Robust and Efficient Hamiltonian Learning

With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the interaction, i.e., to learn the Hamiltonian, which determines both static and dynamic properties of the system. Conventional Hamiltonian learning methods either require costly process tomography or adopt impractical assumptions, such as prior information on the Hamiltonian structure and the ground or thermal states of the system. In this work, we present a robust and efficient Hamiltonian learning method that circumvents these limitations based only on mild assumptions. The proposed method can efficiently learn any Hamiltonian that is sparse on the Pauli basis using only short-time dynamics and local operations without any information on the Hamiltonian or preparing any eigenstates or thermal states. The method has a scalable complexity and a vanishing failure probability regarding the qubit number. Meanwhile, it performs robustly given the presence of state preparation and measurement errors and resiliently against a certain amount of circuit and shot noise. We numerically test the scaling and the estimation accuracy of the method for transverse field Ising Hamiltonian with random interaction strengths and molecular Hamiltonians, both with varying sizes and manually added noise. All these results verify the robustness and efficacy of the method, paving the way for a systematic understanding of the dynamics of large quantum systems.Comment: 41 pages, 6 figures, Open source implementation available at https://github.com/zyHan2077/HamiltonianLearnin

A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data

Distributed Detection and Estimation in Wireless Sensor Networks

In this article we consider the problems of distributed detection and estimation in wireless sensor networks. In the first part, we provide a general framework aimed to show how an efficient design of a sensor network requires a joint organization of in-network processing and communication. Then, we recall the basic features of consensus algorithm, which is a basic tool to reach globally optimal decisions through a distributed approach. The main part of the paper starts addressing the distributed estimation problem. We show first an entirely decentralized approach, where observations and estimations are performed without the intervention of a fusion center. Then, we consider the case where the estimation is performed at a fusion center, showing how to allocate quantization bits and transmit powers in the links between the nodes and the fusion center, in order to accommodate the requirement on the maximum estimation variance, under a constraint on the global transmit power. We extend the approach to the detection problem. Also in this case, we consider the distributed approach, where every node can achieve a globally optimal decision, and the case where the decision is taken at a central node. In the latter case, we show how to allocate coding bits and transmit power in order to maximize the detection probability, under constraints on the false alarm rate and the global transmit power. Then, we generalize consensus algorithms illustrating a distributed procedure that converges to the projection of the observation vector onto a signal subspace. We then address the issue of energy consumption in sensor networks, thus showing how to optimize the network topology in order to minimize the energy necessary to achieve a global consensus. Finally, we address the problem of matching the topology of the network to the graph describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R. Chellapa and S. Theodoridis, Eds., Elsevier, 201

Optimal control and robust estimation for ocean wave energy converters

This thesis deals with the optimal control of wave energy converters and some associated observer design problems. The first part of the thesis will investigate model predictive control of an ocean wave energy converter to maximize extracted power. A generic heaving converter that can have both linear dampers and active elements as a power take-off system is considered and an efficient optimal control algorithm is developed for use within a receding horizon control framework. The optimal control is also characterized analytically. A direct transcription of the optimal control problem is also considered as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard nonlinear program solver. Since the system model is bilinear and the cost function is not convex quadratic, the resulting optimization problem is shown not to be a quadratic program. Results are compared with other methods like optimal latching to demonstrate the improvement in absorbed power under irregular sea condition simulations. In the second part, robust estimation of the radiation forces and states inherent in the optimal control of wave energy converters is considered. Motivated by this, low order H∞ observer design for bilinear systems with input constraints is investigated and numerically tractable methods for design are developed. A bilinear Luenberger type observer is formulated and the resulting synthesis problem reformulated as that for a linear parameter varying system. A bilinear matrix inequality problem is then solved to find nominal and robust quadratically stable observers. The performance of these observers is compared with that of an extended Kalman filter. The robustness of the observers to parameter uncertainty and to variation in the radiation subsystem model order is also investigated. This thesis also explores the numerical integration of bilinear control systems with zero-order hold on the control inputs. Making use of exponential integrators, exact to high accuracy integration is proposed for such systems. New a priori bounds are derived on the computational complexity of integrating bilinear systems with a given error tolerance. Employing our new bounds on computational complexity, we propose a direct exponential integrator to solve bilinear ODEs via the solution of sparse linear systems of equations. Based on this, a novel sparse direct collocation of bilinear systems for optimal control is proposed. These integration schemes are also used within the indirect optimal control method discussed in the first part.Open Acces