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We propose a sparse grids based adaptive noise reduction strategy for electrostatic particle-in-cell (PIC) simulations. Our approach is based on the key idea of relying on sparse grids instead of a regular grid in order to increase the…
In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with…
The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization…
Optically addressable spins are actively investigated in quantum communication, processing and sensing. Optical and spin coherence lifetimes, which determine quantum operation fidelity and storage time, are often limited by spin-spin…
A major goal of developing high-precision control of many-body quantum systems is to realise their potential as quantum computers. Probably the most significant obstacle in this direction is the problem of "decoherence": the extreme…
Gradient clipping is a standard training technique used in deep learning applications such as large-scale language modeling to mitigate exploding gradients. Recent experimental studies have demonstrated a fairly special behavior in the…
Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…
In this paper, we study the electron spin decoherence of single defects in silicon carbide (SiC) nuclear spin bath. We find that, although the natural abundance of $^{29}\rm{Si}$ ($p_{\rm{Si}}=4.7\%$) is about 4 times larger than that of…
Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…
The non-asymptotic analysis of Stochastic Gradient Descent (SGD) typically yields bounds that decompose into a bias term and a variance term. In this work, we focus on the bias component and study the extent to which SGD can match the…
Optically-interfaced spins in the solid state are a promising platform for quantum technologies. A crucial component of these systems is high-fidelity, projective measurement of the spin state. In previous work with laser-cooled atoms and…
Solid-state electronic spin systems such as nitrogen-vacancy (NV) color centers in diamond are promising for applications of quantum information, sensing, and metrology. However, a key challenge for such solid-state systems is to realize a…
Optically addressable spin defects in silicon carbide (SiC) are an emerging platform for quantum information processing. Lending themselves to modern semiconductor nanofabrication, they promise scalable high-efficiency spin-photon…
Hybrid spin-mechanical systems are a promising platform for future quantum technologies. Usually they require application of additional microwave fields to project integer spin to a readable state. We develop a theory of optically detected…
Spin squeezed states provide a seminal example of how the structure of quantum mechanical correlations can be controlled to produce metrologically useful entanglement. Such squeezed states have been demonstrated in a wide variety of…
This paper presents a novel algorithm that leverages Stochastic Gradient Descent strategies in conjunction with Random Features to augment the scalability of Conic Particle Gradient Descent (CPGD) specifically tailored for solving sparse…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
The electron spins of semiconductor defects can have complex interactions with their host, particularly in polar materials like SiC where electrical and mechanical variables are intertwined. By combining pulsed spin resonance with ab-initio…
The spin dynamics and spin relaxation of itinerant electrons in quantum wires with spin-orbit coupling is reviewed. We give an introduction to spin dynamics, and review spin-orbit coupling mechanisms in semiconductors. The spin diffusion…
Decentralized optimization algorithms have attracted intensive interests recently, as it has a balanced communication pattern, especially when solving large-scale machine learning problems. Stochastic Path Integrated Differential Estimator…