We investigate dynamical quantum phase transitions(DQPTs)in Marko-vian open quantum systems using a variational quantum simulation(VQS)algorithm based on quantum state diffusion(QSD).This approach reformulates the Lin...We investigate dynamical quantum phase transitions(DQPTs)in Marko-vian open quantum systems using a variational quantum simulation(VQS)algorithm based on quantum state diffusion(QSD).This approach reformulates the Lindblad master equation as an ensemble of pure-state trajectories,enabling efficient simula-tion of dissipative quantum dynam-ics with effectively reduced quantum resources.Focusing on the one-di-mensional transverse-field Ising mod-el(TFIM),we simulate quench dynamics under both local and global Lindblad dissipation.The QSD-VQS algorithm accurately captures the nonanalytic cusps in the Loschmidt rate function,and reveals their modulation by dissipation strength and system size.Notably,DQPTs are gradually suppressed under strong local dissipation,while they persist under strong global dissipation due to collective environmental effects.Benchmarking against exact Lindblad solutions confirms the high accuracy and scalability of our method.展开更多
Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space devel...Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.展开更多
By casting evolution to the Bloch sphere, the dynamics of 2 × 2 matrix non-Hermitian systems are investigated in detail. This investigation reveals that there are four kinds of dynamical modes for such systems. T...By casting evolution to the Bloch sphere, the dynamics of 2 × 2 matrix non-Hermitian systems are investigated in detail. This investigation reveals that there are four kinds of dynamical modes for such systems. The different modes are classified by different kinds of fixed points, namely,the elliptic point, spiral point, critical node, and degenerate point. The Hermitian systems and the unbroken PT non-Hermitian cases belong to the category with elliptic points. The degenerate point just corresponds to the systems with exceptional point(EP). The topological properties of the fixed point are also discussed. It is interesting that the topological charge for the degenerate point is two, while the others are one.展开更多
The task to estimate all the parameters of an unknown quantum state, also called quantum state tomography, is essential for characterizing and controlling quantum systems. In this paper, we utilize observable time tra...The task to estimate all the parameters of an unknown quantum state, also called quantum state tomography, is essential for characterizing and controlling quantum systems. In this paper, we utilize observable time traces to identify the initial quantum state of a closed quantum system, based on the state space approach in the control theory. In the informationally complete scenario, we show that with a linear regression estimation (LRE), the mean squared error (MSE) scales as , where N is the resource number. In the informationally incomplete scenario, we introduce regularization LRE to perform the state tomography task. We employ PBH test to demonstrate that closed quantum systems with only one observable are informationally incomplete and propose using observables, where d is the dimension of the quantum state, for informational completeness. Numerical examples demonstrate the effectiveness of our method.展开更多
For the n-qubit stochastic open quantum systems,based on the Lyapunov stability theorem and LaSalle’s invariant set principle,a pure state switching control based on on-line estimated state feedback(short for OQST-SF...For the n-qubit stochastic open quantum systems,based on the Lyapunov stability theorem and LaSalle’s invariant set principle,a pure state switching control based on on-line estimated state feedback(short for OQST-SFC)is proposed to realize the state transition the pure state of the target state including eigenstate and superposition state.The proposed switching control consists of a constant control and a control law designed based on the Lyapunov method,in which the Lyapunov function is the state distance of the system.The constant control is used to drive the system state from an initial state to the convergence domain only containing the target state,and a Lyapunov-based control is used to make the state enter the convergence domain and then continue to converge to the target state.At the same time,the continuous weak measurement of quantum system and the quantum state tomography method based on the on-line alternating direction multiplier(QST-OADM)are used to obtain the system information and estimate the quantum state which is used as the input of the quantum system controller.Then,the pure state feedback switching control method based on the on-line estimated state feedback is realized in an n-qubit stochastic open quantum system.The complete derivation process of n-qubit QST-OADM algorithm is given;Through strict theoretical proof and analysis,the convergence conditions to ensure any initial state of the quantum system to converge the target pure state are given.The proposed control method is applied to a 2-qubit stochastic open quantum system for numerical simulation experiments.Four possible different position cases between the initial estimated state and that of the controlled system are studied and discussed,and the performances of the state transition under the corresponding cases are analyzed.展开更多
We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dyna...We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dynamical semigroups. Our findings reveal that the measures of quantumness for the asymptotic states rely on the primary parameter of the quantum model. Furthermore, control over these measures can be achieved through a careful selection of these parameters. Our analysis encompasses various cases, including Bell states, Werner states, and Horodecki states, demonstrating that the asymptotic states can exhibit steering, entanglement, and Bell nonlocality. Additionally, we find that these three quantum measures of correlations can withstand the influence of the environment, maintaining their properties even over extended periods.展开更多
Counterdiabatic driving (CD) offers a fast and robust route to manipulate quantum systems, which has widespreadapplications in quantum technologies. However, for higher-dimensional complex systems, the exact CD term i...Counterdiabatic driving (CD) offers a fast and robust route to manipulate quantum systems, which has widespreadapplications in quantum technologies. However, for higher-dimensional complex systems, the exact CD term involving thespectral properties of the system is difficult to calculate and generally takes a complicated form, impeding its experimentalrealization. Recently, many approximate methods have been proposed for designing CD passages in many-body systems. Inthis topical review, we focus on the CD formalism and briefly introduce several experimental constructions and applicationsof approximate CD driving in spin-chain models with nuclear magnetic resonance (NMR) systems.展开更多
The application of the eigenstate thermalization hypothesis to non-Hermitian quantum systems has become one of the most important topics in dissipative quantum chaos, recently giving rise to intense debates. The proce...The application of the eigenstate thermalization hypothesis to non-Hermitian quantum systems has become one of the most important topics in dissipative quantum chaos, recently giving rise to intense debates. The process of thermalization is intricate, involving many time-evolution trajectories in the reduced Hilbert space of the system. By considering two different expansion forms of the density matrices adopted in the biorthogonal and right-state time evolutions, we derive two versions of the Gorini–Kossakowski–Sudarshan–Lindblad(GKSL)master equations describing the non-Hermitian systems coupled to a bosonic heat bath in thermal equilibrium. By solving the equations, we identify a sufficient condition for thermalization under both time evolutions, resulting in Boltzmann biorthogonal and right-eigenstate statistics, respectively. This finding implies that the recently proposed biorthogonal random matrix theory needs an appropriate revision. Moreover, we exemplify the precise dynamics of thermalization and thermodynamic properties with test models.展开更多
The capacity to extract work from a quantum heat machine is not only of practical value but also lies at the heart of understanding quantum thermodynamics.In this paper,we investigate optimal work extraction for quant...The capacity to extract work from a quantum heat machine is not only of practical value but also lies at the heart of understanding quantum thermodynamics.In this paper,we investigate optimal work extraction for quantum systems with work storage,where extracting work is completed by a unitary evolution on the composite system.We consider the physical requirement of energy conservation both strictly and on average.For both,we construct their corresponding unitaries and propose variational quantum algorithms for optimal work extraction.We show that maximal work extraction in general can be feasible when energy conservation is satisfied on average.We demonstrate with numeral simulations using a continuous-variable work storage.Our work show an implementation of a variational quantum computing approach for simulating work extraction in quantum systems.展开更多
In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First,...In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation.Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.展开更多
To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the tim...To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.展开更多
In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from ...In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.展开更多
We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities .in isolated quantum Hamiltonian sys- tems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks ...We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities .in isolated quantum Hamiltonian sys- tems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some resultsare given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.展开更多
For an N-dimensional quantum system under the influence of continuous measurement, this paper presents a switching control scheme where the control law is of bang-bang type and achieves asymptotic preparation of an ar...For an N-dimensional quantum system under the influence of continuous measurement, this paper presents a switching control scheme where the control law is of bang-bang type and achieves asymptotic preparation of an arbitrarily given eigenstate of a non-degenerate and degenerate measurement operator, respectively. In the switching control strategy, we divide the state space into two parts： a set containing a target state, and its complementary set. By analyzing the stability of the stochastic system model under consideration, we design a constant control law and give some conditions that the control Hamiltonian satisfies so that the system trajectories in the complementary set converge to the set which contains the target state. Further, for the case of a non-degenerate measurement operator, we show that the system trajectories in the set containing the target state will automatically converge to the target state via quantum continuous measurement theory; while for the case of a degenerate measurement operator, the corresponding system trajectories will also converge to the target state via the construction of the control Hamiltonians. The convergence of the whole closed-loop systems under the cases of a non-degenerate and a degenerate measurement operator is strictly proved. The effectiveness of the proposed switching control scheme is verified by the simulation experiments on a finite-dimensional angular momentum system and a two-qubit system.展开更多
We report a design and implementation of a field-programmable-gate-arrays(FPGA)based hardware platform,which is used to realize control and signal readout of trapped-ion-based multi-level quantum systems.This platform...We report a design and implementation of a field-programmable-gate-arrays(FPGA)based hardware platform,which is used to realize control and signal readout of trapped-ion-based multi-level quantum systems.This platform integrates a four-channel 2.8 Gsps@14 bits arbitrary waveform generator,a 16-channel 1 Gsps@14 bits direct-digital-synthesisbased radio-frequency generator,a 16-channel 8 ns resolution pulse generator,a 10-channel 16 bits digital-to-analogconverter module,and a 2-channel proportion integration differentiation controller.The hardware platform can be applied in the trapped-ion-based multi-level quantum systems,enabling quantum control of multi-level quantum system and highdimensional quantum simulation.The platform is scalable and more channels for control and signal readout can be implemented by utilizing more parallel duplications of the hardware.The hardware platform also has a bright future to be applied in scaled trapped-ion-based quantum systems.展开更多
In this paper, we study a quantum anti-Zeno effect （QAZE） purely induced by repetitive measurements for an artificial atom interacting with a structured bath. This bath can be artificially realized with coupled reso...In this paper, we study a quantum anti-Zeno effect （QAZE） purely induced by repetitive measurements for an artificial atom interacting with a structured bath. This bath can be artificially realized with coupled resonators in one dimension and possesses photonic band structure like Bloeh electron in a periodic potential. In the presence of repetitive measurements, the pure QAZE is discovered as the observable decay is not negligible even for the atomic energy level spacing outside of the energy band of the artificial bath. If there were no measurements, the decay would not happen outside of the band. In this sense, the enhanced decay is completely induced by measurements through the relaxation channels provided by the bath. Besides, we also discuss the controversial golden rule decay rates originated from the van Hove＇s singularities and the effects of the counter-rotating terms.展开更多
This work conducts robust H^(∞)analysis for a class of quantum systems subject to perturbations in the interaction Hamiltonian.A necessary and sufficient condition for the robustly strict bounded real property of thi...This work conducts robust H^(∞)analysis for a class of quantum systems subject to perturbations in the interaction Hamiltonian.A necessary and sufficient condition for the robustly strict bounded real property of this type of uncertain quantum system is proposed.This paper focuses on the study of coherent robust H^(∞)controller design for quantum systems with uncertainties in the interaction Hamiltonian.The desired controller is connected with the uncertain quantum system through direct and indirect couplings.A necessary and sufficient condition is provided to build a connection between the robust H^(∞)control problem and the scaled H^(∞)control problem.A numerical procedure is provided to obtain coefficients of a coherent controller.An example is presented to illustrate the controller design method.展开更多
In this paper,we consider the fixed-time stabilization control problem of quantum systems modeled by Schrodinger equations.Firstly,the Lyapunov-based fixed-time stability criterion is extended to finitedimensional clo...In this paper,we consider the fixed-time stabilization control problem of quantum systems modeled by Schrodinger equations.Firstly,the Lyapunov-based fixed-time stability criterion is extended to finitedimensional closed quantum systems in the form of coherence vectors.Then for a two-level quantum system with single control input,a non-smooth fractional-order control law is designed using the relative state distance.By integrating the fixed-time Lyapunov control technique and the bi-limit homogeneity theory,the quantum system is proved to be stabilized to an eigenstate of the inherent Hamiltonian in a fixed time.Comparing with existing methods in quantum system control,the proposed approach can guarantee stabilization in a fixed time without depending on the initial states.展开更多
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...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.展开更多
This paper explores the potential of controlling quantum systems by introducing ancillary systems and then performing unitary operation on the resulting composite systems. It generalizes the concept of pure state cont...This paper explores the potential of controlling quantum systems by introducing ancillary systems and then performing unitary operation on the resulting composite systems. It generalizes the concept of pure state controllability for quantum systems and establishes the link between the operator controllability of the composite system and the generalized pure state controllability of its subsystem. It is constructively demonstrated that if a composite quantum system can be transferred between any pair of orthonormal pure vectors, then its subsystem is generalized pure-state controllable. Furthermore, the unitary operation and the coherent control can be concretely given to transfer the system from an initial state to the target state. Therefore, these properties may be potentially applied in quantum information, such as manipulating multiple quantum bits and creating entangled pure states. A concrete example has been given to illustrate that a maximally entangled pure state of a quantum system can be generated by introducing an ancillary system and performing open-loop coherent control on the resulting composite system.展开更多
基金supported by the National Natural Science Foundation of China(Nos.22273122,T2350009)the Guangdong Provincial Natural Science Foundation(No.2024A1515011504)computational resources and services provided by the national supercomputer center in Guangzhou.
文摘We investigate dynamical quantum phase transitions(DQPTs)in Marko-vian open quantum systems using a variational quantum simulation(VQS)algorithm based on quantum state diffusion(QSD).This approach reformulates the Lindblad master equation as an ensemble of pure-state trajectories,enabling efficient simula-tion of dissipative quantum dynam-ics with effectively reduced quantum resources.Focusing on the one-di-mensional transverse-field Ising mod-el(TFIM),we simulate quench dynamics under both local and global Lindblad dissipation.The QSD-VQS algorithm accurately captures the nonanalytic cusps in the Loschmidt rate function,and reveals their modulation by dissipation strength and system size.Notably,DQPTs are gradually suppressed under strong local dissipation,while they persist under strong global dissipation due to collective environmental effects.Benchmarking against exact Lindblad solutions confirms the high accuracy and scalability of our method.
文摘Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.
基金supported by the National Natural Science Foundation of China(Grant No.12088101,and U2330401).
文摘By casting evolution to the Bloch sphere, the dynamics of 2 × 2 matrix non-Hermitian systems are investigated in detail. This investigation reveals that there are four kinds of dynamical modes for such systems. The different modes are classified by different kinds of fixed points, namely,the elliptic point, spiral point, critical node, and degenerate point. The Hermitian systems and the unbroken PT non-Hermitian cases belong to the category with elliptic points. The degenerate point just corresponds to the systems with exceptional point(EP). The topological properties of the fixed point are also discussed. It is interesting that the topological charge for the degenerate point is two, while the others are one.
基金supported by the National Natural Science Foundation of China(Nos.62173229,12288201)the Australian Research Council Future Fellowship Funding Scheme under Project FT220100656 and the Discovery Project Funding Scheme under Project DP210101938.
文摘The task to estimate all the parameters of an unknown quantum state, also called quantum state tomography, is essential for characterizing and controlling quantum systems. In this paper, we utilize observable time traces to identify the initial quantum state of a closed quantum system, based on the state space approach in the control theory. In the informationally complete scenario, we show that with a linear regression estimation (LRE), the mean squared error (MSE) scales as , where N is the resource number. In the informationally incomplete scenario, we introduce regularization LRE to perform the state tomography task. We employ PBH test to demonstrate that closed quantum systems with only one observable are informationally incomplete and propose using observables, where d is the dimension of the quantum state, for informational completeness. Numerical examples demonstrate the effectiveness of our method.
基金supported by the National Natural Science Foundation of China(62473354).
文摘For the n-qubit stochastic open quantum systems,based on the Lyapunov stability theorem and LaSalle’s invariant set principle,a pure state switching control based on on-line estimated state feedback(short for OQST-SFC)is proposed to realize the state transition the pure state of the target state including eigenstate and superposition state.The proposed switching control consists of a constant control and a control law designed based on the Lyapunov method,in which the Lyapunov function is the state distance of the system.The constant control is used to drive the system state from an initial state to the convergence domain only containing the target state,and a Lyapunov-based control is used to make the state enter the convergence domain and then continue to converge to the target state.At the same time,the continuous weak measurement of quantum system and the quantum state tomography method based on the on-line alternating direction multiplier(QST-OADM)are used to obtain the system information and estimate the quantum state which is used as the input of the quantum system controller.Then,the pure state feedback switching control method based on the on-line estimated state feedback is realized in an n-qubit stochastic open quantum system.The complete derivation process of n-qubit QST-OADM algorithm is given;Through strict theoretical proof and analysis,the convergence conditions to ensure any initial state of the quantum system to converge the target pure state are given.The proposed control method is applied to a 2-qubit stochastic open quantum system for numerical simulation experiments.Four possible different position cases between the initial estimated state and that of the controlled system are studied and discussed,and the performances of the state transition under the corresponding cases are analyzed.
文摘We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dynamical semigroups. Our findings reveal that the measures of quantumness for the asymptotic states rely on the primary parameter of the quantum model. Furthermore, control over these measures can be achieved through a careful selection of these parameters. Our analysis encompasses various cases, including Bell states, Werner states, and Horodecki states, demonstrating that the asymptotic states can exhibit steering, entanglement, and Bell nonlocality. Additionally, we find that these three quantum measures of correlations can withstand the influence of the environment, maintaining their properties even over extended periods.
基金the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0303205)the National Natural Science Foundation of China(Grant Nos.12104282 and 12305014)+1 种基金the Initiative in Quantum Information Technologies of Anhui Province(Grant No.AHY050000)the Fundamental Research Funds for the Central Universities(Grant Nos.JZ2024HGTB0253 and JZ2023HGTA0172).
文摘Counterdiabatic driving (CD) offers a fast and robust route to manipulate quantum systems, which has widespreadapplications in quantum technologies. However, for higher-dimensional complex systems, the exact CD term involving thespectral properties of the system is difficult to calculate and generally takes a complicated form, impeding its experimentalrealization. Recently, many approximate methods have been proposed for designing CD passages in many-body systems. Inthis topical review, we focus on the CD formalism and briefly introduce several experimental constructions and applicationsof approximate CD driving in spin-chain models with nuclear magnetic resonance (NMR) systems.
基金supported by the National Key Research and Development Program of China (Grant No.2022YFA1402700)the National Natural Science Foundation of China (Grant Nos.12174020,12088101,11974244,and U2230402)。
文摘The application of the eigenstate thermalization hypothesis to non-Hermitian quantum systems has become one of the most important topics in dissipative quantum chaos, recently giving rise to intense debates. The process of thermalization is intricate, involving many time-evolution trajectories in the reduced Hilbert space of the system. By considering two different expansion forms of the density matrices adopted in the biorthogonal and right-state time evolutions, we derive two versions of the Gorini–Kossakowski–Sudarshan–Lindblad(GKSL)master equations describing the non-Hermitian systems coupled to a bosonic heat bath in thermal equilibrium. By solving the equations, we identify a sufficient condition for thermalization under both time evolutions, resulting in Boltzmann biorthogonal and right-eigenstate statistics, respectively. This finding implies that the recently proposed biorthogonal random matrix theory needs an appropriate revision. Moreover, we exemplify the precise dynamics of thermalization and thermodynamic properties with test models.
基金Project supported by the Guangdong Basic and Applied Basic Research Fund(Grant No.2023A1515011460)the National Natural Science Foundation of China(Grant No.12375013).
文摘The capacity to extract work from a quantum heat machine is not only of practical value but also lies at the heart of understanding quantum thermodynamics.In this paper,we investigate optimal work extraction for quantum systems with work storage,where extracting work is completed by a unitary evolution on the composite system.We consider the physical requirement of energy conservation both strictly and on average.For both,we construct their corresponding unitaries and propose variational quantum algorithms for optimal work extraction.We show that maximal work extraction in general can be feasible when energy conservation is satisfied on average.We demonstrate with numeral simulations using a continuous-variable work storage.Our work show an implementation of a variational quantum computing approach for simulating work extraction in quantum systems.
基金supported by National Natural Science Foundation of China(61573330)Chinese Academy of Sciences(CAS)the World Academy of Sciences(TWAS)
文摘In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation.Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.
文摘To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.
基金Supported by National Nature Science Foundation of China under Grant No. 10701081
文摘In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.
基金supported by the National Natural Science Foundation of China (Grant No. 11174025)
文摘We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities .in isolated quantum Hamiltonian sys- tems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some resultsare given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.
基金This paper is dedicated to Professor lan R. Petersen on the occasion of his 60th birthday. This work was supported by the Anhui Provincial Natural Science Foundation （No. 1708085MF144） and the National Natural Science Foundation of China （No. 61573330）.Acknowledgements We thank Dr. Daoyi Dong for helpful discussion.
文摘For an N-dimensional quantum system under the influence of continuous measurement, this paper presents a switching control scheme where the control law is of bang-bang type and achieves asymptotic preparation of an arbitrarily given eigenstate of a non-degenerate and degenerate measurement operator, respectively. In the switching control strategy, we divide the state space into two parts： a set containing a target state, and its complementary set. By analyzing the stability of the stochastic system model under consideration, we design a constant control law and give some conditions that the control Hamiltonian satisfies so that the system trajectories in the complementary set converge to the set which contains the target state. Further, for the case of a non-degenerate measurement operator, we show that the system trajectories in the set containing the target state will automatically converge to the target state via quantum continuous measurement theory; while for the case of a degenerate measurement operator, the corresponding system trajectories will also converge to the target state via the construction of the control Hamiltonians. The convergence of the whole closed-loop systems under the cases of a non-degenerate and a degenerate measurement operator is strictly proved. The effectiveness of the proposed switching control scheme is verified by the simulation experiments on a finite-dimensional angular momentum system and a two-qubit system.
基金the Strategic Priority Research Program of CAS(Grant No.XDC07020200)the National Key R&D Program of China(Grants No.2018YFA0306600)+5 种基金the National Natural Science Foundation of China(Grant Nos.11974330 and 92165206)the Chinese Academy of Sciences(Grant No.QYZDY-SSW-SLH004)the Innovation Program for Quantum Science and Technology(Grant Nos.2021ZD0302200 and 2021ZD0301603)the Anhui Initiative in Quantum Information Technologies(Grant No.AHY050000)the Hefei Comprehensive National Science Centerthe Fundamental Research Funds for the Central Universities。
文摘We report a design and implementation of a field-programmable-gate-arrays(FPGA)based hardware platform,which is used to realize control and signal readout of trapped-ion-based multi-level quantum systems.This platform integrates a four-channel 2.8 Gsps@14 bits arbitrary waveform generator,a 16-channel 1 Gsps@14 bits direct-digital-synthesisbased radio-frequency generator,a 16-channel 8 ns resolution pulse generator,a 10-channel 16 bits digital-to-analogconverter module,and a 2-channel proportion integration differentiation controller.The hardware platform can be applied in the trapped-ion-based multi-level quantum systems,enabling quantum control of multi-level quantum system and highdimensional quantum simulation.The platform is scalable and more channels for control and signal readout can be implemented by utilizing more parallel duplications of the hardware.The hardware platform also has a bright future to be applied in scaled trapped-ion-based quantum systems.
基金Supported by the Natural Science Foundation of China under Grant Nos.10974209 and 10935010 the National 973 Program under Grant No.2006CB921205China Postdoctoral Science Foundation under Grant No.20100470584
文摘In this paper, we study a quantum anti-Zeno effect （QAZE） purely induced by repetitive measurements for an artificial atom interacting with a structured bath. This bath can be artificially realized with coupled resonators in one dimension and possesses photonic band structure like Bloeh electron in a periodic potential. In the presence of repetitive measurements, the pure QAZE is discovered as the observable decay is not negligible even for the atomic energy level spacing outside of the energy band of the artificial bath. If there were no measurements, the decay would not happen outside of the band. In this sense, the enhanced decay is completely induced by measurements through the relaxation channels provided by the bath. Besides, we also discuss the controversial golden rule decay rates originated from the van Hove＇s singularities and the effects of the counter-rotating terms.
基金supported by the National Natural Science Foundation of China(61803132,61828303,61803389)the U.S.Office of Naval Research Global(N62909-19-1-2129)the Australian Research’s Discovery Projects Funding Scheme under Project DP190101566。
文摘This work conducts robust H^(∞)analysis for a class of quantum systems subject to perturbations in the interaction Hamiltonian.A necessary and sufficient condition for the robustly strict bounded real property of this type of uncertain quantum system is proposed.This paper focuses on the study of coherent robust H^(∞)controller design for quantum systems with uncertainties in the interaction Hamiltonian.The desired controller is connected with the uncertain quantum system through direct and indirect couplings.A necessary and sufficient condition is provided to build a connection between the robust H^(∞)control problem and the scaled H^(∞)control problem.A numerical procedure is provided to obtain coefficients of a coherent controller.An example is presented to illustrate the controller design method.
基金This work is supported in part by the Ministry of Education(MOE),Singapore under Grant MOE2020-T1-1-067also partially supported by the National Natural Science Foundation of China under Grants 62103352 and 61903319.
文摘In this paper,we consider the fixed-time stabilization control problem of quantum systems modeled by Schrodinger equations.Firstly,the Lyapunov-based fixed-time stability criterion is extended to finitedimensional closed quantum systems in the form of coherence vectors.Then for a two-level quantum system with single control input,a non-smooth fractional-order control law is designed using the relative state distance.By integrating the fixed-time Lyapunov control technique and the bi-limit homogeneity theory,the quantum system is proved to be stabilized to an eigenstate of the inherent Hamiltonian in a fixed time.Comparing with existing methods in quantum system control,the proposed approach can guarantee stabilization in a fixed time without depending on the initial states.
基金ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China （No.61074052 and No.61072032）. Herschel Rabitz acknowledges the support from Army Research Office （ARO）.
文摘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.
基金Project supported by the National Natural Science Foundation of China （Grant No 60674040） and the National Natural Science Fund for Distinguished Young Scholars （Grant No 60225015）.
文摘This paper explores the potential of controlling quantum systems by introducing ancillary systems and then performing unitary operation on the resulting composite systems. It generalizes the concept of pure state controllability for quantum systems and establishes the link between the operator controllability of the composite system and the generalized pure state controllability of its subsystem. It is constructively demonstrated that if a composite quantum system can be transferred between any pair of orthonormal pure vectors, then its subsystem is generalized pure-state controllable. Furthermore, the unitary operation and the coherent control can be concretely given to transfer the system from an initial state to the target state. Therefore, these properties may be potentially applied in quantum information, such as manipulating multiple quantum bits and creating entangled pure states. A concrete example has been given to illustrate that a maximally entangled pure state of a quantum system can be generated by introducing an ancillary system and performing open-loop coherent control on the resulting composite system.
