8 papers
Retraction-Free Optimization over the Stiefel Manifold for the LoRA Fine-Tuning
Yuan Zhang, Jiang Hu, Zhijian Lai +2
Optimization over the Stiefel manifold plays a significant role in various machine learning tasks. Existing methods either use the retraction operators, requiring costly orthonorma…
Quantum Grover Adaptive Search for Discrete Simulation Optimization
Mingjie Hu, Jian-qiang Hu, Enlu Zhou
Quantum computing has advanced rapidly in recent years and has shown advantages in a variety of domains. In this paper, we investigate its potential for discrete simulation optimiz…
Achieving double-logarithmic precision dependence in optimization-based quantum unstructured search
Zhijian Lai, Dong An, Jiang Hu +1
Grover's algorithm is a fundamental quantum algorithm that achieves a quadratic speedup for unstructured search problems of size . Recent studies have reformulated this task as…
A Human-AI Collaborative Workflow for Mathematical Discovery: A Case Study in Grover-Compatible Riemannian Optimization
Chenyi Li, Zhijian Lai, Dong An +2
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for inte…
A Grover-compatible manifold optimization algorithm for quantum search
Zhijian Lai, Dong An, Jiang Hu +1
Grover's algorithm is a fundamental quantum algorithm that offers a quadratic speedup for the unstructured search problem by alternately applying physically implementable oracle an…
Extended parameter shift rules with minimal derivative variance for parameterized quantum circuits
Zhijian Lai, Jiang Hu, Dong An +1
Parameter shift rules (PSRs) are useful methods for computing arbitrary-order derivatives of the cost function in parameterized quantum circuits. The basic idea of PSRs is to evalu…
Riemannian EXTRA: Communication-efficient decentralized optimization over compact submanifolds with data heterogeneity
Jiayuan Wu, Zhanwang Deng, Jiang Hu +2
We consider decentralized optimization over a compact Riemannian submanifold in a network of agents, where each agent holds a smooth, nonconvex local objective defined by its p…
Interpolation-based coordinate descent method for parameterized quantum circuits
Zhijian Lai, Jiang Hu, Taehee Ko +2
Parameterized quantum circuits (PQCs) are ubiquitous in the design of hybrid quantum-classical algorithms. In this work, we propose an interpolation-based coordinate descent (ICD)…