Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the Russian Academy of Sciences Physics

Physical modelling of computational operations with hypercomplex numbers and its role in the development of photon-echo-based quantum memory

I. I. Popov, Vera T. Nigmatullina

Published Feb 1, 2009• 1 citation
Publisher

Abstract

Modelling of the modes of photon echo formation as an analog process, replacing some time-consuming computational operations in numerical calculation of the photon echo in the quaternion algebra formalism, has been performed. This process has been applied in construction of a quaternion computer.
DOI
10.3103/s1062873809020336

Related papers

Photon echo as a method of optical processor construction for realization of computing operations above hypercomplex numbers

Vera T. Nigmatullina, Ivan I. Popov, Vadim A. Kozlov +1 more

We inform on modelling a photon echo (PhE) shaping conditions as analog process which substitutes a part of labourconsuming computing operations at numerical calculation PhE in a formalism of quaternions algebra, and about its application for a computer construction (CC) for quaternion magnitudes.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 3, 2008•1 citation

Input and output principles of quaternion information in optical echo-processor

Anatolii N. Leukhin, Ivan I. Popov, Andrey M. Gladyshev +2 more

Principle possibility of construction of optical echo-processors with hypercomplex architecture on the basis of physics of photon echo for computational process is shown. Mathematical basis of presentation of quaternion type in optical echo processor is developed. Coding and decoding protocols of information processing with quaternion type are offered. Example of calculating quaternion Fourier transform is demonstrated.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 24, 2006•0 citations

Photon echo possibilities with information processing in hypercomplex space

Anatolii N. Leukhin, Ivan I. Popov

Mode of photon echo (PE) exciting is theoretically considered, when in quality the pulse-code is used a set of pulses with the different time and polarizing characteristics. It is offered to consider a combination of polarizing and peak-time characteristics of a PE signal in algebra of quaternion. A principle of information processing with quaternion representation of signals is experimentally realized.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 15, 2001•0 citations

Application of quaternion algebra for calculation of photon echo signal

Anatolii N. Leukhin, Ivan I. Popov

Mathematical formalism of photon echo exciting at interaction of two-level quantum system with an electromagnetic field within the framework of quaternion algebra is offered. The rotation quaternion is used instead of density operator for representation of interaction dynamics of an exterior field with two-level atom, where the components of rotation quaternion are the coordinates of Bloch vector. Liouville fon-Neumann equation for density matrix evolution is substituted by the differential quaternion equation in a quaternion model. The expression for rotation quaternion appropriating to an unitary operator of rotation in matrix representation is obtained. It is shown that the solution of the differential quaternion equation does not require the difficult mathematical operation connected to an evaluation of an exponent from a matrix. The expression for a quaternion superoperator is obtained.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 20, 2004•1 citation

QUANTUM DIGITAL-ANALOGUE COMPUTING

A. Khakhanova, Svetlana V. Chumachenko, Дарія Рахліс +2 more

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.

Radio Electronics Computer Science Control•Dec 4, 2022•2 citations

Physical principles of realization of quantum evaluations in technique of a photon echo

Ivan I. Popov

This work is dedicated to investigation the properties and opportunities of photon echo with the purpose of development the physical principle of embodying the optical evaluations on a superposition state of the group of excited particles of resonant gas, which could serve as a basis for increasing of features of quantum information processing regime which is supposed in work. One of the possible physical representations of a quaternion in the signal of photon echo is offered. The principle of the optical echo-processor operation is described to fulfill the operations with quantities which are introduced by quaternions. The example of optical transformation of quaternion quantity in the optical echo-processor is given.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 20, 2004•0 citations
Mathematical formalism of photon echo exciting at interaction of two-level quantum system with an electromagnetic field within the framework of quaternion algebra is offered. The rotation quaternion is used instead of density operator for representation of interaction dynamics of an exterior field with two-level atom, where the components of rotation quaternion are the coordinates of Bloch vector. Liouville fon-Neumann equation for density matrix evolution is substituted by the differential quaternion equation in a quaternion model. The expression for rotation quaternion appropriating to an unitary operator of rotation in matrix representation is obtained. It is shown that the solution of the differential quaternion equation does not require the difficult mathematical operation connected to an evaluation of an exponent from a matrix. The expression for a quaternion superoperator is obtained.
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.
This work is dedicated to investigation the properties and opportunities of photon echo with the purpose of development the physical principle of embodying the optical evaluations on a superposition state of the group of excited particles of resonant gas, which could serve as a basis for increasing of features of quantum information processing regime which is supposed in work. One of the possible physical representations of a quaternion in the signal of photon echo is offered. The principle of the optical echo-processor operation is described to fulfill the operations with quantities which are introduced by quaternions. The example of optical transformation of quaternion quantity in the optical echo-processor is given.