Arbitrary Initial State Research Articles

Controllability and Optimal Control Design for an Elastic Rod Actuated by Piezoelements

The study is aimed at the optimal control design of longitudinal motions for a rectilinear elastic rod with free ends. Several piezoelectric actuators are attached along its axis. The control is carried out by piezoelectric normal force acting in the cross section. We assume that this force changes piecewise constantly in space, and the intervals of constancy have no gaps and are equal in length. Given an arbitrary initial state and periodic terminal conditions, the optimal control problem is to minimize the mean mechanical energy stored in the rod over a fixed time horizon. For a uniform rod, the minimal admissible horizon is found, and the exact optimal control law is presented.

Homogeneous Generalized Master Equation for an Arbitrary Initial State of a Many-Particle Classical System

Homogeneous Generalized Master Equation for an Arbitrary Initial State of a Many-Particle Classical System

Non-Hermitian critical dynamics and its application to quantum many-body systems

In recent years, two independent research fields, i.e. non-Hermitian andstrongly correlated systems have been merged, forming an important researchfield in physics. The progress of relevant theories and experiments hasreshaped our understanding of matter. In this field, the research object isnot limited to the influence of non-Hermiticity on the energy spectrum andthe eigenstate properties of many-body systems. Researchers have paid more attentionto the manipulation of quantum states. It is universally received that the exceptional point is the most significant featurethat distinguishes non-Hermitian quantum mechanics from Hermitian quantum mechanics. In addition to the recent advances in non-Hermitian topological band theory and quantum sensing around the exceptional points, this paper concentrates on the non-Hermitian critical dynamical phenomenon and its application to the quantum many-body system. When the system has an exceptional point, an arbitrary initial state belonging to the coalescent subspace will be projected on the coalescent state. Based on the directionality of the evolved quantum state, this paper reviews our several representative researches in recent years, including local-field-induced dynamical magnetization, quantum phase transition in transverse field, Ising model at non-zero temperature, quantum mold casting in the center-environment system, as well as superconducting state preparation in the non-Hermitian strongly correlated system. We also focus on the new preparation methods and detection schemes of non-equilibrium quantum states related to exception points.

Interpretable Machine Learning of High-Dimensional Aging Health Trajectories

We have built a computational model of individual aging trajectories of health and survival, that contains physical, functional, and biological variables, and is conditioned on demographic, lifestyle, and medical background information. We combine techniques of modern machine learning with an interpretable network approach, where health variables are coupled by an explicit interaction network within a stochastic dynamical system. Our model is scalable to large longitudinal data sets, is predictive of individual high-dimensional health trajectories and survival from baseline health states, and infers an interpretable network of directed interactions between the health variables. The network identifies plausible physiological connections between health variables and clusters of strongly connected heath variables. We use English Longitudinal Study of Aging (ELSA) data to train our model and show that it performs better than traditional linear models for health outcomes and survival. Our model can also be used to generate synthetic individuals that age realistically, to impute missing data, and to simulate future aging outcomes given an arbitrary initial health state.

Signatures of Liouvillian Exceptional Points in a Quantum Thermal Machine

Viewing a quantum thermal machine as a non-Hermitian quantum system, we characterize in full generality its analytical time-dependent dynamics by deriving the spectrum of its non-Hermitian Liouvillian for an arbitrary initial state. We show that the thermal machine features a number of Liouvillian exceptional points (EPs) for experimentally realistic parameters, in particular a third-dorder exceptional point that leaves signatures both in short and long-time regimes. Remarkably, we demonstrate that this EP corresponds to a regime of critical decay for the quantum thermal machine towards its steady state, bearing a striking resemblance with a critically damped harmonic oscillator. These results open up exciting possibilities for the precise dynamical control of quantum thermal machines exploiting exceptional points from non-Hermitian physics and are amenable to state-of-the-art solid-state platforms such as semiconducting and superconducting devices.

Deep reinforcement learning for universal quantum state preparation via dynamic pulse control

Accurate and efficient preparation of quantum state is a core issue in building a quantum computer. In this paper, we investigate how to prepare a certain single- or two-qubit target state from arbitrary initial states in semiconductor double quantum dots with only a few discrete control pulses by leveraging the deep reinforcement learning. Our method is based on the training of the network over numerous preparing tasks. The results show that once the network is well trained, it works for any initial states in the continuous Hilbert space. Thus repeated training for new preparation tasks is avoided. Our scheme outperforms the traditional optimization approaches based on gradient with both the higher efficiency and the preparation quality in discrete control space. Moreover, we find that the control trajectories designed by our scheme are robust against stochastic fluctuations within certain thresholds, such as the charge and nuclear noises.

Robust control of quantum systems by quantum systems

Quantum systems can be controlled by other quantum systems in a reversible way, without any information leaking to the outside of the system-controller compound. Such coherent quantum control is deterministic, is less noisy than measurement-based feedback control, and has potential applications in a variety of quantum technologies, including quantum computation, quantum communication and quantum metrology. Here we introduce a coherent feedback protocol, consisting of a sequence of identical interactions with controlling quantum systems, that steers a quantum system from an arbitrary initial state towards a target state. We determine the broad class of such coherent feedback channels that achieve convergence to the target state, and then stabilise as well as protect it against noise. Our results imply that also weak system-controller interactions can counter noise if they occur with suitably high frequency. We provide an example of a control scheme that does not require knowledge of the target state encoded in the controllers, which could be the result of a quantum computation. It thus provides a mechanism for autonomous, purely quantum closed-loop control.

Dissipative preparation of fractional Chern insulators

We report on the numerically exact simulation of the dissipative dynamics governed by quantum master equations that feature fractional quantum Hall states as unique steady states. In particular, for the paradigmatic Hofstadter model, we show how Laughlin states can be to good approximation prepared in a dissipative fashion from arbitrary initial states by simply pumping strongly interacting bosons into the lowest Chern band of the corresponding single-particle spectrum. While pure (up to topological degeneracy) steady states are only reached in the low-flux limit or for extended hopping range, we observe a certain robustness regarding the overlap of the steady state with fractional quantum Hall states for experimentally well-controlled flux densities. This may be seen as an encouraging step towards addressing the long-standing challenge of preparing strongly correlated topological phases in quantum simulators.

On the asymptotic stability of advection-diffusion equations of mass transport in a bubble column bioreactor

This study presents an asymptotic stability analysis of a model of a bioreactor converting carbon monoxide (CO) gas into ethanol through a C. autoethanogenum biocatalyst. The configuration is a bubble column reactor with co-current gas-liquid flows where gas feed is introduced by a gas distributor placed at the bottom of the column. A pure culture of C. autoethanogenum is subsequently injected at the bottom of the column; therein, cells are dispersed in the liquid and consume the dissolved gas and release by-products such as ethanol and acetic acid. Cellular growth and byproduct secretion are affected by spatially varying dissolved gas concentrations due to advection-diffusion mass transports which are induced by the effect of the injection pressure and gravitational force. The model accounts for four species representing the biomass, the CO substrate in the liquid phase, and two by-products - ethanol and acetic acid. Substrate dynamics is described by an advection-diffusion equation.We investigate the asymptotic stability of the biomass dynamics that is a requirement for the system’s controllability, i.e. for the possibility to steer a dynamical system from an arbitrary initial state to an arbitrary final state using a set of controls. The concept of stability of the controls is extremely relevant to controllability since almost every workable control system is designed to be stable. If a control system is not stable, it is usually of no use in practice in industrial processes. In the case of a bioreactor, the control is the biomass and controllability is the possibility of modulating through this control the ethanol production. We present a test for asymptotic stability, based on the analysis of the properties of the dynamic function defining its role as storage function.

Structural controllability and time-to-control of directed scale-free networks with minimum number of driver nodes

In this paper we study structural controllability and time-to-control of directed scale-free networks, and propose algorithms to guarantee these properties with the minimum number of driver nodes. Structural controllability is a qualitative (i.e. topological) measure of the ability to steer the network to a desired state from an arbitrary initial state; while time-to-control measures how fast the above steering can be done. First, we develop an algorithm that generates directed scale-free networks which are provably structurally controllable with only one driver node. Moreover, considering the tradeoff between control cost (number of driver nodes) and control performance (time-to-control), we propose another algorithm that constructs directed scale-free networks which can be steered to a desired state within a prescribed time bound and with the minimum number of driver nodes.

Research on reverse engineering strategy of state transfer for open quantum systems

There has long been interest to control the transfer of population between specified quantum states and protect the coherence of the system at the same time. In this paper, from the perspective of engineering implementation, and based on the idea of reverse engineering, we propose a control scheme for state transfer of two-level open quantum system, which is to drive system from arbitrary initial state to desired target state. In order to ensure that the system can process information effectively, we design the control pulse in advance in terms of population number and coherence, and then verify the validity through numerical simulation. The results show that the system can be driven from any initial state to the desired target state by the designed control pulse, and the coherence of the system is well protected during the state transfer. The influences of environmental decoherence on population transfer and coherence control is further discussed. It reveals that the control pulse presented in this paper is robust to the variation of related parameters.

A note on the distributions in quantum mechanical systems

In this paper, we study the distributions and the affine distributions of the quantum mechanical system. Also, we discuss the controllability of the quantum mechanical system with the related question concerning the minimum time needed to steer a quantum system from a unitary evolution U(0) = I of the unitary propagator to a desired unitary propagator Uf . Furthermore, the paper introduces a description of a k⊕p sub-Finsler manifold with its geodesics, which equivalents to the problem of driving the quantum mechanical system from an arbitrary initial state U(0) = I to the target state Uf , some illustrative examples are included. We prove that the Lie group G on a Finsler symmetric manifold G/K can be decomposed into KAK.

Nonlinear Optimal Feedback Control of the Two-Level Open Non-Markovian Stochastic Quantum System

In this paper, a nonlinear optimal feedback control based on the nonlinear state estimator for a two-level open non-Markovian stochastic quantum system is proposed. The proposed nonlinear state estimator is designed by using the state-dependent differential Riccati equation and constructed to optimally estimate the state. The estimated state is updated by the output data of continuous weak measurement of the controlled quantum system and used to design the nonlinear state feedback controller to track the output of the reference model. The output state of reference model is chosen as the desired performance. The numerical simulation results verify the achievability of the proposed state feedback control strategy, and the capability to steer the state of system from any arbitrary initial state to the final reference target state with high state transfer success rate.

Impossibility of achieving Landauer's bound for almost every quantum state

The thermodynamic cost of resetting an arbitrary initial state to a particular desired state is lower bounded by Landauer's bound. However, here we demonstrate that this lower bound is necessarily unachievable for every initial state (except possibly the single minimally dissipative input) for any reliable reset mechanism. Since local heating threatens rapid decoherence, this issue is of substantial importance beyond mere energy efficiency. For the case of qubit reset, we find the minimally dissipative state analytically for any reliable reset protocol, in terms of the entropy-flow vector introduced here. This allows us to verify a recent theorem about initial-state dependence of entropy production for any finite-time transformation, as it pertains to quantum state preparation.

Perfect quantum-state synchronization

We investigate the most general mechanisms that lead to perfect synchronization of the quantum states of all subsystems of an open quantum system starting from an arbitrary initial state. We provide a necessary and sufficient condition for such "quantum-state synchronization", prove tight lower bounds on the dimension of the environment's Hilbert space in two main classes of quantum-state synchronizers, and give an analytical solution for their construction. The functioning of the found quantum-state synchronizer of two qubits is demonstrated experimentally on an IBM quantum computer and we show that the remaining asynchronicity is a sensitive measure of the quantum computer's imperfection.

Quantum Rayleigh problem and thermocoherent Onsager relations

The role of quantum coherence and correlations in heat flow and equilibration is investigated by exploring the Rayleigh's dynamical problem to equilibration in the quantum regime and following Onsager's approach to thermoelectricity. Specifically, we consider a qubit bombarded by two-qubit projectiles from a side. For arbitrary collision times and initial states, we develop the master equation for sequential and collective collisions. By deriving the Fokker-Planck equation out of the master equation, we identify the quantum version of the Rayleigh's heat conduction equation. We find that quantum discord and entanglement shared between the projectiles can contribute to genuine heat flow only when they are associated with so-called heat-exchange coherences. Analogous to Onsager's use of Rayleigh's principle of least dissipation of energy, we use the entropy production rate to identify the coherence current. Both coherence and heat flows can be written in the form of quantum Onsager relations, from which we predict coherent Peltier and coherent Seebeck effects. The effects can be optimized by the collision times and collectivity. Finally, we discuss some of the possible experimental realizations and technological applications of the thermocoherent phenomena in different platforms.

Quantum speed limit for thermal states

Quantum speed limits are rigorous estimates on how fast a state of a quantum system can depart from the initial state in the course of quantum evolution. Most known quantum speed limits, including the celebrated Mandelstam-Tamm and Margolus-Levitin ones, are general bounds applicable to arbitrary initial states. However, when applied to mixed states of many-body systems, they, as a rule, dramatically overestimate the speed of quantum evolution and fail to provide meaningful bounds in the thermodynamic limit. Here we derive a quantum speed limit for a closed system initially prepared in a thermal state and evolving under a time-dependent Hamiltonian. This quantum speed limit exploits the structure of the thermal state and, in particular, explicitly depends on the temperature. In a broad class of many-body setups it proves to be drastically stronger than general quantum speed limits.

Effects of initial states on the quantum correlations in the generalized Grover search algorithm* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11975132 and 61772295), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019YQ01), and Shandong Province Higher Educational Science and Technology Program, China (Grant No. J18KZ012).

We investigate the correlations between two qubits in the Grover search algorithm with arbitrary initial states by numerical simulation. Using a set of suitable bases, we construct the reduced density matrix and give the numerical expression of correlations relating to the iterations. For different initial states, we obtain the concurrence and quantum discord compared with the success probability in the algorithm. The results show that the initial states affect the correlations and the limit point of the correlations in the searching process. However, the initial states do not influence the whole cyclical trend.

Fast and dephasing-tolerant preparation of steady Knill-Laflamme-Milburn states via dissipative Rydberg pumping

We propose a fast and dephasing-tolerant scheme for the preparation of steady Knill-Laflamme-Milburn (KLM) state between a pair of Rydberg atoms by dissipation. In this scheme, arbitrary initial state can be engineered to the KLM state with high fidelity (99.24%). Compared to most schemes based on Rydberg dissipation dynamics, the time to prepare steady state can be significantly reduced in our scheme $(80 \ensuremath{\mu}\mathrm{s})$ due to the use of strong resonant dipole-dipole interactions. In addition, the scheme can effectively suppress the dephasing error of the Rydberg atoms caused by interatomic distance fluctuations, which may severely disrupt the desired systematic dynamics. Thus the present scheme is of interest and deserves further experimental investigation to enrich the dissipation dynamics based on the Rydberg atoms.

General solutions to mathcal {N}-field cosmology with exponential potentials

We construct the general analytical solution for the mathcal {N}-field product-exponential potential in an expanding FLRW background. We demonstrate the relevance of this analytical solution in more general contexts for the derivation of estimates for the transitional time between an arbitrary initial state and the slow-roll solutions. In certain cases, these estimates can also be used to demonstrate the non-linear convergence towards the slow-roll solutions. In addition, we extend the solution to include stiff matter as well.