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Статті в журналах з теми "Quantum computing formalism"

Автор: Grafiati

Опубліковано: 3 червня 2025

Оновлено: 31 липня 2025

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1

PRIVMAN, VLADIMIR. "SHORT-TIME DECOHERENCE AND DEVIATION FROM PURE QUANTUM STATES." Modern Physics Letters B 16, no. 13 (2002): 459–65. http://dx.doi.org/10.1142/s0217984902003920.

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Анотація:

In systems considered for quantum computing, i.e., for control of quantum dynamics with the goal of processing information coherently, decoherence and deviation from pure quantum states, are the main obstacles to error correction. At low temperatures, usually assumed in quantum computing designs, some of the accepted approaches to evaluation of relaxation mechanisms break down. We develop a new formalism for the estimation of decoherence at short times, appropriate for evaluation of quantum computing architectures.

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2

Varpaaniemi, Kimmo, and Leo Ojala. "Modelling and Simulation of Quantum Teleportation and Dense Coding Using Predicate/Transition-Nets." Fundamenta Informaticae 85, no. 1-4 (2008): 465–79. https://doi.org/10.3233/fun-2008-851-432.

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Анотація:

Reachability analysis is one of the most successful methods used in design and validation of protocols for classical communication, whereas the predicate/transition-net formalism is one of the most appropriate formalisms for reachability analysis oriented modelling. Quantum teleportation and dense coding are non-classical communication protocols that have been widely researched in the field of quantum computing. In this article, we present predicate/transitionnet models of these two protocols and use the PROD reachability analysis tool for analysing the models.

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3

Bollinger, Terry. "Yuri Manin on Biomolecules as Quantum Computers." Terry's Archive Online 2021, no. 02 (2021): 0205. http://dx.doi.org/10.48034/20210205.

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Анотація:

In 1980, Russian mathematician Yuri Manin published Computable and Uncomputable. On pages 14 and 15 of his introduction, Manin suggests that “Molecular biology furnishes examples of the behavior of natural (not engineered by humans) systems which we have to describe in terms initially devised for discrete automata.” Manin then describes the remarkable energy efficiency of naturally occurring biomolecular processes such as DNA replication. He proposes modeling such behaviors in terms of unitary rotations in a finite-dimensional Hilbert space. The decomposition of such systems then corresponds t

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4

Bi, Qiao, Liu Guo, and H. E. Ruda. "Quantum Computing in Decoherence-Free Subspace Constructed by Triangulation." Advances in Mathematical Physics 2010 (2010): 1–10. http://dx.doi.org/10.1155/2010/365653.

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Анотація:

A formalism for quantum computing in decoherence-free subspaces is presented. The constructed subspaces are partial triangulated to an index related to environment. The quantum states in the subspaces are just projected states which are ruled by a subdynamic kinetic equation. These projected states can be used to perform ideal quantum logical operations without decoherence.

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5

McKeon, D. G. C. "Evaluation of loop diagrams using quantum mechanics." Canadian Journal of Physics 70, no. 8 (1992): 652–55. http://dx.doi.org/10.1139/p92-105.

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Анотація:

In using the proper time formalism, Schwinger demonstrated that one-loop processes in quantum field theory can be expressed in terms of a matrix element whose form is encountered in quantum mechanics, and which can be evaluated using the Heisenberg formalism. We demonstrate how instead this matrix element can be computed using standard results in the path-integral formalism. The technique of operator regularization allows one to extend this approach to arbitrary loop order. No loop-momentum integrals are ever encountered. This technique is illustrated by computing the two-point function in [Fo

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6

Käding, Christian, and Mario Pitschmann. "Density Matrix Formalism for Interacting Quantum Fields." Universe 8, no. 11 (2022): 601. http://dx.doi.org/10.3390/universe8110601.

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Анотація:

We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar field, and present a practicable formalism for directly computing the density matrix elements of the combined scalar–scalar system. For deriving the main formula, we use techniques from non-equilibrium quantum field theory like thermo-field dynamics and the Schwinger–Keldysh formalism. Our results allow for studies of particle creation/annihilation processes at

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7

Espinel-López, Cristian, Alvaro Martínez-Gómez, Marisol Aguilar-Echeverría, and Hipatia Mañay-Mañay. "Evolución de componentes de computación cuántica y mediciones cuánticas no destructivas en la informática moderna. //Evolution of quantum computing components and non-destructive quantum measurements in modern computing." CIENCIA UNEMI 11, no. 28 (2018): 57–69. http://dx.doi.org/10.29076/issn.2528-7737vol11iss28.2018pp57-69p.

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Анотація:

El presente trabajo, realiza una breve introducción a las medidas QND (Quantum nondemolition measurement) y sus características. Además, se describe teóricamente un qubit acoplado a un oscilador armónico cuántico forzado como ejemplo de una medición QND en un qubit. El formalismo desarrollado para este tipo de sistemas cuánticos acoplados se desenvuelve dentro de la teoría cuántica de la computación. Como parte del estudio de las mediciones QND, se introducen los qubits de flujo que hacen uso de los interferómetros superconductores cuánticos (SQUIDs). El análisis de este esquema informático in

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8

Albantakis, Larissa, Robert Prentner, and Ian Durham. "Reply to Rourk, C. Comment on “Albantakis et al. Computing the Integrated Information of a Quantum Mechanism. Entropy 2023, 25, 449”." Entropy 25, no. 10 (2023): 1442. http://dx.doi.org/10.3390/e25101442.

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Анотація:

In response to a comment by Chris Rourk on our article Computing the Integrated Information of a Quantum Mechanism, we briefly (1) consider the role of potential hybrid/classical mechanisms from the perspective of integrated information theory (IIT), (2) discuss whether the (Q)IIT formalism needs to be extended to capture the hypothesized hybrid mechanism, and (3) clarify our motivation for developing a QIIT formalism and its scope of applicability.

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9

Mousavi, S. V., and S. Miret-Artés. "Quantum Classical Transition for Mixed States: The Scaled Von Neumann Equation." Symmetry 15, no. 6 (2023): 1184. http://dx.doi.org/10.3390/sym15061184.

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Анотація:

In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled statistical theory following the well-known Wigner–Moyal approach of quantum mechanics. This scaled nonequilibrium statistical mechanics has in it all the ingredients of the classical and quantum theory described in terms of a continuous parameter displaying all the dynamical regimes in between the two extreme cases. Finally, a simple application of our scaled forma

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10

Albantakis, Larissa, Robert Prentner, and Ian Durham. "Computing the Integrated Information of a Quantum Mechanism." Entropy 25, no. 3 (2023): 449. http://dx.doi.org/10.3390/e25030449.

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Анотація:

Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about itself. However, it remains to be determined whether IIT as a theory of consciousness is compatible with quantum mechanics as a theory of microphysics. Here, we present an extension of IIT’s latest formalism to evaluate the mechanism integrated information (φ) of a system subset to discrete, finite-dimensional quantum systems (e.g., quantum logic gates). To that

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11

SOIGUINE, Alexander. "The G-Qubit Theory Alternative to Conventional Tensor-Product Explanation of Entanglement." International Journal of Applied Science 6, no. 1 (2022): p1. http://dx.doi.org/10.30560/ijas.v6n1p1.

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Анотація:

Quantum computing rests upon two theoretical pillars: entanglement and superposition. But some physicists say that this is a very shaky foundation and quantum computing success will have to be based on a different theoretical foundation. The g-qubit theory supports this point of view. Current article is the second one of the two and about the entanglement. It gives different, more physically feasible, not mysterious, explanation of what the entanglement is. The suggested formalism demonstrates that the core of future quantum computing should not be in entanglement which only formally follows i

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12

Iyer, Rajan. "Observables physics general formalism." Physics & Astronomy International Journal 6, no. 1 (2022): 17–20. http://dx.doi.org/10.15406/paij.2022.06.00244.

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Анотація:

Observables form the most important real physics proof processes that will make normal science. Since mathematics have integral part in quantifying physical phenomena, theory involves modeling hypothetical logic borne within observations. A proper theory will need to show pulling out observables from parameters using abstractions. These processes that have gotten derived elsewhere are reviewed here in a gist manner that author has been able to configure as a fundamentally grand unifying realistic physics without assumptive inconsistencies. Review here also shows corrections of errata in earlie

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13

Ghassib, H. B., A. S. Sandouqa, B. R. Joudeh, and S. M. Mosameh. "Predicting the borderline between the classical and quantum regimes in 4He gas from the second virial coefficient." Canadian Journal of Physics 92, no. 9 (2014): 997–1001. http://dx.doi.org/10.1139/cjp-2013-0411.

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Анотація:

The second Virial coefficient in both classical and quantum regimes of 4He gas is investigated in the temperature range 4.2–10 K. Full quantum mechanical and classical treatments are undertaken to calculate this coefficient. The main input in computing the quantum coefficient is the “effective” phase shifts. These are determined within the framework of the Galitskii–Migdal–Feynman formalism, using two interatomic potentials. The borderline between the classical and quantum regimes is found to depend on the temperature, the number density, and the interparticle potential.

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14

Qiao, Bi, and H. E. Ruda. "General nonequilibrium statistical ensemble formalism and its application to quantum computing." Physica A: Statistical Mechanics and its Applications 327, no. 3-4 (2003): 425–41. http://dx.doi.org/10.1016/s0378-4371(03)00365-0.

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15

Altaisky, Mikhail V. "Quantum States of Hierarchic Systems." International Journal of Quantum Information 01, no. 02 (2003): 269–78. http://dx.doi.org/10.1142/s0219749903000188.

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Анотація:

The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always implies the averaging over all states of the environment. In practice this is impossible because the environment of the system is the complement of this system to the whole Universe and contains infinitely many degrees of freedom. A novel method of construction density matrix which implies the averaging only over the direct environment is proposed. The Hilbert space of state vectors for the hierarchic quantum systems is constructed.

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16

Marinescu, N., and M. Apostol. "Quantum-Mechanical Concepts in the Waveguides Theory." Zeitschrift für Naturforschung A 47, no. 9 (1992): 935–40. http://dx.doi.org/10.1515/zna-1992-0902.

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Abstract A Klein-Gordon-type equation is derived for the wave propagation in an ideal, uniform waveguide, and its quantum-mechanical interpretation is given. The "cross-section" concept is introduced for a waveguide and the power transmission factor is obtained by using standard methods of quantum mechanics. The spinorial formalism is also employed for deriving the equivalent Dirac-type equation, and the perturbation theory is applied for computing the frequency shifts. The general applicability of the quantum-mechanical concepts to the waveguides theory is discussed

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17

Kryvobok, Artem, and Alan D. Kathman. "Quantum mechanical four-dimensional non-polarizing beamsplitter." Quantum Studies: Mathematics and Foundations 9, no. 1 (2021): 55–70. http://dx.doi.org/10.1007/s40509-021-00256-8.

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AbstractSome quantum optics researchers might not realize that classical electromagnetism predicts a $$\mathbf {\pi }$$ π phase shift between S- and P-polarized reflection and might think the reflection coefficients of the transverse modes are independent, or that such a phase shift has no measurable consequences. In this paper, we discuss theoretical grounds to define elements of a 4x4 matrix to represent the beamsplitter, accurately accounting for transverse polarization modes and phase relations between them. We also provide experimental evidence confirming this matrix representation. From

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18

Tóth, K. "Dirac’s Approach to Quantum Mechanics in Physics Teacher Education: From Linear to Circular Polarisation." Journal of Physics: Conference Series 2750, no. 1 (2024): 012023. http://dx.doi.org/10.1088/1742-6596/2750/1/012023.

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Abstract The teaching/learning of quantum mechanics via two-state systems is continuously spreading in secondary schools due to its promising results in physics education research. One possibility is the use of polarisation states of photons. This paper reports on a polarisation-based introduction to quantum mechanics in physics teacher education. A widely used school material prepares teacher trainees for their future work and also improves their conceptual knowledge. This part includes statistical calculations using only secondary school mathematics and a new formulation of the uncertainty r

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19

de Keijzer, Robert, Oliver Tse, and Servaas Kokkelmans. "Pulse based Variational Quantum Optimal Control for hybrid quantum computing." Quantum 7 (January 26, 2023): 908. http://dx.doi.org/10.22331/q-2023-01-26-908.

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This work studies pulse based variational quantum algorithms (VQAs), which are designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. In contrast to more standard gate based methods, pulse based methods aim to directly optimize the laser pulses interacting with the qubits, instead of using some parametrized gate based circuit. Using the mathematical formalism of optimal control, these laser pulses are optimized. This method has been used in quantum computing to optimize pulses for quantum gate implementations, but has only recently be

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20

Choudhury, Sayantan, Suman Dey, Rakshit Mandish Gharat, Saptarshi Mandal, and Nilesh Pandey. "Schwinger–Keldysh Path Integral Formalism for a Quenched Quantum Inverted Oscillator." Symmetry 16, no. 10 (2024): 1308. http://dx.doi.org/10.3390/sym16101308.

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In this work, we study the time-dependent behavior of quantum correlations of a system of an inverted oscillator governed by out-of-equilibrium dynamics using the well-known Schwinger–Keldysh formalism in the presence of quantum mechanical quench. Considering a generalized structure of a time-dependent Hamiltonian for an inverted oscillator system, we use the invariant operator method to obtain its eigenstate and continuous energy eigenvalues. Using the expression for the eigenstate, we further derive the most general expression for the generating function as well as the out-of-time-ordered co

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21

Mikki, Said. "Generalized Neuromorphism and Artificial Intelligence: Dynamics in Memory Space." Symmetry 16, no. 4 (2024): 492. http://dx.doi.org/10.3390/sym16040492.

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Анотація:

This paper introduces a multidisciplinary conceptual perspective encompassing artificial intelligence (AI), artificial general intelligence (AGI), and cybernetics, framed within what we call the formalism of generalized neuromorphism. Drawing from recent advancements in computing, such as neuromorphic computing and spiking neural networks, as well as principles from the theory of open dynamical systems and stochastic classical and quantum dynamics, this formalism is tailored to model generic networks comprising abstract processing events. A pivotal aspect of our approach is the incorporation o

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22

Riso, Giuseppe De, and Marialaura Noce. "A unified description of cryptosystems: From classical to quantum protocols." Journal of Discrete Mathematical Sciences & Cryptography 26, no. 8 (2023): 2285–99. http://dx.doi.org/10.47974/jdmsc-1718.

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Анотація:

The launch of quantum computing has created new challenges in the field of cryptography. Nowadays this field of research is extremely active in physics, mathematics and computer science. In this paper we present an overview of the most common classical and quantum protocols. The former are usually defined through a 5-uple given by a plaintext space, a ciphertext space, an encryption and decryption space, an encryption function and a decryption function. Here, we show how to unify quantum and classical protocols by using the same formalism of the 5-uple mentioned above.

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23

Chabaud, Ulysse, and Saeed Mehraban. "Holomorphic representation of quantum computations." Quantum 6 (October 6, 2022): 831. http://dx.doi.org/10.22331/q-2022-10-06-831.

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Анотація:

We study bosonic quantum computations using the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which not only gives a canonical description of bosonic quantum computing using basic elements of complex analysis but also provides a unifying picture which delineates the boundary between discrete- and continuous-variable quantum information theory. Using this representation, we show that the evolution of a single bosonic mode under a Gaussian Hamiltonian can be described as an integrable dynamical system of classical Calogero-Moser p

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24

Kryachko, E. S. "On Molecular Bonding Logic and Matrix Representation of Constant and Balanced Boolean Functions." Ukrainian Journal of Physics 56, no. 7 (2022): 694. http://dx.doi.org/10.15407/ujpe56.7.694.

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Representing a bonding manifold of a molecule or molecular cluster by a graph given by a set of vertices associated with atoms and a set of edges imitating bonds, the bonding edge encoding formalism is defined on n-tuples qubits in terms of the NOT logic gate acting on the "non-bonded" string. This formalism is illustrated by the simplest diatomic and triatomic molecules whose adjacency matrices generate different quadratic Boolean functions, among which the balanced function appears. In this regard, we review the Deutsch–Jozsa quantum algorithm, well-known in quantum computing, that discrimin

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25

BI, QIAO, XIAOJING YAO, BIN GU, and H. E. RUDA. "NON-EQUILIBRIUM STATISTICAL DISTRIBUTION, PROJECT GREEN FUNCTIONS AND STABILIZING QUANTUM COMPUTING FOR OPEN SYSTEM." International Journal of Modern Physics B 18, no. 17n19 (2004): 2480–91. http://dx.doi.org/10.1142/s0217979204025543.

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Using the kinetic equation of subdynamics and the suitable time ordering rule we present a type of irreversible Liouville equation and nonlinear Liouville equation for open quantum systems. We also found a spectral relation for obtaining the non-equilibrium statistical distribution based on the boundary conditions which consistent with H theorem. Furthermore, a formalism of non-equilibrium project Green functions is given, and a non-perturbative method to solve the irreversible Liouville equation is studied. Finally, we give a model of spin-based quantum computing to show that the decoherence

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26

Cafaro, Carlo, Newshaw Bahreyni, and Leonardo Rossetti. "From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited." Symmetry 16, no. 6 (2024): 734. http://dx.doi.org/10.3390/sym16060734.

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Alternative mathematical explorations in quantum computing can be of great scientific interest, especially if they come with penetrating physical insights. In this paper, we present a critical revisitation of our application of geometric (Clifford) algebras (GAs) in quantum computing as originally presented in [C. Cafaro and S. Mancini, Adv. Appl. Clifford Algebras 21, 493 (2011)]. Our focus is on testing the usefulness of geometric algebras (GAs) techniques in two quantum computing applications. First, making use of the geometric algebra of a relativistic configuration space (namely multipart

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27

Vinkhuijzen, Lieuwe, Tim Coopmans, David Elkouss, Vedran Dunjko, and Alfons Laarman. "LIMDD: A Decision Diagram for Simulation of Quantum Computing Including Stabilizer States." Quantum 7 (September 11, 2023): 1108. http://dx.doi.org/10.22331/q-2023-09-11-1108.

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Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent Boolean functions, have proven capable of capturing relevant aspects of quantum systems, but their limits are not well understood. In this work, we investigate and bridge the gap between existing DD-based structures and the stabilizer formalism, an important tool for simulating quantum circuits in the tractable regime. We first show that although DDs were suggest

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28

NAGATA, KOJI, SANGKYUNG LEE, and JAEWOOK AHN. "NONLOCALITY IMPROVES DEUTSCH ALGORITHM." International Journal of Quantum Information 07, no. 03 (2009): 603–14. http://dx.doi.org/10.1142/s0219749909005110.

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We show that the Bell inequalities lead to a new type of linear-optical Deutsch algorithms. We have considered the use of entangled photon pairs to determine probabilistically two unknown functions. The usual Deutsch algorithm determines one unknown function and exhibits a two to one speed up in a certain computation on a quantum computer rather than on a classical computer. We found that the violation of Bell locality in the Hilbert space formalism of quantum theory predicts that the proposed probabilistic Deutsch algorithm for computing two unknown functions exhibits at least a [Formula: see

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29

Hartmann, Jean-Gabriel, Denis Janković, Rémi Pasquier, Mario Ruben, and Paul-Antoine Hervieux. "Nonlinearity of the Fidelity in Open Qudit Systems: Gate and Noise Dependence in High-dimensional Quantum Computing." Quantum 9 (April 7, 2025): 1690. https://doi.org/10.22331/q-2025-04-07-1690.

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High-dimensional quantum computing has generated significant interest due to its potential to address scalability and error correction challenges faced by traditional qubit-based systems. This paper investigates the Average Gate Fidelity (AGF) of single qudit systems under Markovian noise in the Lindblad formalism, extending previous work by developing a comprehensive theoretical framework for the calculation of higher-order correction terms. We derive general expressions for the perturbative expansion of the Average Gate Infidelity (AGI) in terms of the environmental coupling coefficient and

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30

Bignell, Ryan, Waseem Kamleh, and Derek Leinweber. "Computing the magnetic field response of the proton." EPJ Web of Conferences 245 (2020): 06033. http://dx.doi.org/10.1051/epjconf/202024506033.

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Background field methods offer an approach through which fundamental non-perturbative hadronic properties can be studied. Lattice QCD is the only ab initio method with which Quantum Chromodynamics can be studied at low energies; it involves numerically calculating expectation values in the path integral formalism. This requires substantial investment in high performance supercomputing resources. A particular challenge of lattice QCD is isolating the desired state, rather than a superposition of excited states. While extensive work has been performed which allows the ground state to be identifi

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31

Delorme, Stéphane, Thierry Gousset, Roland Katz, and Pol-Bernard Gossiaux. "Quarkonium dynamics inside the Quark-Gluon Plasma using open quantum systems." EPJ Web of Conferences 259 (2022): 12001. http://dx.doi.org/10.1051/epjconf/202225912001.

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In recent years, a significant theoretical effort has been made towards a dynamical description of quarkonia inside the Quark-Gluon Plasma (QGP), using the open quantum systems formalism. In this framework, one can get a real-time description of a quantum system (here the quarkonium) in interaction with a thermal bath (the QGP) by integrating out the bath degrees of freedom and studying the system reduced density matrix. We investigate the real-time dynamics of a correlated heavy quark-antiquark pair inside the QGP using a quantum master equation previously derived from first QCD principles in

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32

Choudhury, Sayantan. ":THE COSMOLOGICAL OTOC: Formulating New Cosmological Micro-Canonical Correlation Functions for Random Chaotic Fluctuations in Out-Of-Equilibrium Quantum Statistical Field Theory." Symmetry 12, no. 9 (2020): 1527. http://dx.doi.org/10.3390/sym12091527.

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The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, using for the first time the slogan “Cosmology meets Condensed Matter Physics”, we demonstrate a formalism to compute the Cosmological OTOC during the stochastic particle production during inflation and reheating following the canonical quantization technique. In this computation, two dynamical time scales are involved—out of them, at one time scale, the cosmological perturbation variable, and for the othe

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33

Castellani, Leonardo. "History operators in quantum mechanics." International Journal of Quantum Information 17, no. 08 (2019): 1941001. http://dx.doi.org/10.1142/s0219749919410016.

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Анотація:

It is convenient to describe a quantum system at all times by means of a “history operator” [Formula: see text], encoding measurements and unitary time evolution between measurements. These operators naturally arise when computing the probability of measurement sequences, and generalize the “sum over position histories” of the Feynman path-integral. As we argue in this work, this description has some computational advantages over the usual state vector description, and may help to clarify some issues regarding nonlocality of quantum correlations and collapse. A measurement on a system describe

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34

Liu, Meiyi, Katelyn Youmans, and Jiali Gao. "Dual QM and MM Approach for Computing Equilibrium Isotope Fractionation Factor of Organic Species in Solution." Molecules 23, no. 10 (2018): 2644. http://dx.doi.org/10.3390/molecules23102644.

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A dual QM and MM approach for computing equilibrium isotope effects has been described. In the first partition, the potential energy surface is represented by a combined quantum mechanical and molecular mechanical (QM/MM) method, in which a solute molecule is treated quantum mechanically, and the remaining solvent molecules are approximated classically by molecular mechanics. In the second QM/MM partition, differential nuclear quantum effects responsible for the isotope effect are determined by a statistical mechanical double-averaging formalism, in which the nuclear centroid distribution is s

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35

WERBOS, PAUL J. "CLASSICAL ODE AND PDE WHICH OBEY QUANTUM DYNAMICS." International Journal of Bifurcation and Chaos 12, no. 10 (2002): 2031–49. http://dx.doi.org/10.1142/s021812740200573x.

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It is well known that classical systems governed by ODE or PDE can have extremely complex emergent properties. Many researchers have asked: is it possible that the statistical correlations which emerge over time in classical systems would allow effects as complex as those generated by quantum field theory (QFT)? For example, could parallel computation based on classical statistical correlations in systems based on continuous variables, distributed over space, possibly be as powerful as quantum computing based on entanglement? This paper proves that the answer to this question is essentially "y

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36

Iqbal, Shahid. "Information entropy, fractional revivals and Schrödinger equation with position-dependent mass." Physica Scripta 97, no. 1 (2022): 015001. http://dx.doi.org/10.1088/1402-4896/ac4633.

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Abstract Information entropy has played a key role in a wide range of disciplines, for instance, classical and quantum information processing, quantum computing, quantum dynamics and quantum metrology. Here, we develop an information theoretic formalism using Shannon entropy, to investigate the quantum dynamics of Hamiltonian systems with position-dependent mass. Such systems are of fundamental interest in many areas, for instance, condensed matter, mathematical physics and foundations of quantum mechanics. We explore the phenomenon of fractional revivals for the temporal evolution of wave-pac

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37

P, Vanitha Muthu, and Karthiyayini R. "Optimizing Fractional Routing with Algebraic Transformations, AI, and Quantum Computing for Next-Generation Networks." Symmetry 17, no. 6 (2025): 965. https://doi.org/10.3390/sym17060965.

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In fractional routing, the flows are distributed through different paths; this allows the maximum efficiency to be achieved by using several partial capacities to balance flow. However, the mathematical formalism for dynamic and scalable implementation is yet to be developed. This paper proposes the aforementioned hybrid framework of edge-linear transformations, AIs, and QCs for fractional routing optimizations. The system encodes flows by means of vector linear transformations over finite fields, supports real-time reconfiguration via deep reinforcement learning, and employs quantum algorithm

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38

Licata, Ignazio, and Leonardo Chiatti. "Event-Based Quantum Mechanics: A Context for the Emergence of Classical Information." Symmetry 11, no. 2 (2019): 181. http://dx.doi.org/10.3390/sym11020181.

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This paper explores an event-based version of quantum mechanics which differs from the commonly accepted one, even though the usual elements of quantum formalism, e.g., the Hilbert space, are maintained. This version introduces as primary element the occurrence of micro-events induced by usual physical (mechanical, electromagnetic and so on) interactions. These micro-events correspond to state reductions and are identified with quantum jumps, already introduced by Bohr in his atomic model and experimentally well established today. Macroscopic bodies are defined as clusters of jumps; the emerge

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39

Bhaumik, Mani L. "Is the Quantum State Real in the Hilbert Space Formulation?" Quanta 9, no. 1 (2020): 37–46. http://dx.doi.org/10.12743/quanta.v9i1.142.

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The persistent debate about the reality of a quantum state has recently come under limelight because of its importance to quantum information and the quantum computing community. Almost all of the deliberations are taking place using the elegant and powerful but abstract Hilbert space formalism of quantum mechanics developed with seminal contributions from John von Neumann. Since it is rather difficult to get a direct perception of the events in an abstract vector space, it is hard to trace the progress of a phenomenon. Among the multitude of recent attempts to show the reality of the quantum

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40

Zuev, S. V. "Geometric properties of quantum entanglement and machine learning." Russian Technological Journal 11, no. 5 (2023): 19–33. http://dx.doi.org/10.32362/2500-316x-2023-11-5-19-33.

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Objectives. Fast data analysis based on hidden patterns is one of the main issues for adaptive artificial intelligence systems development. This paper aims to propose and verify a method of such analysis based on the representation of data in the form of a quantum state, or, alternatively, in the form of a geometric object in a space allowing online machine learning.Methods. This paper uses Feynman formalism to represent quantum states and operations on them, the representation of quantum computing in the form of quantum circuits, geometric transformations, topological classification, as well

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41

Coalson, Rob D. "Extended adiabatic formalism for computing thermodynamic properties of a quantum system coupled to a nonadiabatic bosonic bath." Journal of Chemical Physics 92, no. 8 (1990): 4993–5003. http://dx.doi.org/10.1063/1.458559.

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42

Adhikari, Kiran, Sayantan Choudhury, Hardey N. Pandya, and Rohan Srivastava. "Primordial Gravitational Wave Circuit Complexity." Symmetry 15, no. 3 (2023): 664. http://dx.doi.org/10.3390/sym15030664.

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In this article, we investigate the various physical implications of quantum circuit complexity using the squeezed state formalism of Primordial Gravitational Waves (PGW). Recently, quantum information-theoretic concepts, such as entanglement entropy and complexity, have played a pivotal role in understanding the dynamics of quantum systems, even in diverse fields such as high-energy physics and cosmology. This paper is devoted to studying the quantum circuit complexity of PGW for various cosmological models, such as de Sitter, inflation, radiation, reheating, matter, bouncing, cyclic and blac

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43

Mannone, Maria, Antonio Chella, Giovanni Pilato, Valeria Seidita, Filippo Vella, and Salvatore Gaglio. "Modeling Robotic Thinking and Creativity: A Classic–Quantum Dialogue." Mathematics 12, no. 5 (2024): 642. http://dx.doi.org/10.3390/math12050642.

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The human mind can be thought of as a black box, where the external inputs are elaborated in an unknown way and lead to external outputs. D’Ariano and Faggin schematized thinking and consciousness through quantum state dynamics. The complexity of mental states can be formalized through the entanglement of the so-called qualia states. Thus, the interaction between the mind and the external world can be formalized as an interplay between classical and quantum-state dynamics. Since quantum computing is more and more often being applied to robots, and robots constitute a benchmark to test schemati

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44

Bhattacharya, Sourav. "Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime." Journal of Cosmology and Astroparticle Physics 2022, no. 09 (2022): 041. http://dx.doi.org/10.1088/1475-7516/2022/09/041.

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Abstract Massless minimally coupled quantum scalar field with an asymmetric self interaction, V(ϕ) = λϕ 4/4! + βϕ 3/3! (with λ > 0) is considered in the (3+1)-dimensional inflationary de Sitter spacetime. This potential is bounded from below irrespective of the sign of β. Earlier computations mostly considered the quartic part. Our chief motivation behind this study is to assess the vacuum expectation values of V(ϕ) and ϕ, both of which can be negative, and hence may lead to some screening of the inflationary cosmological constant value. First using the in-in formalism, the renormalised qua

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45

Bourahla, Boualem, and Adel Belayadi. "Computing the surface electronic states on the (100), (110) and (111) surfaces of FCC monatomic crystals." International Journal of Modern Physics B 35, no. 05 (2021): 2150066. http://dx.doi.org/10.1142/s0217979221500661.

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In this study, we carry out a simulation of the surface band structures for face-centered cubic (fcc) leads that end up in (100), (110) and (111) surfaces. The surface Hamiltonian matrix is constructed from tight-binding approach and the secular equations of the surface eigenvalue problem. The solution of the problem is performed by integrating the Landauer–Büttiker formalism (LBF) in the phase field matching approach (PFMA). The LBF provides the quantum scattering properties and the PFMA connects the bulk modes to those of the surface based on the quantum scattering coefficients. The combinat

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46

Sakamoto, Kazuki, Hayata Morisaki, Junichi Haruna, Etsuko Itou, Keisuke Fujii, and Kosuke Mitarai. "End-to-end complexity for simulating the Schwinger model on quantum computers." Quantum 8 (September 17, 2024): 1474. http://dx.doi.org/10.22331/q-2024-09-17-1474.

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The Schwinger model is one of the simplest gauge theories. It is known that a topological term of the model leads to the infamous sign problem in the classical Monte Carlo method. In contrast to this, recently, quantum computing in Hamiltonian formalism has gained attention. In this work, we estimate the resources needed for quantum computers to compute physical quantities that are challenging to compute on classical computers. Specifically, we propose an efficient implementation of block-encoding of the Schwinger model Hamiltonian. Considering the structure of the Hamiltonian, this block-enco

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47

Dmytro, Zubov. "BRAIN Journal - Early Warning of Heat/Cold Waves as a Smart City Subsystem: A Retrospective Case Study of Non-anticipative Analog Methodology." BRAIN - Broad Research in Artificial Intelligence and Neuroscience 6, no. 1-2 (2015): 43–53. https://doi.org/10.5281/zenodo.1044160.

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ABSTRACT In this paper, a forecasting of the heat/cold waves is discussed as a subsystem of the smart city concept using the non-anticipative analog method. The prediction algorithm is described by two paradigms. First one (short range) uses quantum computing formalism. D-Wave adiabatic quantum computing Ising model is employed and evaluated for the forecasting of positive extremes of daily mean air temperature. Forecast models are designed with two to five qubits, which represent 2-, 3-, 4-, and 5-day historical data, respectively. Ising model’s real-valued weights and dimensionless coefficie

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48

CHU, H., and H. UMEZAWA. "STABLE QUASIPARTICLE PICTURE IN THERMAL QUANTUM FIELD PHYSICS." International Journal of Modern Physics A 09, no. 10 (1994): 1703–29. http://dx.doi.org/10.1142/s0217751x9400073x.

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It is well known that physical particles are thermally dissipative at finite temperature. In this paper we reformulate both the equilibrium and nonequilibrium thermal field theories in terms of stable quasiparticles. We will redefine the thermal doublets, the double tilde conjugation rules and the thermal Bogoliubov transformations so that our theory can be consistent for most general situations. All operators, including the dissipative physical particle operators, are realized in a Fock space defined by the stable quasiparticles. The propagators of the physical particles are expressed in term

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49

Oshchepkov, Alexander Yu. "Evolutionary equations for studying the dynamics of qubits in variable magnetic fields." Вестник Пермского университета. Физика, no. 2 (2024): 5–18. http://dx.doi.org/10.17072/1994-3598-2024-2-05-18.

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The work develops an approach to researching the dynamics of qubits that makes it possible to monitor the behavior of the system in the process of quantum computing using computer simulation. The study deals with individual and interacting qubits based on spin ½ in a magnetic field. The goal of the work is to obtain evolutionary equations (equations of motion) for observables that adequately describe the state of the system and provide opportunities for computer modeling of processes. The dynamics of qubits are described using the formalism of the density matrix of pure states. The paper shows

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50

"Simulating Strongly Coupled Quantum Field Theory with Quantum Algorithms." JPS Hot Topics 2 (2022). http://dx.doi.org/10.7566/jpsht.2.017.

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Nonperturbative quantum field theory problems can often be difficult to solve with classical algorithms. Researchers now develop quantum computing algorithms to understand such problems in the Hamiltonian formalism.

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