8 papers
Quantum Alternating Direction Method of Multipliers for Semidefinite Programming
Hantao Nie, Dong An, Zaiwen Wen
Semidefinite programming (SDP) is a fundamental convex optimization problem with wide-ranging applications. However, solving large-scale instances remains computationally challengi…
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 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…
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…
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…
Advancing Mathematical Research via Human-AI Interactive Theorem Proving
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…