This work aims to introduce the fundamental concepts required to perform computations on photonic quantum computers by presenting the gates specific to this architecture and highlighting the connections between standard Pauli gates and those available in photonic systems. The introduction navigates between physical considerations related to the optical components used, theoretical aspects concerning quantum operators, and a more applied section introducing implementations using the Perceval library developed by Quandela. This paper is intended for engineers and researchers familiar with Pauli gates and standard quantum concepts, looking at a clear and compact introduction to photonic components. A second part aims to introduce the concept of polarization, not from a theoretical perspective, but through its practical applications. To do so, we compare the similarities and differences between the original Grover's algorithm formulation and a version that leverages polarization. Gates specific to polarization are introduced and described in the context of the computations involved in Grover's algorithm. The description provided is as mathematical as possible and deliberately avoids physical considerations, in order to allow researchers familiar with "conventional" quantum circuits to more easily grasp the concepts.
This work aims to introduce the fundamental concepts required to perform computations on photonic quantum computers by presenting the gates specific to this architecture and highlighting the connections between standard Pauli gates and those available in photonic systems. The introduction navigates between physical considerations related to the optical components used, theoretical aspects concerning quantum operators, and a more applied section introducing implementations using the Perceval library developed by Quandela. This paper is intended for engineers and researchers familiar with Pauli gates and standard quantum concepts, looking at a clear and compact introduction to photonic components. A second part aims to introduce the concept of polarization, not from a theoretical perspective, but through its practical applications. To do so, we compare the similarities and differences between the original Grover's algorithm formulation and a version that leverages polarization. Gates specific to polarization are introduced and described in the context of the computations involved in Grover's algorithm. The description provided is as mathematical as possible and deliberately avoids physical considerations, in order to allow researchers familiar with "conventional" quantum circuits to more easily grasp the concepts.
This manuscript is intended for readers who have a general interest in the subject of quantum computation and provides an overview of the most significant developments in the field. It begins by introducing foundational concepts from quantum mechanics—such as superposition, entanglement, and the no-cloning theorem—that underpin quantum computation. The primary computational models are discussed, including gate-based (circuit) quantum computing, adiabatic quantum computing, measurement-based quantum computing and the quantum Turing machine. A selection of significant quantum algorithms are reviewed, notably Grover’s search algorithm, Shor’s factoring algorithm, and Quantum Singular Value Transformation (QSVT), which enables efficient solutions to linear algebra problems on quantum devices. To assess practical performance, we compare quantum and classical implementations of support vector machines (SVMs) using several synthetic datasets. These experiments offer insight into the capabilities and limitations of near-term quantum classifiers relative to classical counterparts. Finally, we review leading quantum programming platforms—including Qiskit, PennyLane, and Cirq—and discuss their roles in bridging theoretical models with real-world quantum hardware. The paper aims to provide a concise yet comprehensive guide for those looking to understand both the theoretical foundations and applied aspects of quantum computing.
Quantum computing represents a transformative paradigm that exploits the principles of quantum mechanics—superposition, entanglement, and quantum interference—to perform computations beyond the capabilities of classical computers. This review presents a comprehensive overview of the fundamental concepts underlying quantum computation, including qubits, quantum gates, quantum algorithms and measurement theory. It further examines major physical implementations of quantum computers, such as superconducting circuits, trapped ions, photonic systems, spin-based qubits, and topological approaches, highlighting their operational principles, advantages, and technological limitations. Key challenges hindering large-scale quantum computation—decoherence, error rates, qubit scalability, and fault tolerance—are critically discussed. Additionally, recent progress in quantum error correction, hybrid quantum–classical algorithms, and hardware optimization is summarized. The review concludes by outlining future research directions and potential applications of quantum computing in cryptography, materials science, optimization, and drug discovery. By integrating theoretical foundations with experimental advancements, this article aims to provide a clear and accessible reference for students, researchers, and scientists entering the rapidly evolving field of quantum computing.
This book, Quantum Computing: Algorithms, Architectures and Applications, has been carefully developed as a comprehensive resource to navigate the dynamic and complex world of quantum technologies. Intended for students, researchers, engineers, and technology enthusiasts, it aims to connect fundamental concepts with real-world implementation. The journey begins with the core principles of quantum mechanics relevant to computing, laying the groundwork that differentiates quantum systems from classical approaches. It further explores quantum gates, circuits, and computational logic, along with key topics such as error correction, system architectures, entanglement, superposition, and the no-cloning theorem. As the discussion progresses, the book examines foundational quantum algorithms, including the Deutsch–Jozsa algorithm, Simon’s problem, and others. These sections not only explain technical concepts but also encourage readers to rethink computational possibilities and limitations. The book also highlights practical applications and industry adoption. Quantum computing is increasingly influencing fields such as cryptography, finance, drug discovery, and climate science. Through global and regional case studies, readers gain insight into how various sectors are embracing this technological shift. A clear and structured approach has been maintained throughout, making the content accessible to beginners while still valuable for experienced professionals. The aim is to balance depth with clarity, ensuring both rigor and ease of understanding. While quantum computing continues to evolve with ongoing advancements and discoveries, the driving forces behind its progress remain curiosity, innovation, and collaboration.
Optical photons present many interesting aspects in the context of the research for suitable physical representations of quantum bits. Photons are chargeless particles, and do not interact strongly with each other, or even with most matter. They can be guided along long distances with low loss in optical fibers, delayed efficiently using phase shifters, and combined easily using beamsplitters. Photons exhibit typical quantum phenomena, such as the interference produced in two-slit experiments. Furthermore, in principle, photons can be made interact with each other if carefully handled. There are many practical problems with this approach; nevertheless it presents, beyond what has already been noted, an appealing conceptual simplicity.The purpose of this work is to present - at least, in its fundamental principles - a set of optical photon quantum gates that is universal for quantum computation. To do so, we begin by gathering the necessary mathematical and physical tools. We discuss canonical quantization for the electromagnetic field, and we formalize in an abstract context the characteristic properties of every realization of the Fock canonical commutation relationships (CCR). We analize the class of the spaces where it is possible to give such a realization, and that naturally lend themselves to host the physical model of our interest. Once acquired these bases, we turn ourselves to a particular optic system, the Mach-Zehnder interferometer, and we study the general properties of this system and of its essential constituents. At this point we choose a particular encoding of quantum bit and we look at the optical devices just discussed as elements of a quantum circuit. We then discuss the fundamental ideas that may guide the implementation of some important quantum gates: Hadamard gate, π/8 gate and controlled-NOT. We conclude by showing that these three quantum gates form a universal set of gates for quantum computation.
Optical photons present many interesting aspects in the context of the research for suitable physical representations of quantum bits. Photons are chargeless particles, and do not interact strongly with each other, or even with most matter. They can be guided along long distances with low loss in optical fibers, delayed efficiently using phase shifters, and combined easily using beamsplitters. Photons exhibit typical quantum phenomena, such as the interference produced in two-slit experiments. Furthermore, in principle, photons can be made interact with each other if carefully handled. There are many practical problems with this approach; nevertheless it presents, beyond what has already been noted, an appealing conceptual simplicity.The purpose of this work is to present - at least, in its fundamental principles - a set of optical photon quantum gates that is universal for quantum computation. To do so, we begin by gathering the necessary mathematical and physical tools. We discuss canonical quantization for the electromagnetic field, and we formalize in an abstract context the characteristic properties of every realization of the Fock canonical commutation relationships (CCR). We analize the class of the spaces where it is possible to give such a realization, and that naturally lend themselves to host the physical model of our interest. Once acquired these bases, we turn ourselves to a particular optic system, the Mach-Zehnder interferometer, and we study the general properties of this system and of its essential constituents. At this point we choose a particular encoding of quantum bit and we look at the optical devices just discussed as elements of a quantum circuit. We then discuss the fundamental ideas that may guide the implementation of some important quantum gates: Hadamard gate, π/8 gate and controlled-NOT. We conclude by showing that these three quantum gates form a universal set of gates for quantum computation.