Random Initial State Research Articles

Prescribed time convergence and robust zeroing neural network for solving time-varying linear matrix equation

Zeroing neural network offers a new solution method to solve the time-varying linear matrix equation. As an important component, the activation function directly affects the performance of zeroing neural network in solving time-varying linear matrix equation. Focusing on the unification of prescribed time convergence and strong robustness without changing the basic structure of zeroing neural network, a novel activation function is proposed for the first time in this paper. Compared with commonly used activation functions in previous work, the novel activation function has superior performance for zeroing neural network to solve the time-varying linear matrix equation. The first item is global asymptotic convergence, capable of converging from random initial states to the theoretical solution. The second item is the prescribed time convergence, i.e. the upper bound of convergence time is only related to the parameters of the novel activation function and zeroing neural network, which facilitates the prediction of the convergence process. The third item is strong robustness, which ensures that the solution converges in various noisy environments. Theoretical analysis and comparative simulation experiments verify that zeroing neural network with the novel activation function has these performances for both low- or high-dimensional time-varying linear matrix equation.

Optimal Multi-impulse Linear Rendezvous via Reinforcement Learning

A reinforcement learning-based approach is proposed to design the multi-impulse rendezvous trajectories in linear relative motions. For the relative motion in elliptical orbits, the relative state propagation is obtained directly from the state transition matrix. This rendezvous problem is constructed as a Markov decision process that reflects the fuel consumption, the transfer time, the relative state, and the dynamical model. An actor–critic algorithm is used to train policy for generating rendezvous maneuvers. The results of the numerical optimization (e.g., differential evolution) are adopted as the expert data set to accelerate the training process. By deploying a policy network, the multi-impulse rendezvous trajectories can be obtained on board. Moreover, the proposed approach is also applied to generate a feasible solution for many impulses (e.g., 20 impulses), which can be used as an initial value for further optimization. The numerical examples with random initial states show that the proposed method is much faster and has slightly worse performance indexes when compared with the evolutionary algorithm.

Hamiltonian Simulation with Random Inputs.

The algorithmic error of digital quantum simulations is usually explored in terms of the spectral norm distance between the actual and ideal evolution operators. In practice, this worst-case error analysis may be unnecessarily pessimistic. To address this, we develop a theory of average-case performance of Hamiltonian simulation with random initial states. We relate the average-case error to the Frobenius norm of the multiplicative error and give upper bounds for the product formula (PF) and truncated Taylor series methods. As applications, we estimate average-case error for the digital Hamiltonian simulation of general lattice Hamiltonians and k-local Hamiltonians. In particular, for the nearest-neighbor Heisenberg chain with n spins, the error is quadratically reduced from O(n) in the worst case to O(sqrt[n]) on average for both the PF method and the Taylor series method. Numerical evidence suggests that this theory accurately characterizes the average error for concrete models. We also apply our results to error analysis in the simulation of quantum scrambling.

Disorder effects in the Z3 Fock parafermion chain

We study the effects of disorder in a one-dimensional model of $\mathbb{Z}_{3}$ Fock parafermions which can be viewed as a generalization of the prototypical Kitaev chain. Exact diagonalization is employed to determine level statistics, participation ratios, and the dynamics of domain walls. This allows us to identify ergodic as well as finite-size localized phases. In order to distinguish Anderson from many-body localization, we calculate the time evolution of the entanglement entropy in random initial states using tensor networks. We demonstrate that a purely quadratic parafermion model does not feature Anderson but many-body localization due to the nontrivial statistics of the particles.

Hilbert space fragmentation and interaction-induced localization in the extended Fermi-Hubbard model

We study Hilbert space fragmentation in the extended Fermi-Hubbard model with nearest and next-nearest-neighbor interactions. Using a generalized spin/mover picture and saddle point methods, we derive lower bounds for the scaling of the number of frozen states and for the size of the largest block preserved under the dynamics. We find fragmentation for strong nearest- and next-nearest-neighbor repulsions as well as for the combined case. Our results suggest that the involvement of next-nearest-neighbor repulsions leads to an increased tendency for localization. We then model the dynamics for larger systems using Markov simulations to test these findings and unveil in which interaction regimes the dynamics becomes spatially localized. In particular, we show that for strong nearest- and next-nearest-neighbor interactions random initial states will localize provided that the density of initial movers is sufficiently low.

Derivative-Free Observability Analysis for Sensor Placement Optimization of Bioinspired Flexible Flapping Wing System.

Observability analysis of a bioinspired flexible flapping wing system provides a measure of how well the states of flexible flapping wing micro-aerial vehicles can be estimated from real-time measurements during high-speed flight. However, the traditional observability analysis approaches have trouble in terms of lack of quantitative analysis index, high computational complexity, low accuracy, and unavailability in stochastic systems with memory, including bioinspired flexible flapping wing systems. Therefore, a novel derivative-free observability analysis method is proposed here based on the generalized polynomial chaos expansion. By formulating a surrogate model to represent the relationship between the cumulative measurement and the random initial state, the observability coefficient matrix is calculated and the observability rank condition is stated. Consequently, several observability indices are proposed to quantity the observability of the system. Altogether, the proposed method avoids the disadvantages of the traditional approaches, especially in assessing the observability degree of each state and the effect of stochastic noise on observability. The validation of the proposed method is first provided by demonstrating the equivalence between the traditional and proposed methods and subsequently by comparing the observability of the Lorenz system calculated via three different approaches. Finally, the proposed method is applied on a bioinspired flexible wing system to optimize the placement of sensors, which is consistent with the natural configuration of campaniform sensilla on the wing of the hawkmoth.

Autonomous maneuver decision-making method based on reinforcement learning and Monte Carlo tree search

Autonomous maneuver decision-making methods for air combat often rely on human knowledge, such as advantage functions, objective functions, or dense rewards in reinforcement learning, which limits the decision-making ability of unmanned combat aerial vehicle to the scope of human experience and result in slow progress in maneuver decision-making. Therefore, a maneuver decision-making method based on deep reinforcement learning and Monte Carlo tree search is proposed to investigate whether it is feasible for maneuver decision-making without human knowledge or advantage function. To this end, Monte Carlo tree search in continuous action space is proposed and neural networks-guided Monte Carlo tree search with self-play is utilized to improve the ability of air combat agents. It starts from random behaviors and generates samples consisting of states, actions, and results of air combat through self-play without using human knowledge. These samples are used to train the neural network, and the neural network with a greater winning rate is selected by simulations. Then, repeat the above process to gradually improve the maneuver decision-making ability. Simulations are conducted to verify the effectiveness of the proposed method, and the kinematic model of the missile is used in simulations instead of the missile engagement zone to test whether the maneuver decision-making method is effective or not. The simulation results of the fixed initial state and random initial state show that the proposed method is efficient and can meet the real-time requirement.

Influence of tensile stress on magnetic flux leakage signal of ferromagnetic steel after overcoming initial magnetization disturbance

By locally enhancing the intensity of external excitation magnetic field (H0), a relatively stable local flux loop is formed at the test site, which can effectively overcome the problems of random and variable initial magnetization state, small test data base and low signal-to-noise ratio of ferromagnetic specimens in metal magnetic memory testing (MMMT). The results of magneto-mechanical coupling theory and experiment study show that under tensile stress (σt), the ascending part of the magnetization curve is stably constrained within 40 MPa, which is far less than the normal working load, and the descending part of the magnetization curve changes almost linear with the increase of σt. The gradient value of normal component (dHp(z5)/dx) increases by about 105% and the relative gradient value (Δ[dHp(z5)/dx]) increases by about 76% in the range of 0 MPa ≤ σt ≤ 180 MPa with the increase of σt. When H0 reaches 943.4 A/m and 1415.1 A/m, the characteristic parameter namely peak-to-peak amplitude, S(z)p-p, can stably describe σt linearly.

Broadband 1×8 Optical Beamforming Network Based on Anti-resonant Microring Delay Lines

We demonstrate a 1×8 binary tree optical beamforming network (OBFN) chip for a microwave photonic phased array antenna. The OBFN is formed by cascading multiple microring resonators (MRRs) working at the anti-resonant wavelengths. The binary tree topology reduces the MRR amount by reusing the MRRs in the preceding stage, and the anti-resonant MRRs realize continuous delay tuning with a reduced in-band delay fluctuation. The delay adjustment is achieved by digitally tuned MRRs and one continuously tuned MRR in each stage with an improved operating bandwidth. The random initial states of the MRRs are calibrated to produce a flat delay response. Experimental results show that the maximum delay is 560 ps. The beamforming performance of the OBFN is evaluated in 20 ps and 45 ps delay increments. In an 8-GHz operating bandwidth, the maximum delay fluctuation is less than 7.6 ps. The capability of our delay lines to suppress the delay ripple encountered in conventional on-resonance delay lines opens exciting opportunities for the development of compact integrated broadband OBFNs demanded in broadband microwave phased array antennas.

A Distributed Resource Allocation Algorithm for the General Linear Multiagent Systems

We study the distributed resource allocation problem for heterogeneous multiagent systems over an undirected graph, an essential issue in multiagent system coordinated control and complex network system control. The decision variable is subject to global equality and local convex set constraints, and the objective is smooth and convex. It aims to minimize the global objective function by exchanging neighboring information between agents. An adaptive distributed algorithm is designed using the distance function-based exact penalty function method. A state- and time-based triggering condition is designed to avoid continuous communication and reduce the communication burden. From a random initial state, the proposed algorithm asymptotically converges to the optimal value by means of LaSalle’s invariance principle. Finally, examples are provided to demonstrate the effectiveness of our algorithm.

Oscillatory behavior with fiber orientation in the flow–vorticity plane for fiber suspension under large amplitude oscillatory shear flow

In fiber suspensions, fibers with three-dimensional orientation states are dramatically flow-oriented in the flow–flow gradient plane when the flow starts. In contrast, large strains are required for flow orientation in the flow–vorticity plane. Under oscillatory shear flow, when the strain amplitude is small, the flow orientation in the flow–vorticity plane is weakly induced, unlike that in the flow–flow gradient plane. The orientation in the flow–vorticity plane increases with the strain amplitude. At large strain amplitudes, fibers are oriented in the flow–flow gradient plane; thus, the rotational motion of fibers in the flow–flow gradient plane is dominant, i.e., fibers are almost flow-oriented in the flow–vorticity plane. However, contributions of the oscillatory behavior of fiber orientation in the flow–flow gradient and flow–vorticity planes to complex viscosity are unclear. In this study, the objective is to determine the contributions of fiber orientation in each plane to complex viscosity with the two initial orientation states (random and flow-oriented states) for the strain sweep test. The two initial orientation states were controlled by manipulating the upper disk of the parallel disk flow path. The initial random state was induced by sliding the upper disk up and down. The initial flow-oriented state was induced by rotating the upper plate. Furthermore, phase transition behaviors from the random to flow-oriented state in the flow–vorticity plane with increasing strain amplitude were qualitatively estimated as the orientation angle via visualization. Consequently, when the initial orientation was random, the fibers gradually vibrated in a medium strain amplitude region, and complex viscosity was higher than that of the initial flow-oriented state. In the conclusion, we divided the complex viscosity behavior of the strain sweep test into five strain amplitude regions and clarified the dominant orientation state in each region. It is conceivable that this result will help in understanding the relationship between fiber orientation and dynamic viscoelastic properties of fiber suspension like fiber-reinforced thermoplastics.

The Bootstrap Model of Prebiotic Networks of Proteins and Nucleic Acids.

It is not known how life arose from prebiotic physical chemistry. How did fruitful cell-like associations emerge from the two polymer types—informational (nucleic acids, xNAs = DNA or RNA) and functional (proteins)? Our model shows how functional networks could bootstrap from random sequence-independent initial states. For proteins, we adopt the foldamer hypothesis: through persistent nonequilibrium prebiotic syntheses, short random peptides fold and catalyze the elongation of others. The xNAs enter through random binding to the peptides, and all chains can mutate. Chains grow inside colloids that split when they’re large, coupling faster growth speeds to bigger populations. Random and useless at first, these folding and binding events grow protein—xNA networks that resemble today’s protein–protein networks.

A Machine Learning-Based Vulnerability Analysis for Cascading Failures of Integrated Power-Gas Systems

This paper proposes a cascading failure simulation (CFS) method and a hybrid machine learning method for vulnerability analysis of integrated power-gas systems (IPGSs). The CFS method is designed to study the propagating process of cascading failures between the two systems, generating data for machine learning with initial states randomly sampled. The proposed method considers generator and gas well ramping, transmission line and gas pipeline tripping, island issue handling and load shedding strategies. Then, a hybrid machine learning model with a combined random forest (RF) classification and regression algorithms is proposed to investigate the impact of random initial states on the vulnerability metrics of IPGSs. Extensive case studies are carried out on three test IPGSs to verify the proposed models and algorithms. Simulation results show that the proposed models and algorithms can achieve high accuracy for the vulnerability analysis of IPGSs.

Adaptive iterative learning control for high-order nonlinear systems with random initial state shifts

Aiming at the tracking problem for a class of high-order nonlinear systems with arbitrary initial state, this paper proposes different initial state shifts rectifying schemes for systems with different orders from the perspective of solving differential equations to ensure that the systems achieve complete tracking over the specified interval. This method relaxes the requirement of initial positioning in iterative learning control, and solves the problem of iterative learning control for high-order nonlinear systems with arbitrary initial state error. The theoretical analysis shows that the proposed schemes can make all signals in the system bounded, and ensure that the tracking error in the preset interval tends to zero as the number of iterations increases. When designing the controller, the arctangent function is used to avoid flutter of the control signal and related variables. The final simulations verify the effectiveness of the proposed algorithms.

Realization of a discrete time crystal on 57 qubits of a quantum computer.

Unconventional dynamical phases that violate ergodicity have been a subject of extensive research in recent years. A periodically driven system is naively expected to lose all memory of its initial state due to thermalization, yet this can be avoided in the presence of many-body localization. A discrete time crystal represents a driven system whose local observables spontaneously break time translation symmetry and retain memory of the initial state indefinitely. Here, we report the observation of a discrete time crystal on a chain consisting of 57 superconducting qubits on a state-of-the-art quantum computer. We probe random initial states and compare the cases of vanishing and finite disorder to distinguish many-body localization from prethermal dynamics. We further report results on the dynamical phase transition between the discrete time crystal and a thermal regime, which is observed via critical fluctuations in the system’s subharmonic frequency response and a substantial speedup of spin depolarization.

Constructive feedback of non-Markovianity on resources in random quantum states

We explore the impact of non-Markovian channels on the quantum correlations of Haar uniformly generated random two-qubit input states with different ranks: Either one of the qubits (single-sided channel) or both qubits independently (double-sided channel) are passed through a noisy channel. For dephasing and depolarizing channels with varying non-Markovian strength, entanglement and quantum discord of the output states collapse and revive with the increase of noise. By both analytical and numerical means, we find that in the case of the depolarizing double-sided channel, entanglement and quantum discord for random states show a higher number of revivals on average than for single-sided channels with a fixed non-Markovianity strength, irrespective of the rank of the states; we call such a counterintuitive event, constructive feedback of non-Markovianity. In contrast, the mean value of critical noise at which quantum correlations (QCs) first collapse decreases with the increase of non-Markovianity, independently of the rank of the random initial states. However, the average noise at which QCs of random states show the first revival decreases with the increase of the strength of non-Markovian noise, thereby indicating the role of non-Markovian channels in the regeneration of QCs even in the presence of a high amount of noise. Moreover, we observe that the tendency of a state to show regeneration increases with the increase of average QCs of the random input states along with non-Markovianity.

Selkov glycolytic model with diffusion: Patterns, multistability, and stochastic transitions

We consider a distributed variant of the Selkov mathematical model of glycolysis with diffusion and stochastic disturbances. The Turing instability zone, in which nonhomogeneous patterns are formed, is determined parametrically. Diversity of waveform spatial structures with different number of peaks is described and studied depending on the diffusion coefficients. The coexistence of various patterns of different waveforms and amplitudes is demonstrated. The quantitative analysis of the pattern formation from the random initial states is carried out using statistics and harmonic coefficients. Multistage noise‐induced transitions between coexisting spatial structures are discussed.

Realization of a discrete time crystal on 57 qubits of a quantum computer

Novel dynamical phases that violate ergodicity have been a subject of extensive research in recent years. A periodically driven system is naively expected to lose all memory of its initial state due to thermalization, yet this can be avoided in the presence of many-body localization. A discrete time crystal represents a driven system whose local observables spontaneously break time translation symmetry and retain memory of the initial state indefinitely. Here we report the observation of a discrete time crystal on a chain consisting of 57 superconducting qubits on a state--of--the--art quantum computer. We probe random initial states and compare the cases of vanishing and finite disorder to distinguish many-body localization from pre-thermal dynamics. We further report results on the dynamical phase transition between the discrete time crystal and a thermal regime, which is observed via critical fluctuations in the system's sub-harmonic frequency response and a significant speed-up of spin depolarisation.

Improved Approximation Algorithms for Bounded-Degree Local Hamiltonians.

The low-temperature properties of interacting quantum systems are believed to require exponential resources to compute in the general case. Quantifying the extent to which such properties can be approximated using efficient algorithms remains a significant open challenge. Here, we consider the task of approximating the ground state energy of two-local quantum Hamiltonians with bounded-degree interaction graphs. Most existing algorithms optimize the energy over the set of product states. We propose and analyze a family of shallow quantum circuits that can be used to improve the approximation ratio achieved by a given product state. The algorithm takes as input an n-qubit product state with variance Var and improves its energy by an amount proportional to Var^{2}/n. In a typical case, this results in an extensive improvement in the estimated energy. We extend our results to k-local Hamiltonians and entangled initial states.

Weighted Bures length uncovers quantum state sensitivity.

The unitarity of quantum evolutions implies that an overlap between two initial states does not change in time. This property is commonly believed to explain the apparent lack of state sensitivity in quantum theory, a feature that is prevailing in classical chaotic systems. However, classical state sensitivity is based on a distance between two trajectories in phase space which is a completely different mathematical concept than an overlap between two vectors in Hilbert space. It is possible that state sensitivity in quantum theory can be detected with the help of some special metric. Here we show that the recently introduced Weighted Bures length achieves this task. We numerically investigate a unitary cellular automaton of N interacting qubits and analyze how a single-qubit perturbation affects the evolution of WBL between the unperturbed and perturbed states. We observe a linear growth of WBL if the qubits are arranged into a cyclic graph and an exponential growth if they are arranged into a random bipartite graph.