Journal Description
Quantum Reports
Quantum Reports
is an international, peer-reviewed, open access journal on quantum science. It publishes original research articles and review articles in all quantum subfields, from basic quantum theory to a broad array of applications. Quantum Reports is published quarterly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus and other databases.
- Journal Rank: CiteScore - Q2 (Physics and Astronomy (miscellaneous))
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 18.7 days after submission; acceptance to publication is undertaken in 8.5 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Latest Articles
Diversifying Investments and Maximizing Sharpe Ratio: A Novel Quadratic Unconstrained Binary Optimization Formulation
Quantum Rep. 2024, 6(2), 244-262; https://doi.org/10.3390/quantum6020018 - 27 May 2024
Abstract
The optimization of investment portfolios represents a pivotal task within the field of financial economics. Its objective is to identify asset combinations that meet specified criteria for return and risk. Traditionally, the maximization of the Sharpe Ratio, often achieved through quadratic programming, has
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The optimization of investment portfolios represents a pivotal task within the field of financial economics. Its objective is to identify asset combinations that meet specified criteria for return and risk. Traditionally, the maximization of the Sharpe Ratio, often achieved through quadratic programming, has constituted a popular approach for this purpose. However, real-world scenarios frequently necessitate more complex considerations, particularly in relation to portfolio diversification with a view to mitigating sector-specific risks and enhancing stability. The incorporation of diversification alongside the Sharpe Ratio into the optimization model creates a joint optimization task, which can be formulated as Quadratic Unconstrained Binary Optimization (QUBO) and addressed using quantum annealing or hybrid computing techniques. These techniques offer promising solutions. We present a novel QUBO formulation for this optimization, detailing its mathematical formulation and demonstrating its advantages over classical methods, particularly in handling diversification objectives. By leveraging available QUBO solvers and hybrid approaches, we explore the feasibility of handling large-scale problems while highlighting the importance of diversification in achieving robust portfolio performance. We finally elaborate on the results showing the trade-off between the observed values of the portfolio’s Sharpe Ratio and diversification, as a natural consequence of solving a multi-objective optimization problem.
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Open AccessArticle
Wave Function and Information
by
Leonardo Chiatti
Quantum Rep. 2024, 6(2), 231-243; https://doi.org/10.3390/quantum6020017 - 23 May 2024
Abstract
Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to
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Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to the wave equation. The information related to the amplitude measures the strength of the potential coupling of the particle (which is itself aspatial) with each volume of its configuration space, i.e., its tendency to participate in an interaction localized in a region of ordinary physical space corresponding to that volume. The information connected to the phase is that required to obtain the time evolution of the particle as a persistent entity starting from a random succession of bits. It can be considered as the information provided by conservation principles. The meaning of the so-called “quantum potential” in this context is briefly discussed.
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Open AccessFeature PaperArticle
A Dyson Brownian Motion Model for Weak Measurements in Chaotic Quantum Systems
by
Federico Gerbino, Pierre Le Doussal, Guido Giachetti and Andrea De Luca
Quantum Rep. 2024, 6(2), 200-230; https://doi.org/10.3390/quantum6020016 - 16 May 2024
Cited by 1
Abstract
We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every
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We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every time t. Due to invariance by unitary transformations, the dynamics of the eigenvalues of the density matrix decouples from that of the eigenvectors, and is exactly described by stochastic equations that we derive. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large size it matches with the inverse-Marchenko–Pastur distribution. In the case of perfect measurements, instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of ’s at each time t and for each size n. Two relevant regimes emerge: at short times , the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the limit. In that case, all moments of the density matrix become self-averaging and it is possible to exactly characterize the entanglement spectrum. In the limit of large times , one enters instead a regime in which the eigenvalues are exponentially separated , but fluctuations play an essential role. We are still able to characterize the asymptotic behaviors of the entanglement entropy in this regime.
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(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)
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Open AccessArticle
Fisher Information for a System Composed of a Combination of Similar Potential Models
by
Clement Atachegbe Onate, Ituen B. Okon, Edwin Samson Eyube, Ekwevugbe Omugbe, Kizito O. Emeje, Michael C. Onyeaju, Olumide O. Ajani and Jacob A. Akinpelu
Quantum Rep. 2024, 6(2), 184-199; https://doi.org/10.3390/quantum6020015 - 13 May 2024
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The solutions to the radial Schrödinger equation for a pseudoharmonic potential and Kratzer potential have been studied separately in the past. Despite different reports on the Kratzer potential, the fundamental theoretical quantities such as Fisher information have not been reported. In this study,
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The solutions to the radial Schrödinger equation for a pseudoharmonic potential and Kratzer potential have been studied separately in the past. Despite different reports on the Kratzer potential, the fundamental theoretical quantities such as Fisher information have not been reported. In this study, we obtain the solution to the radial Schrödinger equation for the combination of the pseudoharmonic and Kratzer potentials in the presence of a constant-dependent potential, utilizing the concepts and formalism of the supersymmetric and shape invariance approach. The position expectation value and momentum expectation value are calculated employing the Hellmann–Feynman Theory. These expectation values are then used to calculate the Fisher information for both position and momentum spaces in both the absence and presence of the constant-dependent potential. The results obtained revealed that the presence of the constant-dependent potential leads to an increase in the energy eigenvalue, as well as in the position and momentum expectation values. Additionally, the constant-dependent potential increases the Fisher information for both position and momentum spaces. Furthermore, the product of the position expectation value and the momentum expectation value, along with the product of the Fisher information, satisfies both Fisher’s inequality and Cramer–Rao’s inequality.
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Open AccessFeature PaperArticle
Spectral Analysis of Proton Eigenfunctions in Crystalline Environments
by
Luca Gamberale and Giovanni Modanese
Quantum Rep. 2024, 6(2), 172-183; https://doi.org/10.3390/quantum6020014 - 6 May 2024
Abstract
The Schrödinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and non-quadratic potentials, in both one-dimensional and three-dimensional scenarios. Numerical computation
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The Schrödinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and non-quadratic potentials, in both one-dimensional and three-dimensional scenarios. Numerical computation of the energy spectrum of bound eigenfunctions in both cases reveals intriguing structures, including bound states with degeneracy matching the site number , reminiscent of a finite harmonic oscillator spectrum. In contrast to electronic energy bands, the proton system displays a greater number of possible bound states due to the significant mass of protons. Extending previous research, this study rigorously determines the constraints on the energy gap and oscillation amplitude of the previously identified coherent states. The deviations in energy level spacing identified in the computed spectrum, leading to the minor splitting of electromagnetic modes, are analyzed and found not to hinder the onset of coherence. Finally, a more precise value of the energy gap is determined for the proton coherent states, ensuring their stability against thermal decoherence up to the melting temperature of the hosting metal.
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(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)
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Open AccessArticle
Measuring the Density Matrix of Quantum-Modeled Cognitive States
by
Wendy Xiomara Chavarría-Garza, Osvaldo Aquines-Gutiérrez, Ayax Santos-Guevara, Humberto Martínez-Huerta, Jose Ruben Morones-Ibarra and Jonathan Rincon Saucedo
Quantum Rep. 2024, 6(2), 156-171; https://doi.org/10.3390/quantum6020013 - 27 Apr 2024
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Inspired by the principles of quantum mechanics, we constructed a model of students’ misconceptions about heat and temperature, conceptualized as a quantum system represented by a density matrix. Within this framework, the presence or absence of misconceptions is delineated as pure states, while
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Inspired by the principles of quantum mechanics, we constructed a model of students’ misconceptions about heat and temperature, conceptualized as a quantum system represented by a density matrix. Within this framework, the presence or absence of misconceptions is delineated as pure states, while the probability of mixed states is also considered, providing valuable insights into students’ cognition based on the mental models they employ when holding misconceptions. Using the analysis model previously employed by Lei Bao and Edward Redish, we represented these results in a density matrix. In our research, we utilized the Zeo and Zadnik Thermal Concept Evaluation among 282 students from a private university in Northeast Mexico. Our objective was to extract information from the analysis of multiple-choice questions designed to explore preconceptions, offering valuable educational insights beyond the typical Correct–Incorrect binary analysis of classical systems. Our findings reveal a probability of 0.72 for the appearance of misconceptions, 0.28 for their absence, and 0.43 for mixed states, while no significant disparities were observed based on gender or scholarship status, a notable difference was observed among programs (p < 0.05). These results are consistent with the previous literature, confirming a prevalence of misconceptions within the student population.
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Open AccessArticle
A Normalization Condition for the Probability Current in Some Remarkable Cases
by
Antonio Feoli, Elmo Benedetto and Antonella Lucia Iannella
Quantum Rep. 2024, 6(2), 147-155; https://doi.org/10.3390/quantum6020012 - 23 Apr 2024
Abstract
Starting from the dynamics of a bouncing ball in classical and quantum regime, we have suggested in a previous paper to add an arbitrary function of time to the standard expression of the probability current in quantum mechanics. In this paper, we suggest
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Starting from the dynamics of a bouncing ball in classical and quantum regime, we have suggested in a previous paper to add an arbitrary function of time to the standard expression of the probability current in quantum mechanics. In this paper, we suggest a way to determine this function: imposing a suitable normalization condition. The application of our proposal to the case of the harmonic oscillator is discussed.
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Open AccessEditorial
The Many-Worlds Interpretation of Quantum Mechanics: Current Status and Relation to Other Interpretations
by
Lev Vaidman
Quantum Rep. 2024, 6(2), 142-146; https://doi.org/10.3390/quantum6020011 - 18 Apr 2024
Abstract
This is a preface to a Special Issue of Quantum Reports devoted to the results of the workshop “The Many-Worlds Interpretation of Quantum Mechanics: Current Status and Relation to Other Interpretations” [...]
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(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
Open AccessCommunication
Continuum Limit of the Green Function in Scaled Affine
by
Riccardo Fantoni
Quantum Rep. 2024, 6(2), 134-141; https://doi.org/10.3390/quantum6020010 - 14 Apr 2024
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Through path integral Monte Carlo computer experiments, we prove that the affine quantization of the -scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well-defined continuum limit of the one- and two-point functions. Affine
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Through path integral Monte Carlo computer experiments, we prove that the affine quantization of the -scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well-defined continuum limit of the one- and two-point functions. Affine quantization leads to a completely satisfactory quantization of field theories in situations involving scaled behavior, leading to an unexpected term, , which arises only in the quantum aspects.
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Open AccessArticle
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 - 4 Mar 2024
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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
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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.
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Open AccessArticle
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
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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
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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.
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Open AccessArticle
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 - 6 Feb 2024
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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,
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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.
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Open AccessArticle
Quantum Value Valuation Continuum
by
Ünsal Özdilek
Quantum Rep. 2024, 6(1), 74-89; https://doi.org/10.3390/quantum6010006 - 2 Feb 2024
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.
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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.
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(This article belongs to the Special Issue New Reports on Quantum Mechanics: Discoveries, Promising Trends, and Technological Innovations)
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Open AccessArticle
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
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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
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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.
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Open AccessCommunication
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
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)
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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.
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(This article belongs to the Special Issue New Reports on Quantum Mechanics: Discoveries, Promising Trends, and Technological Innovations)
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Open AccessArticle
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
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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
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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.
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Open AccessArticle
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
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
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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.
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Open AccessArticle
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
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
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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.
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(This article belongs to the Special Issue Quantum Computing: A Taxonomy, Systematic Review, and Future Directions)
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Applications of Supersymmetric Polynomials in Statistical Quantum Physics
by
Iryna Chernega, Mariia Martsinkiv, Taras Vasylyshyn and Andriy Zagorodnyuk
Quantum Rep. 2023, 5(4), 683-697; https://doi.org/10.3390/quantum5040043 - 8 Dec 2023
Cited by 1
Abstract
We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences Such an approach
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We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences Such an approach allows us to interpret some of the combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence for , induced by the supersymmetric polynomials, and the semi-ring algebraic structures on the quotient set with respect to this relation. The quotient set is a natural model for the set of energy levels of a quantum system. We introduce two different topological semi-ring structures into this set and discuss their possible physical interpretations.
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(This article belongs to the Special Issue Exploring Information and Complexity Measures in Quantum Systems by Exactly Solvable Models)
Open AccessArticle
A Schrödinger Equation for Evolutionary Dynamics
by
Vi D. Ao, Duy V. Tran, Kien T. Pham, Duc M. Nguyen, Huy D. Tran, Tuan K. Do, Van H. Do and Trung V. Phan
Quantum Rep. 2023, 5(4), 659-682; https://doi.org/10.3390/quantum5040042 - 31 Oct 2023
Cited by 1
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We establish an analogy between the Fokker–Planck equation describing evolutionary landscape dynamics and the Schrödinger equation which characterizes quantum mechanical particles, showing that a population with multiple genetic traits evolves analogously to a wavefunction under a multi-dimensional energy potential in imaginary time. Furthermore,
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We establish an analogy between the Fokker–Planck equation describing evolutionary landscape dynamics and the Schrödinger equation which characterizes quantum mechanical particles, showing that a population with multiple genetic traits evolves analogously to a wavefunction under a multi-dimensional energy potential in imaginary time. Furthermore, we discover within this analogy that the stationary population distribution on the landscape corresponds exactly to the ground-state wavefunction. This mathematical equivalence grants entry to a wide range of analytical tools developed by the quantum mechanics community, such as the Rayleigh–Ritz variational method and the Rayleigh–Schrödinger perturbation theory, allowing us not only the conduct of reasonable quantitative assessments but also exploration of fundamental biological inquiries. We demonstrate the effectiveness of these tools by estimating the population success on landscapes where precise answers are elusive, and unveiling the ecological consequences of stress-induced mutagenesis—a prevalent evolutionary mechanism in pathogenic and neoplastic systems. We show that, even in an unchanging environment, a sharp mutational burst resulting from stress can always be advantageous, while a gradual increase only enhances population size when the number of relevant evolving traits is limited. Our interdisciplinary approach offers novel insights, opening up new avenues for deeper understanding and predictive capability regarding the complex dynamics of evolving populations.
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