the shapes 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 nonidealities. 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.

DOI
10.1103/physrevapplied.23.044045

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The control of flying qubits carried by itinerant photons is ubiquitous in quantum networks. In addition to their logical states, the shapes 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 nonidealities. 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.
The transmission of flying qubits carried by itinerant photons is fundamental in quantum communication networks. To physically match the receiver system, the single photons must be prepared in proper shapes, and this leads to a variety of flying-qubit control problems. In this paper, we introduce the optimal control theory to the shaping of single photons, where the control to be optimized are coherent driving fields. We design gradient-based algorithms to minimize the shape difference between the emitted and desired single photons. Simulation results show that the optimization can achieve high-fidelity in the generation of decaying photon shapes with a two-level atom. However, its performance is limited and hence has to be combined with incoherence controls when the target shape has a rising part.
The control of flying qubits is at the core of quantum networks. When the flying qubits are carried by single-photon fields, the control involves not only their logical states but also their shapes. In this paper we explore a variety of flying-qubit control problems using a three-level atom with time-varying tunable couplings to two input-output channels. It is shown that one can tune the couplings of a $\mathrm{\ensuremath{\Lambda}}$-type atom to distribute a single photon into the two channels with arbitrary shapes, or use a $\mathrm{\ensuremath{\Lambda}}$-type atom or a VVV-type atom to catch an arbitrary-shape distributed single photon. The $\mathrm{\ensuremath{\Lambda}}$-type atom can also be designed to transfer a flying qubit from one channel to the other, with both the central frequency and the photon shape being converted. With a $\mathrm{\ensuremath{\Xi}}$-type atom, one can shape a pair of correlated photons via cascaded emission. In all cases, analytical formulas are derived for the coupling functions to fulfill these control tasks. Their correlation properties and physical limitations are discussed as well. These results provide useful control protocols for high-fidelity quantum information transmission over complex quantum networks.
The control of flying quantum bits (qubits) carried by traveling quantum fields is crucial for coherent information transmission in quantum networks. In this paper, we develop a general framework for modeling the generation, catching and transformation processes of flying qubits. We introduce the quantum stochastic differential equation (QSDE) to describe the flying-qubit input-output relations actuated by a standing quantum system. Under the continuous time-ordered photon-number basis, the infinite-dimensional QSDE is reduced to a low-dimensional deterministic non-unitary differential equation for the state evolution of the standing system, and the outgoing flying-qubit states can be calculated via randomly occurring quantum jumps. This makes it possible, as demonstrated by examples of flying-qubit generation and transformation, 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 a control theoretic point of view, within which advanced control techniques can be incorporated for practical applications.
We present a scheme of control for the arbitrary interplay between a stationary qubit and a flying qubit (carried by a single-photon wavepacket) at a quantum interface composed of a three-level system coupled to a continuum through a cavity. It can be used for generation or reception of an arbitrarily shaped single-photon wavepacket. The generation process can also be controlled to create entanglement between the stationary qubit and flying qubit. The generation and reception operation can be combined to perform quantum network operations such as transfer, swap and entanglement creation for qubits at distant nodes.
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Flying qubit is one type of the basic elements for transmitting quantum information in quantum networks. It can serve as a communication link between quantum computer nodes and represents a vital part of secure data transmission. For high-fidelity information transmission, precise control of flying qubit is highly demanded. Here, based on quantized photons or phonons as the carriers of the flying qubit, we review the basics and the progress of the flying-qubit control in both theoretical and experimental aspects. The flying-qubit control system can be regarded as an open quantum system with N energy levels coupled with multiple quantum channels. Its input includes classical components, such as coherent or incoherent control functions, as well as quantum components, but its output only includes quantum components, and the system is affected by environmental noise. According to the characteristics of quantum input and quantum output fields, the flying-qubit control problems can be divided into 3 categories: generation, reception, and conversion. From a theoretical perspective, the different modeling approaches of the flying-qubit control are discussed and compared, including the master equation, the quantum trajectory, the scattering matrix, the quantum stochastic differential equation, and the quantum Langevin equation. Considering both control design schemes and experimental perspectives, various control strategies and experimental progress have been thoroughly discussed and analyzed. The applications and future directions of flying-qubit control are discussed. The realization of flying qubits plays a vital role in application scenarios such as quantum coherent interconnection, the construction of large-scale quantum chips with a large number of bits, and the link between computers and communication networks.