Related papers: Modified Newton-Raphson GRAPE methods for optimal …
We have designed efficient quantum circuits for the three-qubit Toffoli (controlled-controlled NOT) and the Fredkin (controlled-SWAP) gate, optimized via genetic programming methods. The gates thus obtained were experimentally implemented…
We present a finite-time analysis of two smoothed functional stochastic approximation algorithms for simulation-based optimization. The first is a two time-scale gradient-based method, while the second is a three time-scale Newton-based…
Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…
We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach…
The experimental optimization of a two-qubit controlled-Z (CZ) gate is realized following two different data-driven gradient ascent pulse engineering (GRAPE) protocols in the aim of optimizing the gate operator and the output quantum state,…
Power grid operators typically solve large-scale, nonconvex optimal power flow (OPF) problems throughout the day to determine optimal setpoints for generators while adhering to physical constraints. Despite being at the heart of many OPF…
We propose the generalized Newton's method (GeN) -- a Hessian-informed approach that applies to any optimizer such as SGD and Adam, and covers the Newton-Raphson method as a sub-case. Our method automatically and dynamically selects the…
Many problems in applied mathematics require root finding algorithms. Unfortunately, root finding methods have limitations. Firstly, regarding the convergence, there is a trade-off between the size of it's domain and it's rate. Secondly the…
Designing quantum circuits for ground state preparation is a fundamental task in quantum information science. However, standard Variational Quantum Algorithms (VQAs) are often constrained by limited ansatz expressivity and difficult…
An adaptive regularization algorithm for unconstrained nonconvex optimization is presented in which the objective function is never evaluated, but only derivatives are used. This algorithm belongs to the class of adaptive regularization…
Robust and high-precision quantum control is extremely important but challenging for the functionization of scalable quantum computation. In this paper, we show that this hard problem can be translated to a supervised machine learning task…
High-fidelity control of quantum systems is essential for scalable quantum technologies. We introduce a shooting-based method which yields smooth control pulses designed to implement gates on discrete quantum systems, and demonstrate its…
We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are…
Automatic Robotic Assembly Sequence Planning (RASP) can significantly improve productivity and resilience in modern manufacturing along with the growing need for greater product customization. One of the main challenges in realizing such…
We consider concave minimization problems over non-convex sets.Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where…
We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
The feasibility of high-fidelity single-qubit operations of a hole spin in a quantum dot molecule by electric g tensor control is demonstrated. Apart from a constant external magnetic field the proposed scheme allows for an exclusively…
Convex and nonconvex finite-sum minimization arises in many scientific computing and machine learning applications. Recently, first-order and second-order methods where objective functions, gradients and Hessians are approximated by…
We establish or refute the optimality of inexact second-order methods for unconstrained nonconvex optimization from the point of view of worst-case evaluation complexity, improving and generalizing the results of Cartis, Gould and Toint…