Open Access

ARTICLE

Daniel Koch^1,*, Brian Pardo², Kip Nieman²
Journal of Quantum Computing, Vol.8, pp. 75-100, 2026, DOI:10.32604/jqc.2026.079392 - 26 June 2026
Abstract Quantum Amplitude Amplification (QAA), the generalization of Grover’s algorithm, is capable of yielding optimal solutions to combinatorial optimization problems with high probabilities. In this work we extend the conventional 2-dimensional mathematical representation of Grover’s (marked and non-marked orthogonal collective states) to oracle operators which encode cost functions, such as those shown in previous studies with QUBO (Quadratic Unconstrained Binary Optimization). We show that unconstrained linear cost functions (no quadratic or higher terms) are a special case whereby the symmetry of the system leads to an exact formula for determining optimal oracle parameter settings, the first… More >

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REVIEW

Yuzhen He¹, Zhiguo Qu^1,2,*, Le Sun¹
Journal of Quantum Computing, Vol.8, pp. 55-73, 2026, DOI:10.32604/jqc.2026.083993 - 26 June 2026
Abstract Quantum fuzzy neural networks (QFNNs) integrate fuzzy systems, neural networks, and quantum models, aiming to leverage their complementary strengths in handling uncertainty, parameter learning, and feature representation. However, a unified framework for effectively combining these three components remains lacking, and the existing literature reflects diverse and sometimes inconsistent modeling strategies. This paper provides a comprehensive review of the fundamental theories underlying QFNNs, including the core design principles and mathematical formulations, as well as the major categories of network architectures. Representative training strategies and typical application scenarios are also systematically examined. Furthermore, persistent issues in the More >

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54

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ARTICLE

Martin Bombardelli^1,2,3, Gérard Fleury¹, Philippe Lacomme^1,*, Bogdan Vulpescu²
Journal of Quantum Computing, Vol.8, pp. 13-54, 2026, DOI:10.32604/jqc.2026.075438 - 26 June 2026
Abstract This work aims to present the fundamental concepts necessary for performing computations on photonic quantum computers by detailing the gates specific to this architecture and introducing the relationships between standard Pauli gates and their counterparts in photonic systems. Physical considerations related to the optical components are addressed. Theoretical aspects concerning quantum operators are presented, and applied sections demonstrating implementations using the Perceval library developed by Quandela are given. This paper provides a comprehensive, state-of-the-art description of photonic quantum gates in a formal way. The main contribution of this paper is to allow researchers with prior… More >

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105

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ARTICLE

Reuven Ianconescu^1,2,*, Bin Zhang^1,3, Aharon Friedman⁴, Jacob Scheuer^1,5, Avraham Gover^1,5
Journal of Quantum Computing, Vol.8, pp. 1-11, 2026, DOI:10.32604/jqc.2026.076154 - 27 February 2026
Abstract Interactions between many (initially separate) quantum systems raise the question on how to prepare and how to compute the measurable results of their interaction. When one prepares each system individually and let them interact, one has to tensor multiply their density matrices and apply Hamiltonians on the composite system (i.e., the system which includes all the interacting systems) for definite time intervals. Evaluating the final state of one of the systems after multiple consecutive interactions requires tracing all other systems out of the composite system, which may grow to immense dimensions. For computational efficiency during… More >

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