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Curvilinear, multiblock summation-by-parts finite difference operators with the simultaneous approximation term method provide a stable and accurate framework for solving the wave equation in second order form. That said, the standard…
A series of successive quantizations is considered, starting with the quantization of a non relativistic or relativistic point particle: 1) quantization of a particle's position, 2) quantization of wave function, 3) quantization of wave…
We propose a quantum-state-certification protocol for stabilizer states, motivated by application in in-situ testing of NISQ-era quantum computer systems: The number of qubits is bounded, and in terms of cost of running the protocol,…
Quantum fidelity estimation is essential for benchmarking quantum states and processes on noisy quantum devices. While stabilizer operations form the foundation of fault-tolerant quantum computing, non-stabilizer resources further enable…
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…
Sigma-Delta modulation is a popular method for analog-to-digital conversion of bandlimited signals that employs coarse quantization coupled with oversampling. The standard mathematical model for the error analysis of the method measures the…
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. When such a signal is acquired according to the principles of CS, the measurements still…
We consider an unstable scalar linear stochastic system, $X_{n+1}=a X_n + Z_n - U_n$, where $a \geq 1$ is the system gain, $Z_n$'s are independent random variables with bounded $\alpha$-th moments, and $U_n$'s are the control actions that…
Quantum entanglement plays an important role in quantum computation and communication. It is necessary for many protocols and computations, but causes unexpected disturbance of computational states. Hence, static analysis of quantum…
When are quantum filters asymptotically independent of the initial state? We show that this is the case for absolutely continuous initial states when the quantum stochastic model satisfies an observability condition. When the initial system…
We propose an encoding and control strategy for the stabilization of switched systems with limited information, supposing the controller is given for each mode. Only the quantized output and the active mode of the plant at each sampling…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
The matter of the stability for multi-asset American option pricing problems is a present remaining challenge. In this paper a general transformation of variables allows to remove cross derivative terms reducing the stencil of the proposed…
This paper studies the problem of stabilizing a continuous-time switched linear system by quantized output feedback. We assume that the quantized outputs and the switching signal are available to the controller at all time. We develop an…
We propose a general experimental quantum state engineering scheme for the high-fidelity conditional generation of a large variety of nonclassical states of traveling optical fields. It contains a single measurement, thereby achieving a…
The standard quantum state discrimination problem can be understood as a communication scenario involving a sender and a receiver following these three steps: (i) the sender encodes information in pre-agreed quantum states, (ii) sends them…
Stability and stabilization analysis of fractional-order linear time-invariant (FO-LTI) systems with different derivative orders is studied in this paper. First, by using an appropriate linear matrix function, a single-order equivalent…
Stabilizing an unknown dynamical system is one of the central problems in control theory. In this paper, we study the sample complexity of the learn-to-stabilize problem in Linear Time-Invariant (LTI) systems on a single trajectory. Current…
In this paper we study the quantization stage that is implicit in any compressed sensing signal acquisition paradigm. We propose using Sigma-Delta quantization and a subsequent reconstruction scheme based on convex optimization. We prove…