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    Principles, fundamentals, and applications of programmable integrated photonics

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    [EN] Programmable integrated photonics is an emerging new paradigm that aims at designing common integrated optical hardware resource configurations, capable of implementing an unconstrained variety of functionalities by suitable programming, following a parallel but not identical path to that of integrated electronics in the past two decades of the last century. Programmable integrated photonics is raising considerable interest, as it is driven by the surge of a considerable number of new applications in the fields of telecommunications, quantum information processing, sensing, and neurophotonics, calling for flexible, reconfigurable, low-cost, compact, and low-power-consuming devices that can cooperate with integrated electronic devices to overcome the limitation expected by the demise of Moore¿s Law. Integrated photonic devices exploiting full programmability are expected to scale from application-specific photonic chips (featuring a relatively low number of functionalities) up to very complex application-agnostic complex subsystems much in the same way as field programmable gate arrays and microprocessors operate in electronics. Two main differences need to be considered. First, as opposed to integrated electronics, programmable integrated photonics will carry analog operations over the signals to be processed. Second, the scale of integration density will be several orders of magnitude smaller due to the physical limitations imposed by the wavelength ratio of electrons and light wave photons. The success of programmable integrated photonics will depend on leveraging the properties of integrated photonic devices and, in particular, on research into suitable interconnection hardware architectures that can offer a very high spatial regularity as well as the possibility of independently setting (with a very low power consumption) the interconnection state of each connecting element. Integrated multiport interferometers and waveguide meshes provide regular and periodic geometries, formed by replicating unit elements and cells, respectively. In the case of waveguide meshes, the cells can take the form of a square, hexagon, or triangle, among other configurations. Each side of the cell is formed by two integrated waveguides connected by means of a Mach¿Zehnder interferometer or a tunable directional coupler that can be operated by means of an output control signal as a crossbar switch or as a variable coupler with independent power division ratio and phase shift. In this paper, we provide the basic foundations and principles behind the construction of these complex programmable circuits. We also review some practical aspects that limit the programming and scalability of programmable integrated photonics and provide an overview of some of the most salient applications demonstrated so far.European Research Council; Conselleria d'Educació, Investigació, Cultura i Esport; Ministerio de Ciencia, Innovación y Universidades; European Cooperation in Science and Technology; Horizon 2020 Framework Programme.Pérez-López, D.; Gasulla Mestre, I.; Dasmahapatra, P.; Capmany Francoy, J. (2020). Principles, fundamentals, and applications of programmable integrated photonics. Advances in Optics and Photonics. 12(3):709-786. https://doi.org/10.1364/AOP.387155709786123Lyke, J. C., Christodoulou, C. G., Vera, G. A., & Edwards, A. H. (2015). An Introduction to Reconfigurable Systems. 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    There is a common wisdom according to which many technologies can progress according to some exponential law like the empirical Moore's law that was validated for over half a century with the growth of transistors number in chipsets. As a still in the making technology with a lot of potential promises, quantum computing is supposed to follow the pack and grow inexorably to maturity. The Holy Grail in that domain is a large quantum computer with thousands of errors corrected logical qubits made themselves of thousands, if not more, of physical qubits. These would enable molecular simulations as well as factoring 2048 RSA bit keys among other use cases taken from the intractable classical computing problems book. How far are we from this? Less than 15 years according to many predictions. We will see in this paper that Moore's empirical law cannot easily be translated to an equivalent in quantum computing. Qubits have various figures of merit that won't progress magically thanks to some new manufacturing technique capacity. However, some equivalents of Moore's law may be at play inside and outside the quantum realm like with quantum computers enabling technologies, cryogeny and control electronics. Algorithms, software tools and engineering also play a key role as enablers of quantum computing progress. While much of quantum computing future outcomes depends on qubit fidelities, it is progressing rather slowly, particularly at scale. We will finally see that other figures of merit will come into play and potentially change the landscape like the quality of computed results and the energetics of quantum computing. Although scientific and technological in nature, this inventory has broad business implications, on investment, education and cybersecurity related decision-making processes.Comment: 32 pages, 24 figure

    RESOURCE EFFICIENT DESIGN OF QUANTUM CIRCUITS FOR CRYPTANALYSIS AND SCIENTIFIC COMPUTING APPLICATIONS

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    Quantum computers offer the potential to extend our abilities to tackle computational problems in fields such as number theory, encryption, search and scientific computation. Up to a superpolynomial speedup has been reported for quantum algorithms in these areas. Motivated by the promise of faster computations, the development of quantum machines has caught the attention of both academics and industry researchers. Quantum machines are now at sizes where implementations of quantum algorithms or their components are now becoming possible. In order to implement quantum algorithms on quantum machines, resource efficient circuits and functional blocks must be designed. In this work, we propose quantum circuits for Galois and integer arithmetic. These quantum circuits are necessary building blocks to realize quantum algorithms. The design of resource efficient quantum circuits requires the designer takes into account the gate cost, quantum bit (qubit) cost, depth and garbage outputs of a quantum circuit. Existing quantum machines do not have many qubits meaning that circuits with high qubit cost cannot be implemented. In addition, quantum circuits are more prone to errors and garbage output removal adds to overall cost. As more gates are used, a quantum circuit sees an increased rate of failure. Failures and error rates can be countered by using quantum error correcting codes and fault tolerant implementations of universal gate sets (such as Clifford+T gates). However, Clifford+T gates are costly to implement with the T gate being significantly more costly than the Clifford gates. As a result, designers working with Clifford+T gates seek to minimize the number of T gates (T-count) and the depth of T gates (T-depth). In this work, we propose quantum circuits for Galois and integer arithmetic with lower T-count, T-depth and qubit cost than existing work. This work presents novel quantum circuits for squaring and exponentiation over binary extension fields (Galois fields of form GF(2 m )). The proposed circuits are shown to have lower depth, qubit and gate cost to existing work. We also present quantum circuits for the core operations of multiplication and division which enjoy lower T-count, T-depth and qubit costs compared to existing work. This work also illustrates the design of a T-count and qubit cost efficient design for the square root. This work concludes with an illustration of how the arithmetic circuits can be combined into a functional block to implement quantum image processing algorithms
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