A dichotomy between 'analogue' modeling and 'digital' implementation is often encountered when designing vector quantizers. In the case of digital systems, the requirement of optimality can bring about NP-hard problems. The paper discusses the possibility of using advanced paradigms such as quantum computing for digital optimization processes in order to overcome the limitations of conventional machinery. The presented research provides analytical criteria determining the relative advantages of conventional over quantum-computing approaches.
A dichotomy between 'analogue' modeling and 'digital' implementation is often encountered when designing vector quantizers. In the case of digital systems, the requirement of optimality can bring about NP-hard problems. The paper discusses the possibility of using advanced paradigms such as quantum computing for digital optimization processes in order to overcome the limitations of conventional machinery. The presented research provides analytical criteria determining the relative advantages of conventional over quantum-computing approaches.
In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor’s algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world problems. It is likely that quantum methods can efficiently solve certain (NP-) hard optimization problems where classical approaches fail. In our perspective, we examine the field of quantum optimization, that is, solving optimization problems using quantum computers. We provide an entry point to quantum optimization for researchers from each topic, optimization or quantum computing, by demonstrating advances and obstacles with a suitable use case. We give an overview on problem formulation, available algorithms, and benchmarking. Although we show a proof-of-concept rather than a full benchmark between classical and quantum methods, this gives an idea of the current quality and capabilities of quantum computers for optimization problems. All observations are incorporated in a discussion on some recent quantum optimization breakthroughs, current status, and future directions.
Background: Traditional computers can be inadequate to solve computationally complex problems, generally known as NP-hard problems, for example, optimization, cryptography, and network design. Quantum Computing is referred to as a breakthrough paradigm, that exploits the principles of quantum physics for performing computation in an exceedingly efficient manner.Objective: This study aims to explore the abilities of quantum algorithms in capturing NP-hard problems and discuss their strengths and limitations. The article illustrates how algorithms like Grover's and Shor's may offer exponential or polynomial improvements under specific circumstances.Methodology: The study provides a thorough survey of present-day quantum algorithms and analyzes their capabilities as well as limitations. This article examines advancements in hardware innovation and error correction methods to assess their ability to address the challenges of limited scalability and elevated error rates currently hindering their adoption.Results: The article underscores the profound impact of quantum computing on NP-hard problems. However, significant barriers remain, such as the inherent limitations of hardware, universality with respect to programming language and robust error correction capabilities.Conclusion: The article shows important progress and open problems for solving NP-hard problems using quantum algorithms. The results reveal the capabilities to achieve significant computational speedup with algorithms such as Grover’s and Shor's especially in concert when current quantum hardware matures along with novel error correction techniques. Nevertheless, scholars have to investigate more about scalability and the creation of standard programming languages for quantum computers.
Abstract Quantum computing is gaining popularity across a wide range of scientific disciplines due to its potential to solve long-standing computational problems that are considered intractable with classical computers. One promising area where quantum computing has potential is in the speed-up of NP -hard optimisation problems that are common in industrial areas such as logistics and finance. Newcomers to the field of quantum computing who are interested in using this technology to solve optimisation problems do not have an easily accessible source of information on the current capabilities of quantum computers and algorithms. This paper aims to provide a comprehensive overview of the theory of quantum optimisation techniques and their practical application, focusing on their near-term potential for noisy intermediate scale quantum devices. The paper starts by drawing parallels between classical and quantum optimisation problems, highlighting their conceptual similarities and differences. Two main paradigms for quantum hardware are then discussed: analogue and gate-based quantum computers. While analog devices such as quantum annealers are effective for some optimisation problems, they have limitations and cannot be used for universal quantum computation. In contrast, gate-based quantum computers offer the potential for universal quantum computation, but they face challenges with hardware limitations and accurate gate implementation. The paper provides a detailed mathematical discussion with references to key works in the field, as well as a more practical discussion with relevant examples. The most popular techniques for quantum optimisation on gate-based quantum computers, the quantum approximate optimisation algorithm and the quantum alternating operator ansatz framework, are discussed in detail. However, it is still unclear whether these techniques will yield quantum advantage, even with advancements in hardware and noise reduction. The paper concludes with a discussion of the challenges facing quantum optimisation techniques and the need for further research and development to identify new, effective methods for achieving quantum advantage.
Nature is the relations between processes and phenomena. Nothing exists in a Universe without relations. Computing is the transaction of relations between data using control and execution mechanisms. Quantum relations are a superposition of particles and their states. Quantum computing is unconditional transactions of relations between qubit data. Entanglement is a nonlocal superposition of deterministic states. A quantum computer is an analog device for solving combinatorial problems in parallel. Practically focused definitions of the concepts of quantum computing represent a path to the development of scalable quantum parallel algorithms for solving combinatorial problems. 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 uses previously created primitives-constructs to build an always non-optimal calculator. The deterministic paradigm of creating quantum computing by using photon transactions on the electrons of an atom can exclude the use of quantum logic. The evolutionary path of quantum computing from the classical one: Memory-Address-Transaction (MAT) → Electron-Address-Transaction →Electron-Address-Quantaction (EAQ)→State-Superposition- Logic. What is calculated on a quantum computer can be calculated in parallel on a classical computer due to the redundancy of memory. MAT-computing implements any algorithms through transactions (read-write) in memory. Qubit-vector models for describing functionalities differ from the known truth tables in terms of compactness of description and technological implementation of parallel algorithms for the synthesis and analysis of digital devices and SoC-components. An example is given – a memory-driven algorithm for simulating digital devices based on qubit-vector forms of describing functionalities for a significant increase in the productivity of computing processes by parallel execution of logical operations. Comparative evaluations of the use of qubit models and methods show an increase in the efficiency of algorithms for simulating digital devices in comparison with tabular ones. The superposition of classical, quantum and analog computing is integrally presented, which makes it possible to search the best solutions for recognition and decision making.
Classical computing faces significant limitations when dealing with complex, large-scale scientific problems, driving growing interest in quantum computing as a transformative alternative. Quantum computing leverages the principles of superposition, entanglement, and quantum parallelism to perform computations that are infeasible for classical machines. This paper explores recent advancements in quantum hardware, algorithmic design, and the development of hybrid quantum–classical models that integrate quantum gate operations with classical optimization techniques. The proposed hybrid framework aims to enhance computational accuracy and efficiency by utilizing quantum circuits for high-speed processing while relying on classical methods for error correction and optimization. Simulated experiments and comparative analyses demonstrate a 35% improvement in computational speed and scalability over conventional methods. These findings highlight that quantum computing is not merely an incremental improvement but a fundamental shift in computational paradigms, offering new opportunities for scientific research, cryptography, machine learning, and complex data processing.
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.