The Newton’s laws had been developed on basis experiments with nature signals, and by hand computation for processing of these signals. The signal carries the code of data. The carrier is a wave - the process of transfer in space and time (physical space) of the code. Then the parameters of this transfer determines the state of the signals in time and space. The design of quantum communication systems, information technology, etc. modeling of quantum signals is a complex problem of representation of the carrier, the signal code, and their quantum states. Quantum computing, and explaining on resolving of application tasks (RSA, FFT algorithm, quantum circuits, etc.) in physical the scales theories and practices (in mechanics and quantum mechanics) are different in technics, algorithmic, and the simulation. All of these significantly does complexity of the design of quantum communication systems. This paper discusses the representation of a quantum signal as its general relationship with the difference of digitized sinusoidal functions with different digitization parameters obtained by a classical computer. This difference is considered similar to squeezed states with different sets of digitization parameters. The peculiarities of the obtained difference signatures with respect to similar quantum phenomena are classified. The representation of modeling of a quantum signal by possibilities of the classical computer as it was developed for quantum states, schemes, protocols is offered.
The Newton’s laws had been developed on basis experiments with nature signals, and by hand computation for processing of these signals. The signal carries the code of data. The carrier is a wave - the process of transfer in space and time (physical space) of the code. Then the parameters of this transfer determines the state of the signals in time and space. The design of quantum communication systems, information technology, etc. modeling of quantum signals is a complex problem of representation of the carrier, the signal code, and their quantum states. Quantum computing, and explaining on resolving of application tasks (RSA, FFT algorithm, quantum circuits, etc.) in physical the scales theories and practices (in mechanics and quantum mechanics) are different in technics, algorithmic, and the simulation. All of these significantly does complexity of the design of quantum communication systems. This paper discusses the representation of a quantum signal as its general relationship with the difference of digitized sinusoidal functions with different digitization parameters obtained by a classical computer. This difference is considered similar to squeezed states with different sets of digitization parameters. The peculiarities of the obtained difference signatures with respect to similar quantum phenomena are classified. The representation of modeling of a quantum signal by possibilities of the classical computer as it was developed for quantum states, schemes, protocols is offered.
Context. Nature is the relation among processes and phenomena. Nothing exists in the universe without relations. Computer is transactions of relations between data with the help of control and execution mechanisms. Quantum relations are a superposition of particles and their states. Superposition and entanglement are equivalent concepts. Entanglement is a non-local superposition of deterministic states. A quantum computer is unconditional transactions of relations between qubit data. Quantum computer is an analog device for parallel solution of combinatorial problems. Practically oriented definitions of the quantum computer concepts are the path to development of scalable quantum parallel algorithms for combinatorial problems solving. Any algorithm can be reduced to a sequence of operations without conditions, because any truth table is a collection of a complete system of conditions-states. Any sequence of actions can always be reduced to one parallel operation. Conditions and sequences arise only when the developer wants to use previously created primitive constructs to build an always non-optimal computing unit. The paradigm of quantum computer creation is determined through the use of photonic transactions on the electrons of an atom may exclude the use of quantum logic. The evolutionary path of a quantum computer from the classical one: “memory-address-transaction” (MAT) → “electron-addresstransaction” → “electron-address-quantaction” (EAQ) → state-superposition-logic. The meeting point of classical and quantum computers is photon transactions on the structure of electrons. Everything that is calculated on a quantum computer can be calculated in parallel on a classical one on account of memory redundancy. The given example is a memory-driven algorithm for modeling digital products based on qubit-vector forms of functionality description for significant performance boost of computing processes by parallel execution of logical operations. Objective. Simulation of the correct SoC-component behavior based on vector representation of the logic. Formation of the triggering development of a computing based on the superposition of the classical, quantum and analog computing process, which in its development should be based on technological qubit, tabular and vector data structures for the parallel solution of combinatorial problems. Method. MAT-computing implements any algorithms on account of transactions (read-write) in memory. Qubit-vector models for describing functionalities, which differ from known truth tables in compactness of description and manufacturability for the implementation of parallel algorithms of the synthesis and analysis of digital devices and SoC-components. Results. 1) The metric of the technological data structures, focused on parallel troubleshooting in digital systems based on the usage of two logical vector operations, was proposed for the first time. 2) The metric of relations between the individual components of QC, allowing organizing a quantum deterministic computer, has been further developed. 3) Quantum architectural solutions, that allow solving coverage problems in a quasi-parallel mode, were proposed for the first time. 4) Architectural solutions based on an analog-to-digital computing, which can be used to solve the problems of the digital systems parallel analysis, have been further developed. 5) Vector-qubit structures of the logic data, that allow a quasi-parallel simulation of digital circuits, were proposed. Conclusions. Qubit models, quantum methods and combinatorial algorithms for technical diagnostics of digital devices have been implemented, which can significantly (up to 25%) reduce the time of test synthesis, deductive modeling of faulty and correct behavior, search for defective states by introducing an innovative idea of using qubit-vector data structures for describing logical components. Comparative assessments of qubit models and methods usage show an increase in the efficiency of algorithms for modeling digital devices compared to tabular ones. The superposition of a classical, quantum and analog computer is integrally represented, which allows to find the best solutions for recognition and decision making.
The rapid development of the digital era and the increasing demands of information technologies create a need to create more reliable, secure and efficient communication systems. In this context, quantum signals represent a technology of the future that responds to the challenges that classical signal systems can no longer cope with — for example, the highest level of information security, accuracy and transmission speed. The use of quantum entanglement, superposition and correlations makes it possible to protect and process information at the highest level. Accordingly, the implementation of quantum signals is critically important for areas such as quantum communication, secure cyberinfrastructure, high-tech sensors and quantum computing systems. The paper reviews the role of quantum signals in modern technologies and their potential in the near future. Quantum signal theory combines the principles of quantum physics, information theory and signal processing. These features provide the highest accuracy in information transmission and processing, which is especially important in the development of quantum communication, quantum radars, and quantum sensors. This paper reviews the theoretical foundations of quantum signals, basic models, and their potential applications in modern technologies.
The study of quantum signals is one of the fundamental and strategic directions of telecommunications and engineering sciences, as it is directly related to the in-depth understanding of the laws of matter and energy at the microscopic level and the transition to a new stage of telecommunications systems, as well as the formation of new principles of information transmission and processing and the development of technological innovations. A quantum signal, as a physical object carrying a quantum state, be it a photon, an electron, a qubit localized in a superconducting circuit, or an atomic spin system, contains information encoded through superposition and quantum entanglement. It is thanks to these properties that it becomes possible to perform tasks that are either practically inaccessible or extremely resource-intensive within the framework of classical physics. For example, computational models based on the principles of quantum mechanics provide the basis for quantum systems, which potentially radically change the speed and efficiency of data processing, while quantum communication provides fundamentally secure channels for information transmission, which is especially important in light of modern cybersecurity challenges. Comparative studies of quantum signals in cryogenic and non-cryogenic environments provide important theoretical results.
Quantum computation is by far the most powerful computational model allowed by the laws of physics. By carefully manipulating microscopic systems governed by quantum mechanics, one can efficiently solve computational problems that may be classically intractable; on the contrary, such speed-ups are rarely possible without the help of classical computation, since most quantum algorithms heavily rely on subroutines that are purely classical. A better understanding of the relationship between classical and quantum computation is indispensable, in particular in an era where the first quantum device exceeding classical computational power is within reach. In the first part of the thesis, we study some differences between classical and quantum computation. We first show that quantum cryptographic hashing is maximally resilient against classical leakage, a property beyond reach for any classical hash function. Next, we consider the limitation of strong (amplitude-wise) simulation of quantum computation. We prove an unconditional and explicit complexity lower bound for a category of simulations called monotone strong simulation and further prove conditional complexity lower bounds for general strong simulation techniques. Both results indicate that strong simulation is fundamentally unscalable. In the second part of the thesis, we propose classical algorithms that facilitate quantum computing. We propose a new classical algorithm for the synthesis of a quantum algorithm paradigm called quantum signal processing. Empirically, our algorithm demonstrates numerical stability and acceleration of more than one magnitude compared to state-of-the-art algorithms. Finally, we propose a randomized algorithm for transversally switching between arbitrary stabilizer quantum error-correcting codes. It has the property of preserving the code distance and thus might prove useful for designing fault-tolerant code-switching schemes.
Current communication networks are based on classical physics and classical information-processing. However, for nearly a century, we have known that at its most fundamental level, the universe is governed by the laws of quantum mechanics. With quantum communication, new possibilities arise in our capabilities to transmit and process information which, in many cases, lead to advantages compared to what is classically possible. The entire scope of tasks for which quantum communication can offer improvements has not yet been fully explored, but several quantum protocols are known that can either perform tasks which are impossible with classical resources or can outperform classical protocols. These quantum protocols are well understood from a theoretical point of view, but many of them have never been demonstrated in practice. Thus, in the context of quantum communication, there is a significant gap between theory and experiment that must be removed in order to harness the advantages provided by quantum mechanics in a practical setting. \n \nIn this thesis, we develop a series of tools for developing and testing practical quantum communication protocols. Our main technique is a theoretical reformulation of existing quantum communication protocols that converts them into a form in which they can be demonstrated with existing experimental techniques. More precisely, they can be implemented using only coherent states of light and linear optics circuits while still retaining the crucial properties of the original abstract protocols. We use this result to construct practical protocols for the Hidden Matching problem and quantum fingerprinting. \n \n \nIn the case of quantum fingerprinting, we make a thorough analysis of the role played by experimental errors and show that our practical protocol can still be implemented in the presence of these imperfections. In fact, we report a proof of concept experimental demonstration of a quantum fingerprinting system that is capable of transmitting less information than the best known classical protocol for this problem. Our implementation is based on a modified version of a commercial quantum key distribution system using off-the-shelf optical components over telecom wavelengths, and is practical for messages as large as 100 Mbits, even in the presence of experimental imperfections. \n \nSimilarly, in the context of cryptography, we propose a multiparty quantum signature protocol that can be implemented from any point-to-point quantum key distribution network, proving its security against forging, repudiation and non-transferability. Crucially, since quantum key distribution is already a practical technology, so is this protocol. However, unlike other tasks in quantum communication, there has not been significant theoretical work on establishing a security model for quantum signature schemes. Consequently, we also constructed a security framework for these schemes and proved several properties that these protocols must satisfy in order to achieve their security goals. \n \nFinally, in addition to proposing new practical protocols, we provide a reliable data analysis technique to verify an important property of many quantum communication protocols: the presence of entanglement. Our technique is based on entanglement witnesses and it does not require the specification of a prior distribution nor the assumption of independent measurements. The technique is suitable to be used with nonlinear entanglement witnesses, which we show can be constructed from any linear witness and evaluated from the same experimental data. We also develop numerical tools necessary to employ this approach in practice, rendering the procedure ready to be applied to current experiments. We demonstrate this by analyzing the data of a photonic experiment generating two-photon states whose entanglement is verified with the use of an accessible nonlinear witness.
Existing approaches to emulating quantum computing algorithms using classical electronic hardware are limited by exponential scaling limitations in space, such as circuit size, or time, such as runtime or bandwidth. We introduce a scheme for representing quantum information using analog signals that lessens the bandwidth limitation problem (in certain regimes) seen in existing approaches by taking full advantage of the ability of analog signals to encode information using RMS voltage as well as frequency and phase. We introduce the mathematical framework for this representation, which separates the information relevant for measurement in the computational basis from information that is not relevant to it. We introduce circuits that take advantage of this separation of concerns to achieve simplifications, for working with quantum information in this representation. We argue that it is comparatively very inexpensive (as low as ~$5.00 / qubit) to outmatch the computing capabilities of existing FPGA based emulators, though scaling beyond tens of qubits is still impractical due to constraints of analog hardware module precision. However, our approach opens the door to a new avenue by which classical emulators can hope to improve: by improving on analog electronic circuit performance.