Open Access

ARTICLE

Analysis and Experimental Demonstration of Amplitude Amplification for Combinatorial Optimization

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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67

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REVIEW

Quantum Fuzzy Neural Networks: A Review of Foundations, Modeling Routes, and Open Problems

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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104

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54

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ARTICLE

Foundations of Photonic Quantum Computation. Part 1. Introduction to Quantum Operators

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

On the Validity of Intermediate Tracing in Multiple Quantum Interactions

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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503

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305

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ARTICLE

3-Qubit Circular Quantum Convolution Computation Using the Fourier Transform with Illustrative Examples

Artyom M. Grigoryan^1,*, Sos S. Agaian²

Journal of Quantum Computing, Vol.6, pp. 1-14, 2024, DOI:10.32604/jqc.2023.026981
Abstract In this work, we describe a method of calculation of the 1-D circular quantum convolution of signals represented by 3-qubit superpositions in the computational basis states. The examples of the ideal low pass and high pass filters are described and quantum schemes for the 3-qubit circular convolution are presented. In the proposed method, the 3-qubit Fourier transform is used and one addition qubit, to prepare the quantum superposition for the inverse quantum Fourier transform. It is considered that the discrete Fourier transform of one of the signals is known and calculated in advance and only More >

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3310

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2179

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ARTICLE

Analysis of Innovative Quantum Optimization Solutions for Shor’s Period Finding Algorithm Applied to the Computation of a^x mod 15

Kaleb Dias Antoine KODO^1,*, Eugène C. EZIN^1,2

Journal of Quantum Computing, Vol.7, pp. 17-38, 2025, DOI:10.32604/jqc.2025.059089
Abstract In the rapidly evolving domain of quantum computing, Shor’s algorithm has emerged as a groundbreaking innovation with far-reaching implications for the field of cryptographic security. However, the efficacy of Shor’s algorithm hinges on the critical step of determining the period, a process that poses a substantial computational challenge. This article explores innovative quantum optimization solutions that aim to enhance the efficiency of Shor’s period finding algorithm. The article focuses on quantum development environments, such as Qiskit and Cirq. A detailed analysis is conducted on three notable tools: Qiskit Transpiler, BQSKit, and Mitiq. The performance of More >

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1522

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ARTICLE

Advancing Quantum Technology: Insights Form Mach-Zehnder Interferometer in Quantum State Behaviour and Error Correction

Priyanka¹, Damodarakurup Sajeev², Shaik Ahmed³, Shankar Pidishety³, Ram Soorat^3,*

Journal of Quantum Computing, Vol.6, pp. 53-66, 2024, DOI:10.32604/jqc.2024.054000
Abstract The present study delves into the application of investigating quantum state behaviour, particularly focusing on coherent and superposition states. These states, characterized by their remarkable stability and precision, have found extensive utility in various domains of quantum mechanics and quantum information processing. Coherent states are valuable for manipulating quantum systems with accuracy. Superposition states allow quantum systems to exist in numerous configurations at the same time, which paves the way for quantum computing’s capacity for parallel processing. The research accentuates the crucial role of quantum error correction (QEC) in ensuring the stability and reliability of… More >

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6676

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ARTICLE

IQAOA for Two Routing Problems: A Methodological Contribution with Application to TSP and VRP

Eric Bourreau¹, Gérard Fleury², Philippe Lacomme^2,*

Journal of Quantum Computing, Vol.6, pp. 25-51, 2024, DOI:10.32604/jqc.2024.048792
Abstract The paper presents a novel quantum method for addressing two fundamental routing problems: the Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP), both central to routing challenges. The proposed method, named the Indirect Quantum Approximate Optimization Algorithm (IQAOA), leverages an indirect solution representation using ranking. Our contribution focuses on two main areas: 1) the indirect representation of solutions, and 2) the integration of this representation into an extended version of QAOA, called IQAOA. This approach offers an alternative to QAOA and includes the following components: 1) a quantum parameterized circuit designed to simulate… More >

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2293

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6786

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ARTICLE

Optimized General Uniform Quantum State Preparation

Mark Ariel Levin^*

Journal of Quantum Computing, Vol.6, pp. 15-24, 2024, DOI:10.32604/jqc.2024.047423
Abstract Quantum algorithms for unstructured search problems rely on the preparation of a uniform superposition, traditionally achieved through Hadamard gates. However, this incidentally creates an auxiliary search space consisting of nonsensical answers that do not belong in the search space and reduce the efficiency of the algorithm due to the need to neglect, un-compute, or destructively interfere with them. Previous approaches to removing this auxiliary search space yielded large circuit depth and required the use of ancillary qubits. We have developed an optimized general solver for a circuit that prepares a uniform superposition of any N More >

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2159

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1679

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ARTICLE

A Genetic Approach to Minimising Gate and Qubit Teleportations for Multi-Processor Quantum Circuit Distribution

Oliver Crampton^1,*, Panagiotis Promponas^1,2, Richard Chen¹, Paul Polakos¹, Leandros Tassiulas², Louis Samuel¹

Journal of Quantum Computing, Vol.7, pp. 1-15, 2025, DOI:10.32604/jqc.2025.061275
Abstract Distributed Quantum Computing (DQC) provides a means for scaling available quantum computation by interconnecting multiple quantum processor units (QPUs). A key challenge in this domain is efficiently allocating logical qubits from quantum circuits to the physical qubits within QPUs, a task known to be NP-hard. Traditional approaches, primarily focused on graph partitioning strategies, have sought to reduce the number of required Bell pairs for executing non-local CNOT operations, a form of gate teleportation. However, these methods have limitations in terms of efficiency and scalability. Addressing this, our work jointly considers gate and qubit teleportations introducing… More >

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2048

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1658

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ARTICLE

Comparative Study of CPLEX and D-Wave for Track Finding Resolution

Duy Dao¹, Hervé Kerivin², Philippe Lacomme^2,*, Bogdan Vulpescu³

Journal of Quantum Computing, Vol.7, pp. 39-54, 2025, DOI:10.32604/jqc.2025.064764
Abstract Track finding is a complex optimization problem, originally introduced in particle physics for the reconstruction of the trajectories of particles. A track is typically composed of several consecutive segments, which together form a smooth curve without any bifurcations. In this paper, we investigate various modeling approaches to assess their effectiveness and impact when applied to track finding, using both quantum and classical methods. We present implementations of three classical models using CPLEX, two quantum models on actual D-Wave quantum computers, and one quantum model on a D-Wave simulator. The results show that, while CPLEX provides… More >

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1793

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1098

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ARTICLE

Investigating Techniques to Optimise the Layout of Turbines in a Windfarm Using a Quantum Computer

James Hancock^*, Matthew Craven, Craig McNeile, Davide Vadacchino

Journal of Quantum Computing, Vol.7, pp. 55-79, 2025, DOI:10.32604/jqc.2025.068127
Abstract This paper investigates Windfarm Layout Optimization (WFLO), where we formulate turbine placement considering wake effects as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Wind energy plays a critical role in the transition toward sustainable power systems, but the optimal placement of turbines remains a challenging combinatorial problem due to complex wake interactions. With recent advances in quantum computing, there is growing interest in exploring whether hybrid quantum-classical methods can provide advantages for such computationally intensive tasks. We investigate solving the resulting QUBO problem using the Variational Quantum Eigensolver (VQE) implemented on Qiskit’s quantum computer simulator, More >

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1541

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1183

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ARTICLE

State-Space Reduction Techniques Exploiting Specific Constraints for Quantum Search Initialization, Application to an Outage Planning Problem

Rodolphe Griset^1,#,*, Ioannis Lavdas^2,§, Jiří Guth Jarkovský³

Journal of Quantum Computing, Vol.7, pp. 81-105, 2025, DOI:10.32604/jqc.2025.066064
Abstract Quantum search has emerged as one of the most promising fields in quantum computing. State-of-the-art quantum search algorithms enable the search for specific elements in a distribution by monotonically increasing the density of these elements relative to the rest of the distribution. These kinds of algorithms demonstrate a theoretical quadratic speed-up on the number of queries compared to classical search algorithms in unstructured spaces. Unfortunately, the major part of the existing literature applies quantum search to problems whose size grows exponentially with the input size without exploiting any specific problem structure, rendering this kind of… More >

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680

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585

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ARTICLE

On the Validity of Intermediate Tracing in Multiple Quantum Interactions

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
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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503

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305