Quantum control based on three forms of Lyapunov functions

This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given.

Enhancing quantum metrology for multiple frequencies of oscillating magnetic fields by quantum control

Quantum multi-parameter estimation has recently attracted increased attention due to its wide applications, with a primary goal of designing high-precision measurement schemes for unknown parameters. While existing research has predominantly concentrated on time-independent Hamiltonians, little has been known about quantum multi-parameter estimation for time-dependent Hamiltonians due to the complexity of quantum dynamics. This work bridges the gap by investigating the precision limit of multi-parameter quantum estimation for a qubit in an oscillating magnetic field model with multiple unknown frequencies. As the well-known quantum Cramer–Rao bound is generally unattainable due to the potential incompatibility between the optimal measurements for different parameters, we use the most informative bound instead which is always attainable and equivalent to the Holevo bound in the asymptotic limit. Moreover, we apply additional Hamiltonian to the system to engineer the dynamics of the qubit. By utilizing the quasi-Newton method, we explore the optimal schemes to attain the highest precision for the unknown frequencies of the magnetic field, including the simultaneous optimization of initial state preparation, the control Hamiltonian and the final measurement. The results indicate that the optimization can yield much higher precisions for the field frequencies than those without the optimizations. Finally,we study the robustness of the optimal control scheme with respect to the fluctuation of the interested frequencies, and the optimized scheme exhibits superior robustness to the scenario without any optimization.

Establishing formal state space models via quantization forquantum control systems

Formal state space models of quantum control systems are deduced and a scheme to establish formal state space models via quantization could been obtained for quantum control systems is proposed. State evolution of quantum control systems must accord with Schrdinger equations, so it is foremost to obtain Hamiltonian operators of systems. There are corresponding relations between operators of quantum systems and corresponding physical quantities of classical systems, such as momentum, energy and Hamiltonian, so Schrdinger equation models of corresponding quantum control systems via quantization could been obtained from classical control systems, and then establish formal state space models through the suitable transformation from Schrdinger equations for these quantum control systems. This method provides a new kind of path for modeling in quantum control.

Chaotic state as an output of vacuum state evolving in diffusion channel and generation of displaced chaotic state for quantum controlling

We show that chaotic state can be produced as an output of vacuum state evolving in diffusion channel,while displaced chaotic state is output of a coherent state evolving in diffusion channel.We also introduce the thermo vaccum state for the displaced chaotic state and evaluate the average photon number.The displaced chaotic state may be used exhibiting quantum controlling.

Quantum Control Strategy Based on State Distance

Based on Bures distance, a Lyapunov function that represents the distance between a desired state and the actual state of a quantum system is selected. Considering the cases that an initial state is and is not orthogonal to the desired state respectively, we propose a class of control strategies with state feedback that ensures the stability of the closed-loop control system. Especially, the asymptotic stability of the control system is analyzed, deduced and proved in detail. Finally, a simulation experiment on a spin-1/2 particle system is done and the relation between the system state evolution time and control value is analyzed with diffierent parameters . Research results have general theoretical meaning for control of quantum systems.

Experimental realization of quantum controlled teleportation of arbitrary two-qubit state via a five-qubit entangled state

Quantum controlled teleportation is the transmission of the quantum state under the supervision of a third party.This paper presents the theoretical and experimental results of an arbitrary two-qubit quantum controlled teleportation scheme,in which the sender Alice only needs to perform two Bell state measurements and the receiver Bob can perform an appropriate unitary operation to reconstruct the arbitrary two-qubit states under the control of the supervisor Charlie.The operation process of the scheme is verified on the IBM quantum experience platform,and the accuracy of the transmitted quantum state is further checked by performing quantum state tomography.Meanwhile,a good fidelity is obtained by using the theoretical density matrix and the experimental density matrix.A sequence of photonic states is introduced to analyze the possible intercept-replace-resend,intercept-measure-resend,and entanglement-measure-resend attacks on this scheme.The results proved that our scheme is highly secure.

Optimal and robust control of population transfer in asymmetric quantum-dot molecules

We present an optimal and robust quantum control method for efficient population transfer in asymmetric double quantum-dot molecules.We derive a long-duration control scheme that allows for highly efficient population transfer by accurately controlling the amplitude of a narrow-bandwidth pulse.To overcome fluctuations in control field parameters,we employ a frequency-domain quantum optimal control theory method to optimize the spectral phase of a single pulse with broad bandwidth while preserving the spectral amplitude.It is shown that this spectral-phase-only optimization approach can successfully identify robust and optimal control fields,leading to efficient population transfer to the target state while concurrently suppressing population transfer to undesired states.The method demonstrates resilience to fluctuations in control field parameters,making it a promising approach for reliable and efficient population transfer in practical applications.

Quantum state protection from finite-temperature thermal noise with application to controlled quantum teleportation

We propose a quantum state protection scheme via quantum feedforward control combined with environment-assisted measurement to protect arbitrary unknown initial states from the finite-temperature thermal noise(FTTN).The main strategy is to transfer the quantum system to a noise-robust state by weak measurement and feedforward control before the noise channel.Then we apply the environment-assisted measurement on the noise channel to select our desired damped states that are invertible to the initial state.After the noise channel,the reversal operations are applied to restore the initial state.We consider the protection of a single-qubit system,derive the analytical expressions of the success probability and the fidelity,and analyze the influence of key parameters on the performance of the proposed scheme.Unlike previous studies,there is no trade-off between the fidelity and the success probability in the proposed scheme;hence one could maximize them separately.Simulation results show that the proposed scheme can greatly improve the fidelity of the quantum state with a certain success probability.Moreover,the proposed scheme is successfully applied to improving the fidelity of controlled quantum teleportation through two independent FTTN channels from the perspective of protecting the shared entanglement.

Perfect quantum controlled teleportation via a novel threeparticle partially entangled channel

Recently Li et al. proposed special partially entangled states serving as quantum channel in quantum controlled teleportation, while there are some limitations in their scheme. Based on that, we present a possible improvement in this paper. We construct a novel three-particle partially entangled state which is suitable for perfect controlled teleportation. A simple quantum circuit is designed to obtain this state. We evaluate quantum controlled teleportation from three points of view： teleportation fidelity, success probability and the controller＇s power. Detailed calculations and simulation analyses show that the constructed state is a suitable channel for controlled teleportation of arbitrary qubits, unit teleportation fidelity and 100% success probability can be achieved. Meanwhile, as long as channel＇s entanglement degree equals to or greater than 3/4, the controller＇s power can be guaranteed.

Incoherent control of two classes of finite-level quantum systems

The incoherent control of finite-level quantum systems is investigated. Following a brief introduction to coherent control paradigms in quantum control, a control problem that can not be accomplished using only coherent control is presented. For such a control problem, it is proved that it can be accomplished using incoherent control based on projective measurement and coherent control for two classes of finite-level quantum systems, i.e., eigenstate controllable quantum systems and wavefunction controllable quantum systems.

Experimentally realizing efficient quantum control with reinforcement learning

We experimentally investigate deep reinforcement learning(DRL)as an artificial intelligence approach to control a quantum system.We verify that DRL explores fast and robust digital quantum controls with operation time analytically hinted by shortcuts to adiabaticity.In particular,the protocol’s robustness against both over-rotations and off-resonance errors can still be achieved simultaneously without any priori input.For the thorough comparison,we choose the task as single-qubit flipping,in which various analytical methods are well-developed as the benchmark,ensuring their feasibility in the quantum system as well.Consequently,a gate operation is demonstrated on a trapped^(171) Yb^(+)ion,significantly outperforming analytical pulses in the gate time and energy cost with hybrid robustness,as well as the fidelity after repetitive operations under time-varying stochastic errors.Our experiments reveal a framework of computer-inspired quantum control,which can be extended to other complicated tasks without loss of generality.

Controlling the probability density of quantum systems

A new method to design a quantum controller which directly controls the probability density function（PDF） of quantum systems is proposed.Based on the quantum model from the PDF perspective,two specific control algorithms are proposed with uniform and non-uniform fields,respectively.Then a detailed control algorithm with convergence analysis is given for the small error case.By appropriately estimating the selected Lyapunov function,more accurate control effect is achieved.The proposed scheme provides a constructive method to find appropriate parameters for controller design.

Quantum control with Lyapunov function and bang–bang solution in the optomechanics system

We propose a quantum control scheme with the help of Lyapunov control function in the optomechanics system. The principle of the idea is to design suitable control fields to steer the Lyapunov control function to zero as t → ∞ while the quantum system is driven to the target state. Such an evolution makes no limit on the initial state and one needs not manipulate the laser pulses during the evolution. To prove the effectiveness of the scheme, we show two useful applications in the optomechanics system: one is the cooling of nanomechanical resonator and the other is the quantum fluctuation transfer between membranes. Numerical simulation demonstrates that the perfect and fast cooling of nanomechanical resonator and quantum fluctuation transfer between membranes can be rapidly achieved. Besides, some optimizations are made on the traditional Lyapunov control waveform and the optimized bang–bang control fields makes Lyapunov function V decrease faster. The optimized quantum control scheme can achieve the same goal with greater efficiency. Hence, we hope that this work may open a new avenue of the experimental realization of cooling mechanical oscillator, quantum fluctuations transfer between membranes and other quantum optomechanics tasks and become an alternative candidate for quantum manipulation of macroscopic mechanical devices in the near future.

Optimization Landscape of Quantum Control Systems

Optimization is ubiquitous in the control of quantum dynamics in atomic,molecular,and optical systems.The ease or difficulty of finding control solutions,which is practically crucial for developing quantum technologies,is highly dependent on the geometry of the underlying optimization landscapes.In this review,we give an introduction to the basic concepts in the theory of quantum optimal control landscapes,and their trap-free critical topology under two fundamental assumptions.Furthermore,the effects of various factors on the search effort are discussed,including control constraints,singularities,saddles,noises,and non-topological features of the landscapes.Additionally,we review recent experimental advances in the control of molecular and spin systems.These results provide an overall understanding of the optimization complexity of quantum control dynamics,which may help to develop more efficient optimization algorithms for quantum control systems,and as a promising extension,the training processes in quantum machine learning.

Continuous Controller Design for Quantum Shannon Entropy

This paper proposes the continuous controller design method for quantum Shannon entropy, which can continuously drive the entropy to track a desired trajectory. We also analyzed the controllability of Shannon entropy in very short time interval. Simulations are done on five dimensional quantum system, which can verify the validation of the method.

Comparison of differential evolution, particle swarm optimization,quantum-behaved particle swarm optimization, and quantum evolutionary algorithm for preparation of quantum states

Four intelligent optimization algorithms are compared by searching for control pulses to achieve the preparation of target quantum states for closed and open quantum systems, which include differential evolution(DE), particle swarm optimization(PSO), quantum-behaved particle swarm optimization(QPSO), and quantum evolutionary algorithm(QEA).We compare their control performance and point out their differences. By sampling and learning for uncertain quantum systems, the robustness of control pulses found by these four algorithms is also demonstrated and compared. The resulting research shows that the QPSO nearly outperforms the other three algorithms for all the performance criteria considered.This conclusion provides an important reference for solving complex quantum control problems by optimization algorithms and makes the QPSO be a powerful optimization tool.

The modelling of quantum control systems

High-performance control of quantum dynamics is key to the development of quantum technologies.From quantum-state engineering to quantum metrology,theory and practice of quantum control enable robust and cheaper technologies for future industrial applications.Starting from fundamental matter–field interactions, we overview various approaches to modelling quantum control systems, in which control can be implemented by either changing field or material properties. These models are built in time or frequency domain and can be interconnected to form quantum feedback networks. This review can be taken as a useful reference for engineers to understand the quantum physics behind, or for physicists to resolve control problems from a control engineering point of view.

A controlled quantum teleportation scheme of an N-particle unknown state via three-particle W1 states

In this paper a controlled quantum teleportation scheme of an N-particle unknown state is proposed when N groups of three-particle W1 states are utilized as quantum channels. The quantum information of N-particle unknown state is transmitted from the sender to the recipient under the control of all supervisors. It can be realized with a certain probability. After the sender makes Bell-state measurements and the supervisors perform the computational basis measurements, the recipient will introduce auxiliary particles and carry out unitary transformations depending on classical information from the sender and the supervisors. Finally, the computational basis measurement will be performed by the recipient to confirm whether the teleportation succeeds or not. The successful completion of the scheme relies on all supervisors＇ cooperation. In addition, the fidelity and security of the scheme are discussed.

Fault tolerant controlled quantum dialogue against collective noise

Quantum system is inevitably affected by the external environment in the real world.Two controlled quantum dialogue protocols are put forward based on logicalχ-type states under collective noise environment.One is against collectivedephasing noise,while the other is against collective-rotation noise.Compared with existing protocols,there exist several outstanding advantages in our proposed protocols:Firstly,theχ-type state is utilized as quantum channels,it possesses better entanglement properties than GHZ state,W state as well as cluster state,which make it difficult to be destroyed by local operations.Secondly,two kinds of logicalχ-type states are constructed by us in theory,which can be perfectly immune to the effects of collective noise.Thirdly,the controller can be offline after quantum distribution and permission announcement,without waiting for all the participants to complete the information coding.Fourthly,the security analysis illuminates that our protocols can not only be free from the information leakage,but also resist against the interceptand-resend attack,the entanglement-and-measure attack,the modification attack,the conspiring attack,and especially the dishonest controller’s attacks.

Geometric method in quantum control

In this paper we survey the geometric method in quantum control.By presenting a geometric representation of nonlocal two-qubit quantum operation,we show that the control of two-qubit quantum operations can be reduced to a steering problem in a tetrahedron.Two physical examples are given to illustrate this method.We also provide analytic approaches to construct universal quantum circuit from any arbitrary quantum gate.