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…
Pauli-structured preconditioning for quantum linear system solvers
Hantao Nie, Zhijian Lai, Dong An
Preconditioning is a fundamental technique for accelerating classical linear system solvers, and understanding when its benefits persist in quantum linear system (QLS) solvers is i…
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…
Quantum circuit design from a retraction-based Riemannian optimization framework
Zhijian Lai, Hantao Nie, Jiayuan Wu +1
Designing quantum circuits for ground state preparation is a fundamental task in quantum information science. However, standard Variational Quantum Algorithms (VQAs) are often cons…
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…
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)…