Related papers: Parameter estimation of quantum processes using co…
Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of…
The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. In QAOA, a quantum circuit is trained -- by repeatedly adjusting circuit parameters -- to solve a problem.…
This work shows an approach to reduce the dimensionality of matrix representations of quantum channels. It is achieved by finding a base of the cone of positive semidefinite matrices which represent quantum channels. Next, this is…
Variational quantum algorithms, which utilize Parametrized Quantum Circuits (PQCs), are promising tools to achieve quantum advantage for optimization problems on near-term quantum devices. Their PQCs have been conventionally constructed…
Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…
The problems of optimally estimating a phase, a direction, and the orientation of a Cartesian frame (or trihedron) with general pure states are addressed. Special emphasis is put on estimation schemes that allow for inconclusive answers or…
The optimization of system parameters is a ubiquitous problem in science and engineering. The traditional approach involves setting to zero the partial derivatives of the objective function with respect to each parameter, in order to…
We propose a quantum process tomography scheme that utilizes two-mode squeezed vacuum to realize the parameter estimation with Heisenberg scaling. The objective is to estimate a rotating angle of polarization and parity detection is used as…
The cone of positive-semidefinite (PSD) matrices is fundamental in convex optimization, and we extend this notion to tensors, defining PSD tensors, which correspond to separable quantum states. We study the convex optimization problem over…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…
In many applications, solutions of convex optimization problems are updated on-line, as functions of time. In this paper, we consider parametric semidefinite programs, which are linear optimization problems in the semidefinite cone whose…
We present filtering equations for single shot parameter estimation using continuous quantum measurement. By embedding parameter estimation in the standard quantum filtering formalism, we derive the optimal Bayesian filter for cases when…
Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process…
Multi-objective verification problems of parametric Markov decision processes under optimality criteria can be naturally expressed as nonlinear programs. We observe that many of these computationally demanding problems belong to the…
The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation…
We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting…
We propose novel optimal and parameter-free algorithms for computing an approximate solution with small (projected) gradient norm. Specifically, for computing an approximate solution such that the norm of its (projected) gradient does not…
Quantum metrology is a rapidly developing branch of quantum technologies. While various theories have been established on quantum metrology for Markovian processes, i.e., quantum channel estimation, quantum metrology for non-Markovian…
Variational (or, parameterized) quantum circuits are quantum circuits that contain real-number parameters, that need to be optimized/"trained" in order to achieve the desired quantum-computational effect. For that training, analytic…