arXiv subjects

Ali Al-Bayaty

Publications and source records attributed to Ali Al-Bayaty.

At least 19 recordsLinked to original sources

arXiv2026

Factorization of Exclusive-Sum-Of-Products Expressions with Rectangle Covering to Reduce Quantum Circuit Cost

The implementation of quantum circuits is currently very expensive, especially due to the usage of large Toffoli gates. Therefore, it is critical to optimize circuit costs by factoring expressions as they become more complex. In the proposed algorithms to factor ESOP expressions, each product term is converted into a cell in a 2D matrix, and optimal factored AND/EXOR solutions are determined using Disjoint and Even-Odd Rectangle covering methods. Two Python programs implementing these algorithms were tested and evaluated using well-known benchmarks. The results showed that both the literal counts used in classical logic circuits as well as the Maslov cost used in quantum circuits was reduced by 20%-95% depending on expression size.

quant-ph↗

arXiv2026

MAPS: A Novel Multi-Axial Projective Sphere for Geometrically Visualizing Higher d-Valued Quantum State-Space of Qudits

Visualizing the d-valued quantum state-space of quantum systems serves as a foundational pillar for the scientific research and practical applications in quantum computing and information science, where d >= 2. The 2-valued quantum states of a qubit are elegantly visualized on the three-dimensional Bloch sphere. In contrast, expanding this geometrical paradigm to visualize higher d-valued quantum states of a qudit (d >= 3), e.g., a qutrit (d=3), ququadit (d=4), and quintit (d=5), leads to severe structural and topological complexities. This paper introduces a new generalized three-dimensional framework to effectively visualize higher d-valued quantum states of a qudit, in the aspects of ease of illustration, structural simplicity, and natural representation for researchers and engineers. We called this new framework the "multi-axial projective sphere (MAPS)", which consists of n projectional intersecting spatial axes, where 0 <= n <= d-1. We also propose a group of novel d-valued phase axial-based gates, to swivel and shift d-valued quantum states of a qudit along these n axes. Our generalized framework could be used for visualizing high-dimensional data for practical applications, e.g., machine learning, quantum machine learning, and quantum chemistry, where every axis of the MAPS represents a single feature of such data with its corresponding distinct values.

quant-ph↗

arXiv2026

A Conceptual Technology-Dependent Framework of Ternary Quantum Gates

This paper introduces a conceptual framework of technology-dependent ternary quantum gates that could be implemented and fabricated into future superconducting and photonic quantum systems for operating 3-valued quantum bits (qutrits). The "technology-dependent" means that such ternary quantum gates are on-purpose designed analogy to the contemporary binary quantum gates. Conceptually, the final built technology-dependent one-, two-, and three-qutrit gates are Chrestenson, Z3, 01, 02, 12, +1, +2 (including their corresponding inverse and controlled gates), a non-phase relative SWAP gate, and a cost-effective Toffoli gate, which is a generic ternary Galois Field (GF3) multiplication and addition circuit.

quant-ph↗

arXiv2026

Visualizing the state space and transformations of higher order quantum logics via toric geometry

We propose some new uses of toric variety structures in the study of quantum computation for small radices. In particular, we observe the concurrence of the equivalence classes of quantum states under quantum measurement and the orbits of the toric geometric structure of the state space. Visualizations of these state spaces and of certain fundamental unitary transformations in binary and ternary quantum logic and a method to develop new transformations based on these visualization techniques are presented. Transformations discussed included minimal universal sets for permutative ternary quantum circuits. In addition, general structures and synthesis methods based on quantum multiplexers are presented. A general framework for the design of optimal ternary quantum transformations and circuits is additionally presented. Finally, a number of open research areas that are extensions of the work presented herein are given.

quant-ph↗

arXiv2026

PSSF: Early osteoarthritis detection using physical synthetic knee X-ray scans and AI radiomics models

Knee osteoarthritis (OA) is a major cause of disability worldwide and is still largely assessed using subjective radiographic grading, most commonly the Kellgren-Lawrence (KL) scale. Artificial intelligence (AI) and radiomics offer quantitative tools for OA assessment but depend on large, well-annotated image datasets, mainly X-ray scans, that are often difficult to obtain because of privacy, governance and resourcing constraints. In this research, we introduce a physics-based synthetic simulation framework (PSSF) to fully generate controllable X-ray scans without patients' involvement and violating their privacy and institutional constraints. This PSSF is a 2D X-ray projection simulator of anteroposterior knee radiographs from a parametric anatomical model of the distal femur and proximal tibia. Using PSSF, we create a virtual cohort of 180 subjects (260 knees), each is imaged under three protocols (reference, low-dose, and geometry-shift). Medial joint regions are automatically localized, preprocessed, and processed with the Image Biomarker Standardisation Initiative (IBSI). Practically, three machine learning (ML) models are utilized, logistic regression, random forest, and gradient boosting, to train binary (KL-like "0" vs. "2") and three-class (0-2) prediction radiographic images. Robustness is assessed within IBSI protocol, cross-protocol, and multi-protocol scenarios. Finally, features stability is then evaluated using intraclass correlation coefficients across acquisition changes.

cs.CV↗

arXiv2026

IGAN: A New Inception-based Model for Stable and High-Fidelity Image Synthesis Using Generative Adversarial Networks

Generative Adversarial Networks (GANs) face a significant challenge of striking an optimal balance between high-quality image generation and training stability. Recent techniques, such as DCGAN, BigGAN, and StyleGAN, improve visual fidelity; however, such techniques usually struggle with mode collapse and unstable gradients at high network depth. This paper proposes a novel GAN structural model that incorporates deeper inception-inspired convolution and dilated convolution. This novel model is termed the Inception Generative Adversarial Network (IGAN). The IGAN model generates high-quality synthetic images while maintaining training stability, by reducing mode collapse as well as preventing vanishing and exploding gradients. Our proposed IGAN model achieves the Frechet Inception Distance (FID) of 13.12 and 15.08 on the CUB-200 and ImageNet datasets, respectively, representing a 28-33% improvement in FID over the state-of-the-art GANs. Additionally, the IGAN model attains an Inception Score (IS) of 9.27 and 68.25, reflecting improved image diversity and generation quality. Finally, the two techniques of dropout and spectral normalization are utilized in both the generator and discriminator structures to further mitigate gradient explosion and overfitting. These findings confirm that the IGAN model potentially balances training stability with image generation quality, constituting a scalable and computationally efficient framework for high-fidelity image synthesis.

cs.CV↗

arXiv2026

A Cost-Effective Layout-Aware Quantum Circuit Synthesis For Triangular, Square, and Heavy-Hex Layouts

The quantum layout and the mapping of logical to physical qubits are crucial in quantum circuit synthesis for a real quantum computer. Circuits that include large $n$-bit Toffoli gates ($n \geq 3$), such as those designed from cost-expensive gates and hard-to-decompose Exclusive-or Sum of Products (ESOP) expressions, have complications of effective mappings into contemporary quantum layouts, such as the square grid and heavy-hex layouts. These complications are primarily caused by the limited connectivity among the physical qubits in such layouts, leading to the insertion of many additional SWAP gates. This paper introduces a new quantum circuit synthesis methodology by exploring the advantage of a Positive Davio lattice (PDL) as an intermediate representation to create our proposed triangular layout and layout-aware circuits. From these circuits, we introduce and form the SWAT gate, composed of a SWAP gate followed by a 3-bit Toffoli gate. To illustrate the usefulness of our method for existing industrial quantum layouts, we also introduce cost-effective mappings of the resulting circuits onto square grid and heavy-hex layouts without additional SWAP gates. This is done with the help of the SWAT gate. Our research highlights PDLs as an efficient tool for layout-aware quantum circuit synthesis.

quant-ph↗

arXiv2026

Minimization of AND-XOR Expressions with Decoders for Quantum Circuits

This paper introduces a new logic structure for reversible quantum circuit synthesis. Our synthesis method aims to minimize the quantum cost of reversible quantum circuits with decoders. In this method, multi-valued input, binary output (MVI) functions are utilized as a mathematical concept only, but the circuits are binary. We introduce the new concept of ``Multi-Valued Input Fixed Polarity Reed-Muller (MVI-RM)" forms. Our decoder-based circuit uses three logical levels in contrast to commonly-used methods based on Exclusive-or Sum of Products (ESOP) with two levels (AND-XOR expressions), realized by Toffoli gates. In general, the high number of input qubits in the resulting Toffoli gates is a problem that greatly impacts the quantum cost. Using decoders decreases the number of input qubits in these Toffoli gates. We present two practical algorithms for three-level circuit synthesis by finding the MVI-FPRM: products-matching and the newly developed butterfly diagrams. The best MVI-FPRM forms are factorized and reduced to approximate Multi-Valued Input Generalized Reed-Muller (MVI-GRM) forms.

quant-ph↗

arXiv2026

A Geometrical Design Tool for Building Cost-Effective Layout-Aware n-Bit Quantum Gates Using the Bloch Sphere Approach

The conventional design technique of any n-bit quantum gate is mainly achieved using unitary matrices multiplication, where n >= 2 and 1 <= m <= n-1 for m target qubits and n-m control qubits. These matrices represent quantum rotations by an n-bit quantum gate. For a quantum designer, such a conventional technique requires extensive computational time and effort, which may generate an n-bit quantum gate with a too high quantum cost. The Bloch sphere is only utilized as a visualization tool to verify the conventional design correctness for quantum rotations by a quantum gate. In contrast, this paper introduces a new concept of using the Bloch sphere as a "geometrical design tool" to build cost-effective n-bit quantum gates with lower quantum costs. This concept is termed the "Bloch sphere approach (BSA)". In BSA, a cost-effective n-bit quantum gate is built without using any unitary matrices multiplication. Instead, the quantum rotations for such a gate are visually selected using the geometrical planar intersections of the Bloch sphere. The BSA can efficiently map m targets among n-m controls for an n-bit quantum gate, to satisfy the limited layout connectivity for the physical neighboring qubits of a quantum computer. Experimentally, n-bit quantum gates built using the BSA always have lower quantum costs than those for such gates built using the conventional quantum design techniques.

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arXiv2025

Solving Segment Display Problems Using Quantum Grover's Search Algorithm

This paper introduces a new Boolean-based methodology for constructing Segment Display Problems (SDPs) in the quantum domain and solving them using Grover's quantum search algorithm. In the classical domain, the SDPs are typically solved using various techniques, such as human deduction, heuristic search, and methods for solving Boolean satisfiability (SAT) and constraint satisfaction problems (CSPs) that are based on different problem design models. In this paper, our newly introduced methodology proposes a quantum-based approach for solving such SDPs, by building their quantum oracle using binary reversible circuits and our previously proposed step-decreasing structures shaped operators (Stesso). To demonstrate the usability of this proposed method, we experimentally solve an SDP instance of the matchstick problem using Grover's algorithm with a noisy simulated quantum computer implemented in Qiskit.

quant-ph↗

arXiv2025

Stesso: A reconfigurable decomposition of $n$-bit Toffoli gates using symmetrical logical structures and adjustable support qubits

An $(n+1)$-bit Toffoli gate is mainly utilized to construct other quantum gates and operators, such as Fredkin gates, arithmetical adders, and logical comparators, where $n \geq 2$. Several researchers introduced different methods to decompose $(n+1)$-bit Toffoli gates in a quantum circuit into a set of standard 3-bit Toffoli gates or a set of elementary quantum gates, such as single-qubit and two-qubit gates. However, these methods are not effectively reconfigurable for linearly connected symmetrical structures (layouts) of contemporary quantum computers, usually utilizing more ancilla qubits. This paper introduces a new structural design method to effectively decompose $(n+1)$-bit Toffoli gates by utilizing configurable ancilla qubits, which we named the ``support qubits". Collectively, we call our decomposition method for symmetrical structures using support qubits the ``step-decreasing structures shaped operators (Stesso)". The main advantage of Stesso is to configurable construct different decomposed operators of various polarities and intermediate sub-circuits, such as Positive Polarity-Stesso, Mixed Polarity-Stesso, and Generalized-Stesso. With Stesso, it has been experimentally proven that $(n+1)$-bit Toffoli gates always have lower quantum costs than using conventional composition methods.

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arXiv2025

A Cost-Effective Quantum Boolean-Phase SWAP Gate with Only Two CNOT Gates

A new Boolean-Phase swapping gate is presented with improved quantum generality and cost-effectiveness. Our swapping gate is termed the "p-SWAP gate", where p is the phase difference selected for a set of swapped qubits. The phase p is expressed in radians and $-π~{\leq}$ p ${\leq}~+π$. The generality of p-SWAP gate is demonstrated for Phase applications for selected values of p and for Boolean applications when the value of p is ignored. The cost-effectiveness of p-SWAP gate follows from the lower quantum cost and depth of its final realized (transpiled) quantum circuit, when compared to the standard SWAP gate composed of three Feynman (CNOT) gates. Specifically, our presented p-SWAP gate utilizes only two CNOT gates. The quantum circuit of the p-SWAP gate is visually designed using our previously developed Bloch sphere approach. Experimentally, after transpilation for an IBM quantum computer, the transpiled p-SWAP gate shows an approximate 23% quantum cost reduction and an approximate 26% depth minimization compared to the transpiled standard SWAP gate.

quant-ph↗

arXiv2025

p-SWAP: A Generic Cost-Effective Quantum Boolean-Phase SWAP Gate Using Two CNOT Gates and the Bloch Sphere Approach

A Boolean-Phase swapping gate is introduced for quantum generality and cost-effectiveness, which is termed the "p-SWAP gate", where p is a customizable phase difference for a set of swapped qubits and 0 <= p <= ${\pm π}$ radians. The generality of the p-SWAP gate is proposed for quantum Phase oracles requiring a desirable p for a set of swapped qubits, as well as for quantum Boolean oracles when p is ignored. The cost-effectiveness of the p-SWAP gate comes from the lower quantum cost and depth for its final synthesized (transpiled) quantum circuit into a quantum computer, as compared to the standard SWAP gate. In general, the standard SWAP gate is constructed using three Feynman (CNOT) gates, while our p-SWAP gate only utilizes two CNOT gates. In this paper, the desirability of p is geometrically chosen using our proposed Bloch sphere approach, without using any matrices multiplication and unitary representations. After transpilation, the final transpiled p-SWAP gate has approximately 23% quantum cost reduction and 26% depth minimization than those of the final transpiled standard SWAP gate.

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arXiv2024

EQB: Synthesizing Permutative Quantum Gates and Circuits Using Rotation-Based Group Decomposition

The decomposition from the group theory-based methods of Sasao and Saraivanov is extended to design binary quantum cascades, using the quantum rotational gates by the X-axis (CNOT and RX), Y-axis (RY), and Z-axis (controlled-Z) of the Bloch sphere. A class of local transformations is also presented to simplify the final canonical cascade circuits. Our proposed methodology is well suited for quantum layouts, as each single-qubit gate has one target qubit and each double-qubit gate has one control qubit and one target qubit, thereby never creating a graph of triangular connectivity.

quant-ph↗

arXiv2024

Cost-Effective Realization of n-Bit Toffoli Gates for IBM Quantum Computers Using the Bloch Sphere Approach and IBM Native Gates

A cost-effective n-bit Toffoli gate is proposed to be realized (or transpiled) based on the layouts (linear, T-like, and I-like) and the number of n physical qubits for IBM quantum computers. This proposed gate is termed the "layout-aware n-bit Toffoli gate". The layout-aware n-bit Toffoli gate is designed using the visual approach of the Bloch sphere, from the visual representations of the rotational quantum operations for IBM native gates. In this paper, we also proposed a new formula for the quantum cost, which calculates the total number of native gates, the crossing connections, and the depth of the final transpiled quantum circuit. This formula is termed the "transpilation quantum cost". After transpilation, our proposed layout-aware n-bit Toffoli gate always has a much lower transpilation quantum cost than that of the conventional n-bit Toffoli gate, where 3 <= n <= 7 qubits, for different IBM quantum computers.

quant-ph↗

arXiv2024

CALA-$n$: A Quantum Library for Realizing Cost-Effective 2-, 3-, 4-, and 5-bit Gates on IBM Quantum Computers using Bloch Sphere Approach, Clifford+T Gates, and Layouts

We introduce a new quantum layout-aware approach to realize cost-effective $n$-bit gates using the Bloch sphere, for $2 \le n \le 5$ qubits. These $n$-bit gates are entirely constructed from the Clifford+T gates, in the approach of selecting sequences of rotations visualized on the Bloch sphere. This Bloch sphere approach ensures to match the quantum layout for synthesizing (transpiling) these $n$-bit gates into an IBM quantum computer. Various standard $n$-bit gates (Toffoli, Fredkin, etc.) and their operational equivalent of our proposed $n$-bit gates are examined and evaluated, in the context of the final quantum costs, as the final counts of generated IBM native gates. In this paper, we demonstrate that all our $n$-bit gates always have lower quantum costs than those of standard $n$-bit gates after transpilation. Hence, our Bloch sphere approach can be used to build a quantum library of various cost-effective $n$-bit gates for different layouts of IBM quantum computers.

quant-ph↗

arXiv2024

BHT-QAOA: Generalizing Quantum Approximate Optimization Algorithm to Solve Arbitrary Boolean Problems as Hamiltonians

A new methodology is proposed to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). Our methodology successfully finds all optimized approximated solutions for Boolean problems, after converting them from Boolean oracles (in different structures) into Phase oracles, and then into the Hamiltonians of QAOA. From such a conversion, we noticed that the total utilized numbers of qubits and quantum gates are dramatically minimized for the final quantum circuits of Hamiltonians. In this paper, arbitrary classical Boolean problems are examined by successfully solving them with our proposed methodology, using structures based on various logic synthesis methods, an IBM quantum computer, and a classical optimization minimizer. Accordingly, this methodology will provide broad opportunities to solve many classical Boolean problems as Hamiltonians, for the practical engineering applications of several algorithms, robotics, machine learning, just to name a few, in the hybrid classical-quantum domain.

quant-ph↗

arXiv2017

An IoT Real-Time Biometric Authentication System Based on ECG Fiducial Extracted Features Using Discrete Cosine Transform

The conventional authentication technologies, like RFID tags and authentication cards/badges, suffer from different weaknesses, therefore a prompt replacement to use biometric method of authentication should be applied instead. Biometrics, such as fingerprints, voices, and ECG signals, are unique human characters that can be used for authentication processing. In this work, we present an IoT real-time authentication system based on using extracted ECG features to identify the unknown persons. The Discrete Cosine Transform (DCT) is used as an ECG feature extraction, where it has better characteristics for real-time system implementations. There are a substantial number of researches with a high accuracy of authentication, but most of them ignore the real-time capability of authenticating individuals. With the accuracy rate of 97.78% at around 1.21 seconds of processing time, the proposed system is more suitable for use in many applications that require fast and reliable authentication processing demands.

cs.CV↗