Quantum Reports

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

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

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

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

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

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

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

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

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

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 ${\mathcal{\ell }}_1\left({\mathbb{Z}}_0\right).$ 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 ${\mathcal{\ell }}_1\left({\mathbb{Z}}_0\right)$, 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. Full article

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. Full article

We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on quadratic unconstrained binary optimization (QUBO) problems, which are well-suited for qubit superposition states. Specifically, we demonstrate circuit designs which encode QUBOs as ‘cost oracle’ operations $U_{\mathrm{C}}$, which distribute phases across the basis states proportional to a cost function. We then show that when $U_{\mathrm{C}}$ is combined with the standard Grover diffusion operator $U_{\mathrm{s}}$, one can achieve high probabilities of measurement for states corresponding to optimal and near optimal solutions while still only requiring O($\frac{\pi }{4}\sqrt{2^N/M}$) iterations. In order to achieve these probabilities, a single scalar parameter $p_{\mathrm{s}}$ is required, which we show can be found through a variational quantum–classical hybrid approach and can be used for heuristic solutions. Full article

Arguments have been made that the violation of the CHSH and similar inequalities shows that reality at the quantum level must be non-local. The derivation of Bell inequality is re-examined, and it is shown that violations of these inequalities merely demonstrate the existence of contextuality—they say nothing about the causal influences underlying such contextuality. It is argued that contextual systems do not possess enduring (propositional) properties, merely contingent properties. An example of a classical situation is presented: a two-player co-operative game, the random variables of which are consistently connected in the sense of Dzhafarov, which is contextual, and violates the CHSH inequality. In fact, it also violates the Tsirel’son bound. The key is that this system is generated, and its properties are disposed of, not determined. Full article

Quantum computing is a rapidly developing field that has the potential to revolutionize the way we process data. In this article, we will introduce quantum computers, their hardware and the challenges associated with their development. One of the key concepts in quantum computing is the qubit, which is the basic unit of quantum information. We will discuss this concept in greater detail, exploring how qubits work and the unique properties that make them so powerful. There are currently three leading models of quantum computers: superconducting, ion trap, and neutral-atom qubits. We will compare these models, highlighting their respective advantages and limitations, and discuss the current state of research in each area. In addition to exploring the hardware of quantum computers, we will also introduce some of the innovative research projects related to qubits. Finally, we will examine the market around the quantum computing industry, outlining some of the fundamental challenges we may face. Full article

The deterministic nature of EQM (the Everett Interpretation of Quantum Mechanics) seems to be inconsistent with the use of probability in EQM, giving rise to what is known as the “incoherence problem”. In this paper, I explore approaches to solve the incoherence problem of EQM via pre-measurement uncertainty. Previous discussions on the validity of pre-measurement uncertainty have leaned heavily on intricate aspects of the theory of semantics and reference, the embrace of either four-dimensionalism or three-dimensionalism of personhood, or the ontology of EQM. In this paper, I argue that, regardless of the adoption of three-dimensionalism or four-dimensionalism of personhood, the overlapping view or the divergence view of the ontology of EQM, the pre-measurement uncertainty approach to the incoherence problem of EQM can only achive success while contradicting fundamental principles of physicalism. I also use the divergence view of EQM as an example to illustrate my analyses. Full article

Mismatch repair is a critical step in DNA replication that occurs after base selection and proofreading, significantly increasing fidelity. However, the mechanism of mismatch recognition has not been established for any repair enzyme. Speculations in this area mainly focus on exploiting thermodynamic equilibrium and free energy. Nevertheless, non-equilibrium processes may play a more significant role in enhancing mismatch recognition accuracy by utilizing adenosine triphosphate (ATP). This study aimed to investigate this possibility. Considering our limited knowledge of actual mismatch repair enzymes, we proposed a hypothetical enzyme that operates as a quantum system with three discrete energy levels. When the enzyme is raised to its highest energy level, a quantum transition occurs, leading to one of two low-energy levels representing potential recognition outcomes: a correct match or a mismatch. The probabilities of the two outcomes are exponentially different, determined by the energy gap between the two low energy levels. By flipping the energy gap, discrimination between mismatches and correct matches can be achieved. Within a framework that combines quantum mechanics with thermodynamics, we established a relationship between energy cost and the recognition error. Full article

In physics, mathematics, and other disciplines, new integrable equations have been found using the P-test. Novel insights and discoveries in several domains have resulted from this. Whether a solution is oscillatory, decaying, or expanding exponentially can be observed by using the AEM approach. In this work, we examined the integrability of the triple nonlinear fractional Schrödinger equation (TNFSE) via the Painlevé test (P-test) and a number of optical solitary wave solutions such as bright dromions (solitons), hyperbolic, singular, periodic, domain wall, doubly periodic, trigonometric, dark singular, plane-wave solution, combined optical solitons, rational solutions, etc., via the auxiliary equation mapping (AEM) technique. In mathematical physics and in engineering sciences, this equation plays a very important role. Moreover, the graphical representation (3D, 2D, and contour) of the obtained optical solitary-wave solutions will facilitate the understanding of the physical phenomenon of this system. The computational work and conclusions indicate that the suggested approaches are efficient and productive. Full article

Quantum systems with dynamical symmetries have conserved quantities that are preserved under coherent control. Therefore, such systems cannot be completely controlled by means of only coherent control. In particular, for such systems, the maximum transition probability between some pairs of states over all coherent controls can be less than one. However, incoherent control can break this dynamical symmetry and increase the maximum attainable transition probability. The simplest example of such a situation occurs in a three-level quantum system with dynamical symmetry, for which the maximum probability of transition between the ground and intermediate states using only coherent control is $1/2$, whereas it is about $0.687$ using coherent control assisted by incoherent control implemented through the non-selective measurement of the ground state, as was previously analytically computed. In this work, we study and completely characterize all critical points of the kinematic quantum control landscape for this measurement-assisted transition probability, which is considered as a function of the kinematic control parameters (Euler angles). The measurement-driven control used in this work is different from both quantum feedback and Zeno-type control. We show that all critical points are global maxima, global minima, saddle points or second-order traps. For comparison, we study the transition probability between the ground and highest excited states, as well as the case when both these transition probabilities are assisted by incoherent control implemented through the measurement of the intermediate state. Full article

Quantum teleportation is the name of a problem: How can the real-valued parameters encoding the state at Alice’s location make their way to Bob’s location via shared entanglement and only two bits of classical communication? Without an explanation, teleportation appears to be a conjuring trick. Investigating the phenomenon with Schrödinger states and reduced density matrices shall always leave loose ends because they are not local and complete descriptions of quantum systems. Upon demonstrating that the Heisenberg picture admits a local and complete description, Deutsch and Hayden rendered its explanatory power manifest by revealing the trick behind teleportation, namely, by providing an entirely local account. Their analysis is re-exposed and further developed. Full article