Quantum Polynomial Root Finding and Entanglement-enhanced Spacial Encoding for High-dimensional Data Processing
POSTER
Abstract
We present a novel quantum algorithmic framework that leverages quantum trignometic encoding for polynomial root finding and high-dimensional spatial data encoding.
Our approach introduces three key innovations: (1) a quantum polynomial root finding algorithm utilizing amplitude amplification and phase estimation,
(2) a quantum gradient descent method that enhances optimization in exponentially large parameter spaces, and
(3) an entanglement-based spatial encoding technique that employs Walsh-Hadamard transforms for efficient data representation. We demonstrate quantum advantages in computational complexity, achieving polynomial-to-exponential speedups over classical methods for specific problem instances. Experimental validation on IBM quantum processing units (QPUs) confirms the effectiveness and scalability of our framework for near-term quantum devices.
Our approach introduces three key innovations: (1) a quantum polynomial root finding algorithm utilizing amplitude amplification and phase estimation,
(2) a quantum gradient descent method that enhances optimization in exponentially large parameter spaces, and
(3) an entanglement-based spatial encoding technique that employs Walsh-Hadamard transforms for efficient data representation. We demonstrate quantum advantages in computational complexity, achieving polynomial-to-exponential speedups over classical methods for specific problem instances. Experimental validation on IBM quantum processing units (QPUs) confirms the effectiveness and scalability of our framework for near-term quantum devices.
*This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility This study was supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 using NERSC award NERSC DDR-ERCAP0034486
Publication: https://www.arxiv.org/abs/2508.18464 (accepted to AAAI Quantum Symposium 2025)
https://arxiv.org/abs/2504.04021 (accepted to international conference on quantum computing and engineering 2025)
Presenters
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Ziqing Guo
- Texas Tech University