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Quantum Rep., Volume 6, Issue 1 (March 2024) – 9 articles

Cover Story (view full-size image): Exploring the intersection of economics and quantum theory, this study applies quantum mechanics to enhance economic valuation. Traditional PCI methods are extended, revealing deeper insights. Like quantum superposition, commodities possess multiple potential value states, crystallizing into a definitive value state upon observation. This analogy highlights our advancement in rethinking valuation, introducing quantum-informed perspectives to refine decision making. View this paper
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14 pages, 5095 KiB  
Article
Quantized Approach to Damped Transversal Mechanical Waves
by Ferenc Márkus and Katalin Gambár
Quantum Rep. 2024, 6(1), 120-133; https://doi.org/10.3390/quantum6010009 - 04 Mar 2024
Viewed by 543
Abstract
In information transfer, the dissipation of a signal is of crucial importance. The feasibility of reconstructing the distorted signal depends on the related permanent loss. Therefore, understanding the quantized dissipative transversal mechanical waves might result in deep insights. In particular, it may be [...] Read more.
In information transfer, the dissipation of a signal is of crucial importance. The feasibility of reconstructing the distorted signal depends on the related permanent loss. Therefore, understanding the quantized dissipative transversal mechanical waves might result in deep insights. In particular, it may be valid on the nanoscale in the case of signal distortion, loss, or even restoration. Based on the description of the damped quantum oscillator, we generalize the canonical quantization procedure for the case of the transversal waves. Then, we deduce the related damped wave equation and the state function. We point out the two possible solutions of the propagating-damping wave equation. One involves the well-known Gaussian spreading solution superposed with the damping oscillation, in which the loss of information is complete. The other is the Airy function solution, which is non-spreading–propagating, so the information loss is only due to oscillation damping. However, the structure of the wave shape remains unchanged for the latter. Consequently, this fact may allow signal reconstruction, resulting in the capability of restoring the lost information. Full article
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10 pages, 567 KiB  
Article
Does the Blackbody Radiation Spectrum Suggest an Intrinsic Structure of Photons?
by Alex Khaneles
Quantum Rep. 2024, 6(1), 110-119; https://doi.org/10.3390/quantum6010008 - 13 Feb 2024
Viewed by 992
Abstract
Photons are considered to be elementary bosons in the Standard Model. The assumption that photons are not elementary particles is assessed from an outlook of computational statistical mechanics. A prediction of variations in the shape of the blackbody radiation spectrum with polarization is [...] Read more.
Photons are considered to be elementary bosons in the Standard Model. The assumption that photons are not elementary particles is assessed from an outlook of computational statistical mechanics. A prediction of variations in the shape of the blackbody radiation spectrum with polarization is made. A better understanding of the origins of quantum statistics could be crucial for theories beyond the Standard Model. Full article
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20 pages, 468 KiB  
Article
Geometric Aspects of Mixed Quantum States Inside the Bloch Sphere
by Paul M. Alsing, Carlo Cafaro, Domenico Felice and Orlando Luongo
Quantum Rep. 2024, 6(1), 90-109; https://doi.org/10.3390/quantum6010007 - 06 Feb 2024
Viewed by 626
Abstract
When studying the geometry of quantum states, it is acknowledged that mixed states can be distinguished by infinitely many metrics. Unfortunately, this freedom causes metric-dependent interpretations of physically significant geometric quantities such as the complexity and volume of quantum states. In this paper, [...] Read more.
When studying the geometry of quantum states, it is acknowledged that mixed states can be distinguished by infinitely many metrics. Unfortunately, this freedom causes metric-dependent interpretations of physically significant geometric quantities such as the complexity and volume of quantum states. In this paper, we present an insightful discussion on the differences between the Bures and the Sjöqvist metrics inside a Bloch sphere. First, we begin with a formal comparative analysis between the two metrics by critically discussing three alternative interpretations for each metric. Second, we explicitly illustrate the distinct behaviors of the geodesic paths on each one of the two metric manifolds. Third, we compare the finite distances between an initial state and the final mixed state when calculated with the two metrics. Interestingly, in analogy with what happens when studying the topological aspects of real Euclidean spaces equipped with distinct metric functions (for instance, the usual Euclidean metric and the taxicab metric), we observe that the relative ranking based on the concept of a finite distance between mixed quantum states is not preserved when comparing distances determined with the Bures and the Sjöqvist metrics. Finally, we conclude with a brief discussion on the consequences of this violation of a metric-based relative ranking on the concept of the complexity and volume of mixed quantum states. Full article
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16 pages, 2542 KiB  
Article
Quantum Value Valuation Continuum
by Ünsal Özdilek
Quantum Rep. 2024, 6(1), 74-89; https://doi.org/10.3390/quantum6010006 - 02 Feb 2024
Viewed by 632
Abstract
Price, cost, and income (PCI) methods are traditionally used to approximate the value state of an economic commodity such as a property. Based on the estimates of these methods, we explore how quantum theory represents the fundamental process of value valuation in practice. [...] Read more.
Price, cost, and income (PCI) methods are traditionally used to approximate the value state of an economic commodity such as a property. Based on the estimates of these methods, we explore how quantum theory represents the fundamental process of value valuation in practice. We propose that the mathematical formalism of quantum theory is a promising view and measure of economic value. To ground our exploration, we first map traditional PCI estimates onto three-dimensional spherical coordinates, which were then transformed into two-dimensional quantum states using the Bloch sphere. This step enabled the computation of eigenvalues and eigenvectors of the Hamiltonian matrix, from which the value state measures were derived. The results exhibit practical applications as well as fundamental insights into potential connections between economic and quantum value states. Full article
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16 pages, 444 KiB  
Article
Tomographic Universality of the Discrete Wigner Function
by Isabel Sainz, Ernesto Camacho, Andrés García and Andrei B. Klimov
Quantum Rep. 2024, 6(1), 58-73; https://doi.org/10.3390/quantum6010005 - 19 Jan 2024
Viewed by 543
Abstract
We observe that the discrete Wigner functions (DWFs) of n-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the n-qubit case, this property does not hold [...] Read more.
We observe that the discrete Wigner functions (DWFs) of n-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the n-qubit case, this property does not hold due to the non-factorization of the mapping kernel, the explicit form of which depends on a particular partition of the discrete phase space. Nonetheless, it turns out that the DWF for some specific stabilizers, not included in the set used for the construction of the Wigner map, takes on the form of a delta function. This implies that the possibility of classical simulations of Pauli measurements in a given stabilizer state for qubit systems is closely tied to the experimental setup. Full article
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17 pages, 2913 KiB  
Communication
An Ultra-Energy-Efficient Reversible Quantum-Dot Cellular Automata 8:1 Multiplexer Circuit
by Mohammed Alharbi, Gerard Edwards and Richard Stocker
Quantum Rep. 2024, 6(1), 41-57; https://doi.org/10.3390/quantum6010004 - 16 Jan 2024
Viewed by 734
Abstract
Energy efficiency considerations in terms of reduced power dissipation are a significant issue in the design of digital circuits for very large-scale integration (VLSI) systems. Quantum-dot cellular automata (QCA) is an emerging ultralow power dissipation approach, distinct from traditional, complementary metal-oxide semiconductor (CMOS) [...] Read more.
Energy efficiency considerations in terms of reduced power dissipation are a significant issue in the design of digital circuits for very large-scale integration (VLSI) systems. Quantum-dot cellular automata (QCA) is an emerging ultralow power dissipation approach, distinct from traditional, complementary metal-oxide semiconductor (CMOS) technology, for building digital computing circuits. Developing fully reversible QCA circuits has the potential to significantly reduce energy dissipation. Multiplexers are fundamental elements in the construction of useful digital circuits. In this paper, a novel, multilayer, fully reversible QCA 8:1 multiplexer circuit with ultralow energy dissipation is introduced. The power dissipation of the proposed multiplexer is simulated using the QCADesigner-E version 2.2 tool, describing the microscopic physical mechanisms underlying the QCA operation. The results show that the proposed reversible QCA 8:1 multiplexer consumes 89% less energy than the most energy-efficient 8:1 multiplexer circuit previously presented in the literature. Full article
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12 pages, 2493 KiB  
Article
The Rise of Quantum Information and Communication Technologies
by Antonio Manzalini and Luigi Artusio
Quantum Rep. 2024, 6(1), 29-40; https://doi.org/10.3390/quantum6010003 - 11 Jan 2024
Viewed by 1061
Abstract
Today, we are already using several-component devices and systems based on the technologies developed during the first quantum revolution. Examples include microchips for servers, laptops and smartphones, medical imaging devices, LED, lasers, etc. Now, a second quantum revolution is progressing fast, exploiting technological [...] Read more.
Today, we are already using several-component devices and systems based on the technologies developed during the first quantum revolution. Examples include microchips for servers, laptops and smartphones, medical imaging devices, LED, lasers, etc. Now, a second quantum revolution is progressing fast, exploiting technological advances for the ability to engineer and manipulate other quantum phenomena such as superposition, entanglement and measurement. As a matter of fact, there is an impressive increase in research and development activities, innovation, public and private investments in a new wave of quantum services and applications. In this scenario, quantum information and communication technologies (QICTs) can be defined as a set of technological components, devices, systems and methods for elaborating, storing and transmitting/sharing quantum information. This paper addresses the challenges and opportunities enabling the rise of QICTs. In order to provide a concrete example, the paper describes an overview of the European project EQUO (European Quantum ecOsystems) dealing with ongoing innovation activities in the QICT avenue; in fact, EQUO aims at developing and demonstrating the feasibility of QKD (quantum key distribution) networks and their related integration in current telecommunications infrastructures towards the quantum internet. Full article
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15 pages, 311 KiB  
Article
Quantum Spacetime Geometrization: QED at High Curvature and Direct Formation of Supermassive Black Holes from the Big Bang
by Piero Chiarelli
Quantum Rep. 2024, 6(1), 14-28; https://doi.org/10.3390/quantum6010002 - 26 Dec 2023
Viewed by 618
Abstract
In this work, the author employs the quantum hydrodynamic formalism to achieve the geometrization of spacetime for describing the gravitational interaction within the framework of quantum theory. This approach allows for the development of an equation of gravity that is mathematically connected to [...] Read more.
In this work, the author employs the quantum hydrodynamic formalism to achieve the geometrization of spacetime for describing the gravitational interaction within the framework of quantum theory. This approach allows for the development of an equation of gravity that is mathematically connected to the fermion and boson fields. This achievement is accomplished by incorporating two fundamental principles: covariance of the quantum field equations and the principle of least action. By considering these principles, a theory is established that enables the calculation of gravitational corrections to quantum electrodynamics and, potentially, to the standard model of particle physics as well. The theory also provides an explanation for two phenomena: the existence of a cosmological pressure density similar to quintessence, which is compatible with the small value of the observed cosmological constant, and the breaking of matter–antimatter symmetry at high energies, offering insights into why there is an imbalance between the two in the early universe. In the cosmological modeling of the theory, there exists a proposal to account for the formation of supermassive black holes that are accompanied by their own surrounding galaxies, without relying on the process of mass accretion. The model, in accordance with recent observations conducted by the James Webb Space Telescope, supports the notion that galactic configurations were established relatively early in the history of the universe, shortly after the occurrence of the Big Bang. Full article
13 pages, 2016 KiB  
Article
The Quantum Amplitude Estimation Algorithms on Near-Term Devices: A Practical Guide
by Marco Maronese, Massimiliano Incudini, Luca Asproni and Enrico Prati
Quantum Rep. 2024, 6(1), 1-13; https://doi.org/10.3390/quantum6010001 - 24 Dec 2023
Viewed by 1108
Abstract
The Quantum Amplitude Estimation (QAE) algorithm is a major quantum algorithm designed to achieve a quadratic speed-up. Until fault-tolerant quantum computing is achieved, being competitive over classical Monte Carlo (MC) remains elusive. Alternative methods have been developed so as to require fewer resources [...] Read more.
The Quantum Amplitude Estimation (QAE) algorithm is a major quantum algorithm designed to achieve a quadratic speed-up. Until fault-tolerant quantum computing is achieved, being competitive over classical Monte Carlo (MC) remains elusive. Alternative methods have been developed so as to require fewer resources while maintaining an advantageous theoretical scaling. We compared the standard QAE algorithm with two Noisy Intermediate-Scale Quantum (NISQ)-friendly versions of QAE on a numerical integration task, with the Monte Carlo technique of Metropolis–Hastings as a classical benchmark. The algorithms were evaluated in terms of the estimation error as a function of the number of samples, computational time, and length of the quantum circuits required by the solutions, respectively. The effectiveness of the two QAE alternatives was tested on an 11-qubit trapped-ion quantum computer in order to verify which solution can first provide a speed-up in the integral estimation problems. We concluded that an alternative approach is preferable with respect to employing the phase estimation routine. Indeed, the Maximum Likelihood estimation guaranteed the best trade-off between the length of the quantum circuits and the precision in the integral estimation, as well as greater resistance to noise. Full article
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