Search Results (88)

We start presenting an overview on recent applications of linear polymers and networks in condensed matter physics, chemistry and biology by briefly discussing selected papers (published within 2022–2024) in some detail. They are organized into three main subsections: polymers in physics (further subdivided into simulations of coarse-grained models and structural properties of materials), chemistry (quantum mechanical calculations, environmental issues and rheological properties of viscoelastic composites) and biology (macromolecules, proteins and biomedical applications). The core of the work is devoted to a review of theoretical aspects of linear polymers, with emphasis on self-avoiding walk (SAW) chains, in regular lattices and in both deterministic and random fractal structures. Values of critical exponents describing the structure of SAWs in different environments are updated whenever available. The case of random fractal structures is modeled by percolation clusters at criticality, and the issue of multifractality, which is typical of these complex systems, is illustrated. Applications of these models are suggested, and references to known results in the literature are provided. A detailed discussion of the reptation method and its many interesting applications are provided. The problem of protein folding and protein evolution are also considered, and the key issues and open questions are highlighted. We include an experimental section on polymers which introduces the most relevant aspects of linear polymers relevant to this work. The last two sections are dedicated to applications, one in materials science, such as fractal features of plasma-treated polymeric materials surfaces and the growth of polymer thin films, and a second one in biology, by considering among others long linear polymers, such as DNA, confined within a finite domain. Full article

We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics are recorded using unitary dynamics interspersed stroboscopically by measurements, which are implemented on IBM quantum computers with a midcircuit readout option. Unlike classical hitting times, the statistical aspect of the problem depends on the way we construct the measured path, an effect that we quantify experimentally. First, we experimentally verify the theoretical prediction that the mean return time to a target state is quantized, with abrupt discontinuities found for specific sampling times and other control parameters, which has a well-known topological interpretation. Second, depending on the initial state, system parameters, and measurement protocol, the detection probability can be less than one or even zero, which is related to dark-state physics. Both return-time quantization and the appearance of the dark states are related to degeneracies in the eigenvalues of the unitary time evolution operator. We conclude that, for the IBM quantum computer under study, the first hitting times of monitored quantum walks are resilient to noise. However, a finite number of measurements leads to broadening effects, which modify the topological quantization and chiral effects of the asymptotic theory with an infinite number of measurements. Full article

In this work, the dynamics of a quantum walker on glued trees is revisited to understand the influence of the architecture of the graph on the efficiency of the transfer between the two roots. Instead of considering regular binary trees, we focus our attention on leafier structures where each parent node could give rise to a larger number of children. Through extensive numerical simulations, we uncover a significant dependence of the transfer on the underlying graph architecture, particularly influenced by the branching rate (M) relative to the root degree (N). Our study reveals that the behavior of the walker is isomorphic to that of a particle moving on a finite-size chain. This chain exhibits defects that originate in the specific nature of both the roots and the leaves. Therefore, the energy spectrum of the chain showcases rich features, which lead to diverse regimes for the quantum-state transfer. Notably, the formation of quasi-degenerate localized states due to significant disparities between M and N triggers a localization process on the roots. Through analytical development, we demonstrate that these states play a crucial role in facilitating almost perfect quantum beats between the roots, thereby enhancing the transfer efficiency. Our findings offer valuable insights into the mechanisms governing quantum-state transfer on trees, with potential applications for the transfer of quantum information. Full article

The double random phase encoding (DRPE) image encryption method has garnered significant attention in color image processing and optical encryption thanks to its R, G, and B parallel encryption. However, DRPE-based color image encryption faces two challenges. Firstly, it disregards the correlation of R, G, and B, compromising the encrypted image’s robustness. Secondly, DRPE schemes relying on Discrete Fourier Transform (DFT) and Discrete Fractional Fourier Transform (DFRFT) are vulnerable to linear attacks, such as Known Plaintext Attack (KPA) and Chosen Plaintext Attack (CPA). Quantum walk is a powerful tool for modern cryptography, offering robust resistance to classical and quantum attacks. Therefore, this study presents an optical color image encryption algorithm that combines two-dimensional quantum walking (TDQW) with 24-bit plane permutation, dubbed OCT. This approach employs pseudo-random numbers generated by TDQW for phase modulation in DRPE and scrambles the encrypted image’s real and imaginary parts using the generalized Arnold transform. The 24-bit plane permutation helps reduce the R, G, and B correlation, while the generalized Arnold transform bolsters DRPE’s resistance to linear attacks. By incorporating TDQW, the key space is significantly expanded. The experimental results validate the effectiveness and security of the proposed method. Full article

Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation due to its discrete nature. Current implementations, however, are usually characterized by quantum circuits of large size and depth, which leads to a higher computational cost and severely limits the number of time steps that can be reliably implemented on current quantum computers. In this work, we propose an efficient and scalable quantum circuit implementing the DTQW on the $2^n$-cycle based on the diagonalization of the conditional shift operator. For t time steps of the DTQW, the proposed circuit requires only $O(n^2+nt)$ two-qubit gates compared to the $O\left(n^{2}t\right)$ of the current most efficient implementation based on quantum Fourier transforms. We test the proposed circuit on an IBM quantum device for a Hadamard DTQW on the 4-cycle and 8-cycle characterized by periodic dynamics and by recurrent generation of maximally entangled single-particle states. Experimental results are meaningful well beyond the regime of few time steps, paving the way for reliable implementation and use on quantum computers. Full article

Phase transitions happen at critical values of the controlling parameters, such as the critical temperature in classical phase transitions, and system critical parameters in the quantum case. However, true criticality happens only at the thermodynamic limit, when the number of particles goes to infinity with constant density. To perform the calculations for the critical parameters, a finite-size scaling approach was developed to extrapolate information from a finite system to the thermodynamic limit. With the advancement in the experimental and theoretical work in the field of ultra-cold systems, particularly trapping and controlling single atomic and molecular systems, one can ask: do finite systems exhibit quantum phase transition? To address this question, finite-size scaling for finite systems was developed to calculate the quantum critical parameters. The recent observation of a quantum phase transition in a single trapped ¹⁷¹ Yb⁺ ion indicates the possibility of quantum phase transitions in finite systems. This perspective focuses on examining chemical processes at ultra-cold temperatures, as quantum phase transitions—particularly the formation and dissociation of chemical bonds—are the basic processes for understanding the whole of chemistry. Full article

We claim that quantum collapse, as per the Copenhagen interpretation of quantum mechanics, follows naturally from the energetics of measurement. We argue that a realistic device generates an interaction energy that drives a random walk in Hilbert space and generates the probabilistic interpretation of Born. Full article

For many years, chaotic maps have been widely used in the design of various algorithms in cryptographic systems. In this paper, a new model (compound chaotic system) of quantum random walks controlled by a hyper-chaotic map is constructed and a novel scheme for constructing a dynamic S-Box based on the new model is proposed. Through aperiodic evaluation and statistical complexity measurement, it is shown that the compound chaotic system has features such as complex structure and stronger randomness than classical chaotic systems. Based on the chaotic sequence generated by the composite system, we design a dynamic S-Box generation mechanism. The mechanism can quickly generate high-security S-Boxes. Then, an example of randomly generating S-Boxes is given alongside an analytical evaluation of S-Box standard performance criteria such as bijection, boomerang uniformity, bit independence, nonlinearity, linear approximate probability, strict avalanche effect, differential uniformity, the and generalized majority logic criterion. The evaluation results confirm that the performance of the S-Box is excellent. Thus, the proposed dynamic S-Box construction technique can be used to generate cryptographically strong substitution-boxes in practical information security systems. Full article

We describe particles in a potential by a special diffusion process, the maximal entropy random walk (MERW) on a lattice. Since MERW originates in a variational problem, it shares the linear algebra of Hilbert spaces with quantum mechanics. The Born rule appears from measurements between equilibrium states in the past and the same equilibrium states in the future. Introducing potentials by the observation that time, in a gravitational field running in different heights with a different speed, MERW respects the rule that all trajectories of the same duration are counted with equal probability. In this way, MERW allows us to derive the Schrödinger equation for a particle in a potential and the Darwin term of the nonrelativistic expansion of the Dirac equation. Finally, we discuss why quantum mechanics cannot be simply a result of MERW, but, due to the many analogies, MERW may pave the way for further understanding. Full article

A Multilayer network is a potent platform that paves the way for the study of the interactions among entities in various networks with multiple types of relationships. This study explores the dynamics of discrete-time quantum walks on a multilayer network. We derive a recurrence formula for the coefficients of the wave function of a quantum walker on an undirected graph with a finite number of nodes. By extending this formula to include extra layers, we develop a simulation model to describe the time evolution of the quantum walker on a multilayer network. The time-averaged probability and the return probability of the quantum walker are studied with Fourier, and Grover walks on multilayer networks. Furthermore, we analyze the impact of decoherence on quantum transport, shedding light on how environmental interactions may impact the behavior of quantum walkers on multilayer network structures. Full article

We suggest a new technique for developing noisy tree data structures. We call it a “walking tree”. As applications of the technique we present a noisy Self-Balanced Binary Search Tree (we use a Red–Black tree as an implementation) and a noisy segment tree. The asymptotic complexity of the main operations for the tree data structures does not change compared to the case without noise. We apply the data structures in quantum algorithms for several problems on strings like the string-sorting problem and auto-complete problem. For both problems, we obtain quantum speed-up. Moreover, for the string-sorting problem, we show a quantum lower bound. Full article

Quantum sensors are expected to offer significant advantages in magnetic- and gravity-aided navigation. However, these techniques depend on the local environmental conditions and require an alternative solution to ensure high position accuracy on shorter timescales. This paper explores the potential of a hypothetical quantum Inertial Measurement Unit (IMU) with much better performance than classical IMUs when used for dead reckoning position estimation preceded by an alignment period to achieve a relative inertial navigation solution. We show that significantly reduced noise levels (velocity random walk) for the accelerometer and/or gyroscope cannot be automatically exploited. In practice, axis misalignment and initial state errors in orientation limit performance. Incorrect orientation causes errors in compensating for the gravity vector, having a dominant effect. This research proposes to introduce an alignment period with a reliable velocity sensor, prior to starting the mission relying solely on inertial navigation. The orientation errors can be estimated with numerical optimization, in which we match the dead reckoning estimate to the reference velocity signal. The fact that quantum IMUs have a much more accurate measurement means that these orientation errors could be compensated much more accurately. When mitigating these dominant error sources, there is a significant benefit to using a quantum IMU for inertial navigation. The initial position error growth is significantly smaller than existing systems. Some estimates are given for the necessary quality of the IMUs to benefit from these protocols and offer a similar position solution quality to high-end or military-grade IMUs. In the future, military operations that do not rely on Global Navigation Satellite System (GNSS) for their Positioning, Navigation and Timing (PNT) information may be performed with unprecedented position accuracy when using a quantum IMU complemented with velocity-aided alignment period, thereby increasing the effectiveness and dependability of the operation. Full article

Human soundscape perceptions exist through the perceived environment rather than the physical environment itself and are determined not only by the acoustic environment but also by the visual environment and their interaction. However, these relationships have mainly been established at the individual level, which may impede the efficient delivery of human-oriented considerations in improving the quality of large-scale urban spaces. Using the Chengdu Outer Ring Ecological Zone as an example, this study aims to develop an approach to predict human perceptions in large-scale urban green spaces. The site’s visual attributes, i.e., landscape composition, were calculated using space syntax and the quantum geographic information system (QGIS); its aural attributes, i.e., the sound level, were measured on site using a multi-channel signal analyzer; and its functional attributes, i.e., vitality, were documented through on-site observations and mapping. This was performed whilst obtaining people’s perceived soundscape through sound walks and a questionnaire-based on-site survey. The above environmental information was collected at micro-scale measurement spots selected within the site and then used together to formulate a model for predicting people’s soundscape perceptions in the whole site. The prediction results suggested that people’s perceived soundscape satisfaction increased as the distance from the ring road increased, and it gradually reached its highest level in the green spaces stretched outside the ring road. The prediction results of soundscape perception were then visualized using QGIS to develop planning and design implications, along with maps describing the site’s visual, aural, and functional features. Planning and design implications were suggested, including setting green buffers between noise sources and vulnerable areas; identifying and preserving areas with special visual and acoustic characteristics; employing sound shields around traffic facilities; and using natural landscapes to distract people’s attention from noise and to block their view of the source of noise. This study innovatively predicts individual-scale soundscape perception in large-scale UGSs based on environmental visual, aural, and functional characteristics through cross-level measurements, analyses, and model construction. By introducing a systematic perspective, the outcome of this study makes people’s soundscape perceptions more applicable in the planning and design practices of large-scale urban settings. Full article

This exploratory study investigates a human agent’s evolving judgements of reliability when interacting with an AI system. Two aims drove this investigation: (1) compare the predictive performance of quantum vs. Markov random walk models regarding human reliability judgements of an AI system and (2) identify a neural correlate of the perturbation of a human agent’s judgement of the AI’s reliability. As AI becomes more prevalent, it is important to understand how humans trust these technologies and how trust evolves when interacting with them. A mixed-methods experiment was developed for exploring reliability calibration in human–AI interactions. The behavioural data collected were used as a baseline to assess the predictive performance of the quantum and Markov models. We found the quantum model to better predict the evolving reliability ratings than the Markov model. This may be due to the quantum model being more amenable to represent the sometimes pronounced within-subject variability of reliability ratings. Additionally, a clear event-related potential response was found in the electroencephalographic (EEG) data, which is attributed to the expectations of reliability being perturbed. The identification of a trust-related EEG-based measure opens the door to explore how it could be used to adapt the parameters of the quantum model in real time. Full article

Parkinson’s disease (PD) is a neurological disorder affecting the nerve cells. PD gives rise to various neurological conditions, including gradual reduction in movement speed, tremors, limb stiffness, and alterations in walking patterns. Identifying Parkinson’s disease in its initial phases is crucial to preserving the well-being of those afflicted. However, accurately identifying PD in its early phases is intricate due to the aging population. Therefore, in this paper, we harnessed machine learning-based ensemble methodologies and focused on the premotor stage of PD to create a precise and reliable early-stage PD detection model named PDD-ET. We compiled a tailored, extensive dataset encompassing patient mobility, medication habits, prior medical history, rigidity, gender, and age group. The PDD-ET model amalgamates the outcomes of various ML techniques, resulting in an impressive 97.52% accuracy in early-stage PD detection. Furthermore, the PDD-ET model effectively distinguishes between multiple stages of PD and accurately categorizes the severity levels of patients affected by PD. The evaluation findings demonstrate that the PDD-ET model outperforms the SVR, CNN, Stacked LSTM, LSTM, GRU, Alex Net, [Decision Tree, RF, and SVR], Deep Neural Network, HOG, Quantum ReLU Activator, Improved KNN, Adaptive Boosting, RF, and Deep Learning Model techniques by the approximate margins of 37%, 30%, 20%, 27%, 25%, 18%, 19%, 27%, 25%, 23%, 45%, 40%, 42%, and 16%, respectively. Full article