Quantum Reports

(1) Background: One of the greatest challenges students face when studying quantum mechanics is the lack of daily experience and intuition about its concepts. This article introduces a holistic activity designed to present some foundational ideas of quantum mechanics in a new pedagogical approach to enhance students’ motivation. Using real open data from CERN, the activity connects classical concepts of dynamics and electromagnetism to their quantum counterparts, emphasizing both their similarities and differences. Teaching physics must consider the way the brain learns. That is why the activity is based on observed neuroscientific principles of physics learning. The approach maintains the rigor and precision required for these abstract concepts. (2) Methods: To evaluate the activity’s impact by gender, intrinsic motivation was assessed using a Likert-type scale with 81 undergraduate students from fields including artificial intelligence systems engineering, computer engineering, mathematical engineering, and architecture. (3) Results: a Mann–Whitney U test analysis indicates the activity significantly enhances students’ intrinsic motivation to study quantum mechanics, with improvements observed in both male and female students. (4) Conclusions: This result highlights the potential of the activity to promote greater interest in physics, both in men and women, since no significant differences have been observed between both samples. Full article

The Bogomolny approach to the Ginzburg–Landau equations in the context of strong and semi-strong necessary conditions is formulated for various superconducting structures in a quasi-one-dimensional description, considering both flat and curved geometries. This formulation is justified by a perturbative approach to the Ginzburg–Landau theory applied to a superconducting structure that is polarized by an electric charge moving across two neighboring quantum dots. The situation considered involves an interface between a Josephson junction and a semiconductor quantum dot system in a one-dimensional setting. Full article

Optimization is a crucial challenge across various domains, including finance, resource allocation, and mobility. Quantum computing has the potential to redefine the way we handle complex problems by reducing computational complexity and enhancing solution quality. Optimization, particularly of objective functions, stands to benefit significantly from quantum solvers, which leverage principles of quantum mechanics like superposition, entanglement, and tunneling. The Ising and Quadratic Unconstrained Binary Optimization (QUBO) models are the most suitable formulations for these solvers, involving binary variables and constraints treated as penalties within the overall objective function. To harness quantum approaches for optimization, two primary strategies are employed: exploiting quantum annealers—special-purpose optimization devices—and designing algorithms based on quantum circuits. This review provides a comprehensive overview of quantum optimization methods, examining their advantages, challenges, and limitations. It demonstrates their application to real-world scenarios and outlines the steps to convert generic optimization problems into quantum-compliant models. Lastly, it discusses available tools and frameworks that facilitate the exploration of quantum solutions for optimization tasks. Full article

Optimizing quantum circuits is critical for enhancing computational speed and mitigating errors caused by quantum noise. Effective optimization must be achieved without compromising the correctness of the computations. This survey explores recent advancements in quantum circuit optimization, encompassing both hardware-independent and hardware-dependent techniques. It reviews state-of-the-art approaches, including analytical algorithms, heuristic strategies, machine learning-based methods, and hybrid quantum-classical frameworks. The paper highlights the strengths and limitations of each method, along with the challenges they pose. Furthermore, it identifies potential research opportunities in this evolving field, offering insights into the future directions of quantum circuit optimization. Full article

This paper introduces the integration of the Cobb–Douglas (CD) utility model with quantum computation using the Clairaut-type differential formula. We propose a novel economic–physical model employing envelope theory to establish a link with quantum entanglement, defining emergent probabilities in the optimal utility function for two goods within a given expenditure limit. The study explores the interaction between the CD model and quantum computation, emphasizing system entropy and Clairaut differential equations in understanding utility’s optimal envelopes. Algorithms using the 2D Clairaut equation are introduced for the quantum formulation of the CD function, showcasing representation in quantum circuits for one and two qubits. Our findings, validated through IBM-Q simulations, align with the predictions, demonstrating the robustness of our approach. This methodology articulates the utility–budget relationship through envelope representation, where normalized intercepts signify probabilities. The precision of our results, especially in modeling quantum entanglement, surpasses that of IBM-Q simulations, which require extensive iterations for similar accuracy. Full article

In cryptography, techniques and tools developed in the subfield of linear cryptanalysis have previously successfully been used to allow attackers to break many sophisticated cryptographic ciphers. Since these linear cryptanalytic techniques require exploitable linear approximations to relate the input and output of vectorial Boolean functions, e.g., the plaintext, ciphertext, and key of the cryptographic function, finding these approximations is essential. For this purpose, the Correlation Extraction Algorithm (CEA), which leverages the emerging field of quantum computing, appears promising. However, there has been no comprehensive analysis of the CEA regarding finding an exploitable linear approximation for linear cryptanalysis. In this paper, we conduct a thorough theoretical analysis of the CEA. We aim to investigate its potential in finding a linear approximation with prescribed statistical characteristics. To support our theoretical work, we also present the results of a small empirical study based on a computer simulation. The analysis in this paper shows that an approach that uses the CEA to find exploitable linear approximations has an asymptotic advantage, reducing a linear factor to a logarithmic one in terms of time complexity, and an exponential advantage in terms of space complexity compared to a classical approach that uses the fast Walsh transform. Furthermore, we show that in specific scenarios, CEA can exponentially reduce the search space for exploitable linear approximations in terms of the number of input bits of the cipher. Neglecting the unresolved issue of efficiently checking the property of linear approximations measured by the CEA, our results indicate that the CEA can support the linear cryptanalysis of vectorial Boolean functions with relatively few (e.g., $n\le 32$) output bits. Full article

I propose a possible way to introduce the effect of temperature (defined through the virial theorem) into Einstein’s theory of general relativity. This requires the computation of a path integral on a ten-dimensional flat space in a four-dimensional spacetime lattice. Standard path integral Monte Carlo methods can be used to compute this. Full article

The electronic and optical properties of a mesoscopic heterostructure of a two-dimensional quantum ring composed of Gallium Arsenide (GaAs) semiconductors are investigated. Using the confinement potential proposed by Tan and Inkson to describe the system under analysis, we conducted a numerical study of the photoionization cross-section for a 2D quantum ring with and without rotation effects. The interior of the quantum ring is traversed by an Aharonov–Bohm (AB) flux. Our research aims to investigate how this mesoscopic structure’s electronic and optical properties respond to variations in the following parameters: average radius, AB flux, angular velocity, and incident photon energy. Under these conditions, we establish that optical transitions occur from the ground state to the next excited state in the conduction subband, following a specific selection rule. One of the fundamental objectives of this study is to analyze how these rules can influence the general properties of two-dimensional quantum rings. To clarify the influence of rotation on the photoionization process within the system, we offer findings that illuminate the effects of the pertinent physical parameters within the described model. We emphasize that, although this is a review, it provides critical commentary, analysis, and new perspectives on existing research. Some results presented in this paper can be compared with those in the literature; however, new physical parameters and quantum ring configurations are used. Full article

Potential applications of quantum dots in the nanotechnology industry make these systems an important field of study in various areas of physics. In particular, thermodynamics has a significant role in technological innovations. With this in mind, we studied some thermodynamic properties in quantum dots, such as entropy and heat capacity, as a function of the magnetic field over a wide range of temperatures. The density of states plays an important role in our analyses. At low temperatures, the variation in the magnetic field induces an oscillatory behavior in all thermodynamic properties. The depopulation of subbands is the trigger for the appearance of the oscillations. Full article

Quantum computing stands at the precipice of technological revolution, promising unprecedented computational capabilities to tackle some of humanity’s most complex problems. The field is highly collaborative and recent developments such as superconducting qubits with increased scaling, reduced error rates, and improved cryogenic infrastructure, trapped-ion qubits with high-fidelity gates and reduced control hardware complexity, and photonic qubits with exploring room-temperature quantum computing are some of the key developments pushing the field closer to demonstrating real-world applications. However, the path to realizing this promise is fraught with significant obstacles across several key platforms, including sensitivity to errors, decoherence, scalability, and the need for new materials and technologies. Through an exploration of various quantum systems, this paper highlights both the potential and the challenges of quantum computing and discusses the essential role of middleware, quantum hardware development, and the strategic investments required to propel the field forward. With a focus on overcoming technical hurdles through innovation and interdisciplinary research, this review underscores the transformative impact quantum computing could have across diverse sectors. Full article

The current developments in the theory of quantum static triplet correlations and their associated structures (real r-space and Fourier k-space) in monatomic fluids are reviewed. The main framework utilized is Feynman’s path integral formalism (PI), and the issues addressed cover quantum diffraction effects and zero-spin bosonic exchange. The structures are associated with the external weak fields that reveal their nature, and due attention is paid to the underlying pair-level structures. Without the pair, level one cannot fully grasp the triplet extensions in the hierarchical ladder of structures, as both the pair and the triplet structures are essential ingredients in the triplet response functions. Three general classes of PI structures do arise: centroid, total continuous linear response, and instantaneous. Use of functional differentiation techniques is widely made, and, as a bonus, this leads to the identification of an exact extension of the “classical isomorphism” when the centroid structures are considered. In this connection, the direct correlation functions, as borrowed from classical statistical mechanics, play a key role (either exact or approximate) in the corresponding quantum applications. Additionally, as an auxiliary framework, the traditional closure schemes for triplets are also discussed, owing to their potential usefulness for rationalizing PI triplet results. To illustrate some basic concepts, new numerical calculations (path integral Monte Carlo PIMC and closures) are reported. They are focused on the purely diffraction regime and deal with supercritical helium-3 and the quantum hard-sphere fluid. Full article

Grover’s search algorithm (GSA) offers quadratic speedup in searching unstructured databases but suffers from exponential circuit depth complexity. Here, we present two quantum circuits called HX and Ry layers for the searching problem. Remarkably, both circuits maintain a fixed circuit depth of two and one, respectively, irrespective of the number of qubits used. When the target element’s position index is known, we prove that either circuit, combined with a single multi-controlled X gate, effectively amplifies the target element’s probability to over 0.99 for any qubit number greater than seven. To search unknown databases, we use the depth-1 Ry layer as the ansatz in the Variational Quantum Search (VQS), whose efficacy is validated through numerical experiments on databases with up to 26 qubits. The VQS with the Ry layer exhibits an exponential advantage, in circuit depth, over the GSA for databases of up to 26 qubits. Full article

As wireless networks advance toward the Sixth Generation (6G), which will support highly heterogeneous scenarios and massive data traffic, conventional computing methods may struggle to meet the immense processing demands in a resource-efficient manner. This paper explores the potential of quantum computing (QC) to address these challenges, specifically by enhancing the efficiency of Maximum-Likelihood detection in Multiple-Input Multiple-Output (MIMO) Non-Orthogonal Multiple Access (NOMA) communication systems, an essential technology anticipated for 6G. The study proposes the use of the Quantum Approximate Optimization Algorithm (QAOA), a variational quantum algorithm known for providing quantum advantages in certain combinatorial optimization problems. While current quantum systems are not yet capable of managing millions of physical qubits or performing high-fidelity, long gate sequences, the results indicate that QAOA is a promising QC approach for radio signal processing tasks. This research provides valuable insights into the potential transformative impact of QC on future wireless networks. This sets the stage for discussions on practical implementation challenges, such as constrained problem sizes and sensitivity to noise, and opens pathways for future research aimed at fully harnessing the potential of QC for 6G and beyond. Full article

A novel solution to the quantum measurement problem is presented by using a new asymmetric equation that is complementary to the Schrödinger equation. Solved for the hydrogen atom, the new equation describes the temporal and spatial evolution of the wavefunction, and the latter is used to calculate the radial probability density for different measurements. The obtained results show that Born’s position measurement postulates naturally emerge from the theory and its first principles. Experimental verification of the theory and its predictions are also proposed. Full article

While the development of quantum computers promises a myriad of advantages over their classical counterparts, care must be taken when designing algorithms that substitute a classical technique with a potentially advantageous quantum method. The probabilistic nature of many quantum algorithms may result in new behavior that could negatively impact the performance of the larger algorithm. The purpose of this work is to preserve the advantages of applying quantum search methods for generalized pattern search algorithms (GPSs) without violating the convergence criteria. It is well known that quantum search methods are able to reduce the expected number of oracle calls needed for finding the solution to a search problem from $O\left(N\right)$ to $O\left(\sqrt{N}\right)$ However, the number of oracle calls needed to determine that no solution exists with certainty is exceedingly high and potentially infinite. In the case of GPS, this is a significant problem since overlooking a solution during an iteration will violate a needed assumption for convergence. Here, we overcome this problem by introducing the quantum improved point search (QIPS), a classical–quantum hybrid variant of the quantum search algorithm QSearch. QIPS retains the $O\left(\sqrt{N}\right)$ oracle query complexity of QSearch when a solution exists. However, it is able to determine when no solution exists, with certainty, using only $O\left(N\right)$ oracle calls. Full article

In this article, I start with a general presentation of the ideas behind sigma models and higher gauge theories and introduce the possibility of a higher entanglement structure. Using a higher categorial interpretation of entanglement involving gauge theories and $\sigma$-models instead of qubits, one recovers T-duality as a form of ancilla aided entanglement generation. This opens the way towards new dualities in gauge theories and $\sigma$-models produced by means of analogies with quantum circuits of various types. Full article

Recent developments in the quantization of general relativity theory provide a new perspective on matter and even the whole universe. Already, in 1922, Eddington suggested that a future quantum gravity theory had to be linked to Planck length. This is today the main view among many working with quantum gravity. Recently, it has been demonstrated how Planck length, the Planck time, can be extracted from gravity observations with no knowledge of G, ℏ, or even c. Rooted in this, both general relativity theory and multiple other gravity theories can be quantized and linked to the Planck scale. A revelation from this is that matter seems to be ticking at the reduced Compton frequency, where each tick can be seen as one bit, and one bit corresponds to a Planck mass event. This new speculative way of looking at gravity can also potentially tell us considerably about what quantum gravity computers are and what they potentially can do. We will conjecture that that all quantum gravity and quantum gravity computers are directly linked to the Planck scale and the Compton frequency in matter, something we will discuss in this paper. Quantum gravity computers, we will see, in many ways, are nature’s own designed computers with enormous capacity to 3D “print” real time. So, somewhat speculatively, we suggest we live inside a gigantic quantum gravity computer known as the Hubble sphere, and we even are quantum gravity computers. The observable universe is based on this model, basically a quantum gravity computer that calculates approximately ${10}^{104}$ bits per second (bps). Full article

This paper examines no-hidden-variables theorems in quantum mechanics from the point of view of statistical mechanics. It presents a general analysis of the measurement process in the Boltzmannian framework that leads to a characterization of (in)compatible measurements and reproduces several features of quantum probabilities often described as “non-classical”. The analysis is applied to versions of the Kochen–Specker and Bell theorems to shed more light on their implications. It is shown how, once the measurement device and the active role of the measurement process are taken into account, contextuality appears as a natural feature of random variables. This corroborates Bell’s criticism that no-go results of the Kochen–Specker type are based on gratuitous assumptions. In contrast, Bell-type theorems are much more profound, but should be understood as nonlocality theorems rather than no-hidden-variables theorems. Finally, the paper addresses misunderstandings and misleading terminology that have confused the debate about hidden variables in quantum mechanics. Full article

Quantum annealers conventionally use forward annealing to generate heuristic solutions. Reverse annealing can potentially generate better solutions but necessitates an appropriate initial state. Ways to find such states are generally unknown or highly problem dependent, offer limited success, and severely restrict the scope of reverse annealing. We use a general method that improves the overall solution quality and quantity by feeding reverse annealing with low-quality solutions obtained from forward annealing. An experimental demonstration of solving the graph coloring problem using the D-Wave quantum annealers shows that our method is able to convert invalid solutions obtained from forward annealing to at least one valid solution obtained after assisted reverse annealing for $57\%$ of 459 random Erdos–Rényi graphs. Our method significantly outperforms random initial states, obtains more unique solutions on average, and widens the applicability of reverse annealing. Although the average number of valid solutions obtained drops exponentially with the problem size, a scaling analysis for the graph coloring problem shows that our method effectively extends the computational reach of conventional forward annealing using reverse annealing. Full article