Published In
Quantum Reports
Document Type
Article
Publication Date
9-24-2026
Subjects
Quantum computing
Abstract
Optimization problems in machine-learning (ML) applications can be computationally challenging for classical methods, particularly when they involve large, unstructured search spaces. Quantum computing offers a promising approach to combinatorial optimization by utilizing quantum superposition and amplitude amplification. This paper presents a new methodology using logic-based quantum machine learning (QML) as a complete framework for employing a multi-solution ternary Grover’s algorithm to minimize incomplete binary functions represented by Pseudo-Kronecker Reed–Muller (PKRO) expansions, consistent with Occam’s razor principle. Unlike previous quantum approaches based on Kronecker Reed–Muller (KRO) or fixed-polarity Reed–Muller (FPRM) representations, our work introduces the first Grover-based optimization framework for PKRO forms. This framework formulates logic minimization as a quantum search problem to identify minimum-cost AND-XOR representations with the fewest nonzero coefficients. A hybrid binary–ternary quantum architecture is developed to explore the enlarged PKRO search space, enabling optimization of both completely and incompletely specified binary functions. Owing to the greater flexibility of PKRO expansions, our framework produces more compact AND–XOR representations than KRO- and FPRM-based approaches. Across all 256 3-variable binary functions, PKRO provides less nonzero coefficients for 4.688% of functions compared with KRO and for 37.5% compared with FPRM, with average reductions of 0.047 and 0.484 nonzero coefficients, respectively. Our multi-solution ternary Grover search reduces the number of Grover iterations by more than 91% compared with the single-solution approach.
Rights
Copyright (c) 2026 The Authors
This work is licensed under a Creative Commons Attribution 4.0 International License.
Locate the Document
DOI
10.3390/quantum8030092
Persistent Identifier
https://archives.pdx.edu/ds/psu/45162
Citation Details
Lee, S., Al-Bayaty, A., & Perkowski, M. (2026). Multi-Solution Ternary Grover’s Algorithm for Logic-Based Quantum Machine Learning with Pseudo-Kronecker Reed–Muller Form Minimization. Quantum Reports, 8(3), 92.