5 papers
Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy
Baicheng Li, Haizhao Yang, Shijun Zhang
In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks. We first show that any function in $W^{2…
Finite Expression Method with TranNet-based Function Learning for High-Dimensional Partial Differential Equations
Phuoc-Toan Huynh, Feng Bao, Haizhao Yang +1
In this paper, we study a machine-learning-based solver for high-dimensional partial differential equations (PDEs). Computing accurate solutions efficiently for such problems remai…
Randomized Subsystem Descent for Fermion-to-Qubit Mapping
Gengzhi Yang, Di Wu, Haizhao Yang +2
We propose a versatile and efficient algorithmic framework for optimizing fermion-to-qubit mappings by generalizing the idea of randomized block coordinate descent. Our greedy appr…
Quantum Circuit Encodings of Polynomial Chaos Expansions
Junaid Aftab, Christoph Schwab, Haizhao Yang +1
This work investigates the expressive power of quantum circuits in approximating high-dimensional, real-valued functions. We focus on countably-parametric holomorphic maps $u:U\to…
Approximating Korobov Functions via Quantum Circuits
Junaid Aftab, Haizhao Yang
Understanding the capacity of quantum circuits through the lens of approximation theory is essential for evaluating the complexity of quantum circuits required to solve various pro…