Real-time Information, Uncertainty and Quantum Feedback Control

Feedback is the core concept in cybernetics and its effective use has made great success in but not limited to the fields of engineering, biology, and computer science. When feedback is used to quantum systems, two major types of feedback control protocols including coherent feedback control (CFC) and measurement-based feedback control (MFC) have been developed. In this paper, we compare the two types of quantum feedback control protocols by focusing on the real-time information used in the feedback loop and the capability in dealing with parameter uncertainty. An equivalent relationship is established between quantum CFC and non-selective quantum MFC in the form of operator-sum representation. Using several examples of quantum feedback control, we show that quantum MFC can theoretically achieve better performance than quantum CFC in stabilizing a quantum state and dealing with Hamiltonian parameter uncertainty. The results enrich understanding of the relative advantages between quantum MFC and quantum CFC, and can provide useful information in choosing suitable feedback protocols for quantum systems.Comment: 24 page

Robust manipulation of superconducting qubits in the presence of fluctuations

Superconducting quantum systems are promising candidates for quantum information processing due to their scalability and design flexibility. However, the existence of defects, fluctuations, and inaccuracies is unavoidable for practical superconducting quantum circuits. In this paper, a sampling-based learning control (SLC) method is used to guide the design of control fields for manipulating superconducting quantum systems. Numerical results for one-qubit systems and coupled two-qubit systems show that the "smart" fields learned using the SLC method can achieve robust manipulation of superconducting qubits, even in the presence of large fluctuations and inaccuracies.Comment: 10 pages, 6 figure

Methane–propane hydrate formation and memory effect study with a reaction kinetics model

Although natural gas hydrates and hydrate exploration have been extensively studied for decades, the reaction kinetics and nucleation mechanism of hydrate formation is not fully understood. In its early stage, gas hydrate formation can be assumed to be an autocatalytic kinetic reaction with nucleation and initial growth. In this work, a reaction kinetics model has been established to form structure II methane–propane hydrate in an isochoric reactor. The computational model consists of six pseudo-elementary reactions for three dynamic processes: (1) gas dissolution into the bulk liquid, (2) a slow buildup of hydrate precursors for nucleation onset, and (3) rapid and autocatalytic hydrate growth after onset. The model was programmed using FORTRAN, with initiating parameters and rate constants that were derived or obtained from data fitted using experimental results. The simulations indicate that the length of nucleation induction is determined largely by an accumulation of oligomeric hydrate precursors up to a threshold value. The slow accumulation of precursors is the rate-limiting step for the overall hydrate formation, and its conversion into hydrate particles is critical for the rapid, autocatalytic reaction. By applying this model, the memory effect for hydrate nucleation was studied by assigning varied initial amounts of precursor or hydrate species in the simulations. The presence of pre-existing precursors or hydrate particles could facilitate the nucleation stage with a reduced induction time, and without affecting hydrate growth. The computational model with the performed simulations provides insight into the reaction kinetics and nucleation mechanism of hydrate formation.publishedVersio

Tensioned flexible riser vibrations under wave excitation, an investigation on the scale effect

In order to study the scale effect in wave-structure interactions and the role that structure-related parameters (tension T or bending stiffness EI) plays, riser model tests under regular waves were conducted using the model with multiple geometric scales (1:15, 1:12 and 1:9) in a wave basin. The riser model used is a novel structural design combing the outer polyvinyl chloride pipe with the core steel rod which could be simplified as a cantilever beam. Different initial tension T acting on the riser are tested by adjusting the slotted weight. The results show that the amplitude varies in a cubic fashion with the distance from the fixed end. In addition, the influence of the wave period and top tension T on the amplitude are investigated, which ultimately leads to a dimensionless number π1 = KCd·TL2/EI where KC is the classical Keulegan–Carpenter number (KC), EI shows the bending stiffness of the riser model and L gives the pipe length. With the KC number revised to take the distance from the fixed end into the calculation, this parameter provides a good measure in estimating the amplitudes of the riser vibrations induced by the waves

Residual Tensor Train: A Quantum-inspired Approach for Learning Multiple Multilinear Correlations

States of quantum many-body systems are defined in a high-dimensional Hilbert space, where rich and complex interactions among subsystems can be modelled. In machine learning, complex multiple multilinear correlations may also exist within input features. In this paper, we present a quantum-inspired multilinear model, named Residual Tensor Train (ResTT), to capture the multiple multilinear correlations of features, from low to high orders, within a single model. ResTT is able to build a robust decision boundary in a high-dimensional space for solving fitting and classification tasks. In particular, we prove that the fully-connected layer and the Volterra series can be taken as special cases of ResTT. Furthermore, we derive the rule for weight initialization that stabilizes the training of ResTT based on a mean-field analysis. We prove that such a rule is much more relaxed than that of TT, which means ResTT can easily address the vanishing and exploding gradient problem that exists in the existing TT models. Numerical experiments demonstrate that ResTT outperforms the state-of-the-art tensor network and benchmark deep learning models on MNIST and Fashion-MNIST datasets. Moreover, ResTT achieves better performance than other statistical methods on two practical examples with limited data which are known to have complex feature interactions.Comment: 12 pages, 6 figure

Sampling-based learning control of inhomogeneous quantum ensembles

Compensation for parameter dispersion is a significant challenge for control of inhomogeneous quantum ensembles. In this paper, we present a systematic methodology of sampling-based learning control (SLC) for simultaneously steering the members of inhomogeneous quantum ensembles to the same desired state. The SLC method is employed for optimal control of the state-to-state transition probability for inhomogeneous quantum ensembles of spins as well as $\Lambda$ type atomic systems. The procedure involves the steps of (i) training and (ii) testing. In the training step, a generalized system is constructed by sampling members according to the distribution of inhomogeneous parameters drawn from the ensemble. A gradient flow based learning and optimization algorithm is adopted to find the control for the generalized system. In the process of testing, a number of additional ensemble members are randomly selected to evaluate the control performance. Numerical results are presented showing the success of the SLC method.Comment: 8 pages, 9 figure

Sampling-based Learning Control for Quantum Systems with Uncertainties

Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for control design of quantum systems with uncertainties. The SLC method includes two steps of "training" and "testing". In the training step, an augmented system is constructed using artificial samples generated by sampling uncertainty parameters according to a given distribution. A gradient flow based learning algorithm is developed to find the control for the augmented system. In the process of testing, a number of additional samples are tested to evaluate the control performance where these samples are obtained through sampling the uncertainty parameters according to a possible distribution. The SLC method is applied to three significant examples of quantum robust control including state preparation in a three-level quantum system, robust entanglement generation in a two-qubit superconducting circuit and quantum entanglement control in a two-atom system interacting with a quantized field in a cavity. Numerical results demonstrate the effectiveness of the SLC approach even when uncertainties are quite large, and show its potential for robust control design of quantum systems.Comment: 11 pages, 9 figures, in press, IEEE Transactions on Control Systems Technology, 201