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.
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.
The control of flying qubits is crucial for the interconnection of quantum information processing units in the future applications. Physically, this class of problems can be modeled by the radiation of optical fields from a standing qubit (natural or artificial atoms). The photon statistics of the output field emitted from a quantum system coupled to multiple waveguides is complicated when the exciton number is not conserved, especially in presence of coherent driving that is crucial for control and optimization. In this paper, we use quantum stochastic differential equation (QSDE) to describe the photon generation process, and derive the dynamical jumps induced by photon emission. Numerical simulations show that this model can be applied to analyze the manipulation process of single qubits.
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.
The flying-qubit control is crucial for quantum information science and technology, and holds significant research importance. This article presents a model for controlling extendable multichannel multiphoton flying qubits when driven simultaneously by non-vacuum inputs and classical fields. The model can be used to describe the generation, reception, conversion, routing, feedback, measurement, and networking of flying qubits with arbitrary wave packets. Unlike traditional approaches that utilize auxiliary systems to represent equivalent non-vacuum inputs, this model is based only on temporal photon number state vectors and quantum stochastic differential equations. Compared with existing relevant conclusions, this model is analogous to path integrals and possesses transient analysis and scalability, which are very useful for understanding and applying quantum control.
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 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 V-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.
Abstract Control of the stochastic dynamics of a quantum system is indispensable in fields such as quantum information processing and metrology. However, there is no general ready-made approach to the design of efficient control strategies. Here, we propose a framework for the automated design of control schemes based on differentiable programming. We apply this approach to the state preparation and stabilization of a qubit subjected to homodyne detection. To this end, we formulate the control task as an optimization problem where the loss function quantifies the distance from the target state, and we employ neural networks (NNs) as controllers. The system’s time evolution is governed by a stochastic differential equation (SDE). To implement efficient training, we backpropagate the gradient information from the loss function through the SDE solver using adjoint sensitivity methods. As a first example, we feed the quantum state to the controller and focus on different methods of obtaining gradients. As a second example, we directly feed the homodyne detection signal to the controller. The instantaneous value of the homodyne current contains only very limited information on the actual state of the system, masked by unavoidable photon-number fluctuations. Despite the resulting poor signal-to-noise ratio, we can train our controller to prepare and stabilize the qubit to a target state with a mean fidelity of around 85%. We also compare the solutions found by the NN to a hand-crafted control strategy.