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.

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.

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.

Simulations of superconducting quantum gates by digital flux tuner for qubits

The interconnection bottleneck caused by limitations of cable number, inner space and cooling power of dilution refrigerators has been an outstanding challenge for building scalable superconducting quantum computers with the increasing number of qubits in quantum processors. To surmount such an obstacle, it is desirable to integrate qubits with quantum–classical interface(QCI) circuits based on rapid single flux quantum(RSFQ) circuits. In this work, a digital flux tuner for qubits(DFTQ) is proposed for manipulating flux of qubits as a crucial part of the interface circuit. A schematic diagram of the DFTQ is presented, consisting of a coarse tuning unit and a fine-tuning unit for providing magnetic flux with different precision to qubits. The method of using DFTQ to provide flux for gate operations is discussed from the optimization of circuit design and input signal. To verify the effectiveness of the method, simulations of a single DFTQ and quantum gates including a Z gate and an iSWAP gate with DFTQs are performed for flux-tunable transmons. The quantum process tomography corresponding to the two gates is also carried out to analyze the sources of gate error. The results of tomography show that the gate fidelities independent of the initial states of the Z gate and the iSWAP gate are 99.935% and 99.676%,respectively. With DFTQs inside, the QCI would be a powerful tool for building large-scale quantum computers.

Balancing the minimum error rate and minimum copy consumption in quantum state discrimination

Extracting more information and saving quantum resources are two main aims for quantum measurements.However,the optimization of strategies for these two objectives varies when discriminating between quantum states■and■through multiple measurements.In this study,we introduce a novel state discrimination model that reveals the intricate relationship between the average error rate and average copy consumption.By integrating these two crucial metrics and minimizing their weighted sum for any given weight value,our research underscores the infeasibility of simultaneously minimizing these metrics through local measurements with one-way communication.Our findings present a compelling trade-off curve,highlighting the advantages of achieving a balance between error rate and copy consumption in quantum discrimination tasks,offering valuable insights into the optimization of quantum resources while ensuring the accuracy of quantum state discrimination.

DIRECT SELF-REPAIRING CONTROL FOR HELICOPTER VIA QUANTUM CONTROL AND ADAPTIVE COMPENSATOR

A direct self-repairing control approach is proposed for helicopter via quantum control techniques and adaptive compensator when some complex faults occur. For a linear varying-parameter helicopter control system, the model reference adaptive control law is designed and an adaptive compensator is used for improving its self-re- pairing capability. To enhance anti-interference capability of helicopter, quantum control feedforward is added be- tween fault and disturbance. Simulation results illustrate the effectiveness and feasibility of the approach.

Hamiltonian Reduction of Quantum Systems Controlled by Pulses

We explores Hamiltonian reduction in pulse-controlled finite-dimensional quantum systems with near-degenerate eigenstates. A quantum system with a non-degenerate ground state and several near-degenerate excited states is controlled by a short pulse, and the objective is to maximize the collective population on all excited states when we treat all of them as one level. Two cases of the systems are shown to be equivalent to effective two-level systems. When the pulse is weak, simple relations between the original systems and the reduced systems are obtained. When the pulse is strong, these relations are still available for pulses with only one frequency under the first-order approximation.

Controlled Secure Quantum Dialogue Using a Pure Entangled GHZ States

We present a controlled secure quantum dialogue protocol using a non-maximally （pure） entangled Greenberger-Horne-Zeibinger （GHZ） states at first, and then discuss the requirements for a real quantum dialogue. We show that the authorized two users can exchange their secret messages after purifying the non-maximally entangled GHZ states quantum channel unconditionally securely and simultaneously under the control of a third party.

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.

Controlled Quantum Teleportation of a One-Particle Unknown State via a Three-Particle Entangled State

A kind of three-particle entangled state is applied as quantum channel of the controlled quantum teleporration of a one-particle unknown state. The one-particle unknown state is transmitted from the sender to the recipient under the control of the supervisor. After the sender makes Bell-state measurement and the supervisor performs von Neumann measurement, the recipient carries out unitary transformation on his own particle depending on classical information from the sender and the supervisor. The teleportation cannot be completed successfully by the recipient if the supervisor does not agree to cooperate. The roles of the recipient and the supervisor may be exchanged in this scheme. The scheme is flexible and feasible because the sequence of manipulation of the sender and the supervisor may be exchanged and only simple unitary transformation is included.

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.

Analysis and Improvement of an Efficient Controlled Quantum Secure Direct Communication and Authentication Protocol

The controlled quantum secure direct communication(CQSDC)with authentication protocol based on four particle cluster states via quantum one-time pad and local unitary operations is cryptanalyzed.It is found that there are some serious security issues in this protocol.An eavesdropper(Eve)can eavesdrop on some information of the identity strings of the receiver and the controller without being detected by the selective-CNOT-operation(SCNO)attack.By the same attack,Eve can also steal some information of the secret message that the sender transmits.In addition,the receiver can take the same kind of attack to eavesdrop on some information of the secret message out of the control of the controller.This means that the requirements of CQSDC are not satisfied.At last,we improve the original CQSDC protocol to a secure one.

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.

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.

Controlled Teleportation of Multi-qudit Quantum Information by Entanglement Swapping

In this paper, we present a scheme for teleporting multi-qudit quantum state, from the sender Alice to the receiver Charlie via many controllers Bobs, whose control parameters are obtained using entanglement swapping of maximally d-dimensional EPR pair. In our scheme, Yang＇s qutrit controlled teleportation protocol [Commun. Theor. Phys. 49 （2008） 338] based on Bell-state entanglement swapping is generalized to the qudit case. The scheme of multi-qudit owns the advantage of having higher code capacity and better security than that of multi-qutrit.

Controlled Quantum Network Coding Without Loss of Information

Quantum network coding is used to solve the congestion problem in quantum communication,which will promote the transmission efficiency of quantum information and the total throughput of quantum network.We propose a novel controlled quantum network coding without information loss.The effective transmission of quantum states on the butterfly network requires the consent form a third-party controller Charlie.Firstly,two pairs of threeparticle non-maximum entangled states are pre-shared between senders and controller.By adding auxiliary particles and local operations,the senders can predict whether a certain quantum state can be successfully transmitted within the butterfly network based on the Z-{10>,|1>}basis.Secondly,when trans-mission fails upon prediction,the quantum state will not be lost,and it will sill be held by the sender.Subsequently,the controller Charlie re-prepares another three-particle non-maximum entangled state to start a new round.When the predicted transmission is successful,the quantum state can be transmitted successfully within the butterfly network.If the receiver wants to receive the effective quantum state,the quantum measurements from Charlie are needed.Thirdly,when the transmission fails,Charlie does not need to integrate the X-{1+>,1->}basis to measure its own particles,by which quantum resources are saved.Charlie not only controls the effective transmission of quantum states,but also the usage of classical and quantum channels.Finally,the implementation of the quantum circuits,as well as a flow chart and safety analysis of our scheme,is proposed.

Probabilistic and controlled teleportation of tripartite state in a general form and its quantum networks

We discuss a scheme for probabilistic and controlled teleportation of an unknown arbitrary three-particle state by constructing a peculiar non-maximally entangled state as a controlled quantum channel, which is teleported between two sides with the help of the auxiliary particle and the cooperation of the third side （Charlie） as a supervisor. In comparison with some existing schemes, on the receiver＇s side it is easy to have the sender＇s state through operating two uniform unitary transformations in turn. In addition, we also give an efficient quantum network for implementing the new scheme by means of some primitive operations.

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.

Controlled remote implementation of quantum operations with high-dimensional systems

We present two protocols for the controlled remote implementation of quantum operations between three-party high-dimensional systems. Firstly, the controlled teleportation of an arbitrary unitary operation by bidirectional quantum state teleportaion （BQST） with high-dimensional systems is considered. Then, instead of using the BQST method, a protocol for controlled remote implementation of partially unknown operations belonging to some restricted sets in high-dimensional systems is proposed. It is shown that, in these protocols, if and only if the controller would like to help the sender with the remote operations, the controlled remote implementation of quantum operations for high-dimensional systems can be completed.