We show that, if time comes when quantum algorithms can be used for universal parallel computation, the "quantum-parallel" computer hardware will most probably be a classical physical system corresponding to a Hilbert space and the actual realization may be the combination of analog and digital circuits. We first point out the practical difficulties of universal quantum computing which may prohibit practical applications as universal computers. Then we show how to apply analog microelectronic circuits to realize the architecture, data processing and parallel computing abilities of quantum computing via Hilbert space computing with analog circuits. Such a Hilbert-space-analog (HSA) computer simulates the Hilbert space and its operators, and it is able to use and test quantum algorithms developed for the real quantum computers. Such a computer would be free of most of the practical difficulties of realizing and running a real quantum computer. This computer can be made universal. It is remarkable that by using the same numbers of transistors as in today's PCs, such a HSA computer can manipulate ~107 analog numbers corresponding to ~22 qubits, simultaneously, by quantum-parallel processing.
We show that, if time comes when quantum algorithms can be used for universal parallel computation, the "quantum-parallel" computer hardware will most probably be a classical physical system corresponding to a Hilbert space and the actual realization may be the combination of analog and digital circuits. We first point out the practical difficulties of universal quantum computing which may prohibit practical applications as universal computers. Then we show how to apply analog microelectronic circuits to realize the architecture, data processing and parallel computing abilities of quantum computing via Hilbert space computing with analog circuits. Such a Hilbert-space-analog (HSA) computer simulates the Hilbert space and its operators, and it is able to use and test quantum algorithms developed for the real quantum computers. Such a computer would be free of most of the practical difficulties of realizing and running a real quantum computer. This computer can be made universal. It is remarkable that by using the same numbers of transistors as in today's PCs, such a HSA computer can manipulate ~107 analog numbers corresponding to ~22 qubits, simultaneously, by quantum-parallel processing.
We first point out the practical difficulties of universal quantum computing which may prohibit practical applications as universal computers. Then we show how to apply analog microelectronic circuits to realize the architecture, data processing and parallel computing abilities of quantum computing via Hilbert space computing with analog circuits. Such a Hilbert-space-analog (HSA) computer simulates the Hilbert space and its operators and it is able to use and test quantum algorithms developed for the real quantum computers. Such a computer would be free of most of the practical difficulties of realizing and running a real quantum computer. This computer can be made universal. It is remarkable that by using the same numbers of transistors as in today's PCs, such a HSA computer can manipulate ~107 analog numbers corresponding to ~23 qubits, simultaneously, by quantum-parallel processing.
Quantum computers are regarded as the future of computing, as they are believed to be capable of solving extremely complex problems that are intractable on conventional digital computers. However, near-term quantum computers are prone to a plethora of noise sources that are difficult to mitigate, possibly limiting their scalability and precluding us from running any useful algorithms. Quantum emulation is an alternative approach that uses classical analog hardware to emulate the properties of superposition and entanglement, thereby mimicking quantum parallelism to attain similar speeds. By contrast, the use of classical digital hardware, such as field programmable gate arrays (FPGA), is less inefficient at emulating a quantum computer, as it does not take advantage of the fundamentally analog nature of quantum states. Consequently, this approach adds an inherent hardware overhead that also prevents scaling. In this work, an energy-efficient quantum emulator based on analog circuits realized in UMC 180-nm CMOS technology is proposed along with the design methodologies for a scalable computing architecture. A six-fold improvement in power consumption was observed over the FPGA-based approach for a ten-qubit emulation of Grover's search algorithm. The proposed emulator is also about 400 times faster than a Ryzen 5600x six-core processor performing a simulation of six-qubit Grover's search algorithm
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.
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary operations on a finite-dimensional Hilbert space, are not unique to quantum systems but may be found in certain classical systems as well. Previously, it has been shown that one can represent an arbitrary multi-qubit quantum state in terms of classical analog signals using nested quadrature amplitude modulated signals. Furthermore, using digitally controlled analog electronics one may manipulate these signals to perform quantum gate operations and thereby execute quantum algorithms. The computational capacity of a single signal is, however, limited by the required bandwidth, which scales exponentially with the number of qubits when represented using frequency-based encoding. To overcome this limitation, we introduce a method to extend this approach to multiple parallel signals. Doing so allows a larger quantum state to be emulated with the same gate time required for processing frequency-encoded signals. In the proposed representation, each doubling of the number of signals corresponds to an additional qubit in the spatial domain. Single quit gate operations are similarly extended so as to operate on qubits represented using either frequency-based or spatial encoding schemes. Furthermore, we describe a method to perform gate operations between pairs of qubits represented using frequency or spatial encoding or between frequency-based and spatially encoded qubits. Finally, we describe how this approach may be extended to represent qubits in the time domain as well.
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.
This paper explores the feasibility of simulating universal computation using analog quantum circuits. We present a core claim that it is possible to design and implement analog quantum circuits capable of mimicking any universal computational model, such as a Turing machine. The proposed mechanism centers around the architecture of coupled qubits with dynamically tunable interactions, allowing for universal computation through precise manipulation of the circuit. This work emphasizes a practical approach to analog quantum simulation, moving beyond theoretical considerations to a design strategy suitable for experimental realization. The core concepts and theoretical underpinnings of this approach are detailed, outlining the potential for achieving universal computation through analog quantum circuits. The paper's focus is on the design considerations and the necessary conditions for realizing this simulation, rather than presenting experimental results. We explore the mathematical framework required for this simulation, including the representation of quantum states and the evolution operators.