Quantum Model Research Articles

Chirality reversal quantum phase transition in flat-band topological insulators.

Quantum anomalous Hall effect generates dissipationless chiral conductive edge states in materials with large spin-orbit coupling and strong, intrinsic, or proximity magnetization. The topological indexes of the energy bands are robust to smooth variations in the relevant parameters. Topological quantum phase transitions between states with different Chern numbers require the closing of the bulk bandgap: C=1→C=1/2 corresponds to the transition from a topological insulator to gapless in k=0 state- quantum anomalous semimetal. Within the Bernevig-Hughes-Zhang model of 2D topological quantum well, this study identifies another type of topological phase transition induced by a magnetic field. The transition C=±1→C=∓1occurs when the monotonic Zeeman field reaches the threshold value and thus triggers the reversal of edge modes chirality. The calculated threshold depends on the width of the conduction and valence bands and is more experimentally achievable the flatter the bands. The effect of the topological phase transition ∆C=2 can be observed experimentally as a jump in magnetoresistance.&#xD.

A many-body quantum model is proposed as the mechanism responsible for accelerating rates of heat uptake by oceans as anthropogenic heat inputs rise

Abstract A recent many-body quantum approach to thermal radiation (1) reveals that the energy capacitance of heated water is about twice its heat capacitance, due to energy stored as local hybrid pairs of photons coupled resonantly to local matter excitations, with pair density weighted by mass density. Energy exchange between photons and localised dipole excitations inside water at steady temperature T, occurs at sites where a hybridisation potential within the Hamiltonian couples local oscillation modes to “free” photon modes. Photon modes in both directions are phase retarded at exit sides of a hybrid site. Optically sharp variations with frequency in the index of refraction n(f) and photon density of states follow. Exit spectral intensities at equilibrium temperature T carry quantum information on the energy density of matter excitations coupled to photons, while occupied hybrid sites are the source of all “free” photons and internal spectral intensities. The matter excitations coupled locally to photons are distinct from those that define specific heat, but in water both arise from molecular oscillations. The energy capacitance CEX(T) of hybrid pairs depends on mass density and is independent of heat capacitance CHT(T) which sets temperature T. CEX(T) is sensitive to T and doubles as a capacitance of energy and of “quantum information”. Expressions for CEX(T) are derived from first principles and applied to water. The density of occupied hybrids is amplified near surfaces by photons reflected off the surface, which create new hybrid pairs, but not extra heat. Energy capacitance CEX(T)+CHT(T) sets dT(t)/dt prior to a new equilibrium state emerging, after input heating rate dQ/dt is switched. Rising atmospheric intensities then raise T, dQ/dt, CEX(T) and CHT(T). The times available to cool overnight are fixed, so that a rising capacitance, adds to energy stored at an accelerating rate. 


Quantum correlations and parameter estimation for two superconducting qubits interacting with a quantized field

In the present manuscript, we introduce a quantum system of two superconducting qubits (S–Qs) interacting with a quantized field under the influence of the Kerr nonlinear medium and Ising interaction. We formulate the Hamiltonian of the quantum model and determine the density operator of whole quantum system as well as quantum subsystems. We examine the dynamics of the quantumness measures for subsequent times including the S–Qs entanglement, S–Qs-field entanglement and quantum Fisher information in relation to the system parameters. Finally, we display the connection among the measures of quantumness during the time evolution.

Probability Updating in the Classical and the Quantum Model

Imagine a Bayesian decision agent who is keen to invest only in technologies or businesses that are conductive to achieving a sustainable economic future. Being initially keen to invest in a certain technology, subsequently two pieces of new information are received that both individually reduce the agent’s inclination to make that investment. In such a situation, it would be natural to assume that the simultaneous consideration of both pieces of information should further reduce the agent’s initial enthusiasm; after all the Bayesian method has been called “ nothing but common sense reduced to calculation.” Somewhat surprisingly, making general statements like this about the double conditional probability requires substantial additional assumptions in classical Bayesian probability theory. We investigate four schemes of assumptions that allow ‘reasonable’ conclusions about the double conditional probability. We compare this with two schemes for the quantum probability model where the double conditional results from sequential updating through projections.

Correlated tunneling in high-order above threshold dissociative ionization of H2

Comprehension of photon-triggered molecular processes is essential in the study of various important topics in physics, chemistry, and biology. Here we propose a correlated tunneling picture to understand the dissociative ionization process of molecules in intense laser fields based on a quantum model developed in the framework of many-body S-matrix theory including nuclear vibrational motion. In this quantum correlation picture, the single ionization of H2 and the subsequent electron-ion recollision-induced dissociation are considered as an entangled correlated process. It enables us to attribute the interference pattern in the joint-energy spectra to combined effects of single-slit diffraction and multi-slit interference of correlated electron-nuclear wave packets in the time domain. Our work opens a new avenue to understanding molecular dissociative ionization processes in external fields.

Competing excitation quenching and charge exchange in ultracold Li-Ba+ collisions

Abstract Hybrid atom-ion systems are a rich and powerful platform for studying chemical reactions, as they feature both excellent control over the electronic state preparation and readout as well as a versatile tunability over the scattering energy, ranging from the few-partial wave regime to the quantum regime. In this work, we make use of these excellent control knobs, and present a joint experimental and theoretical study of the collisions of a single 138Ba+ ion prepared in the 5d 2D3/2,5/2 metastable states with a ground state 6Li gas near quantum degeneracy. We show that in contrast to previously reported atom-ion mixtures, several non-radiative processes, including charge exchange, excitation exchange and quenching, compete with each other due to the inherent complexity of the ion-atom molecular structure. We present a full quantum model based on high-level electronic structure calculations involving spin-orbit couplings. Results are in excellent agreement with observations, highlighting the strong coupling between the internal angular momenta and the mechanical rotation of the colliding pair, which is relevant in any other hybrid system composed of an alkali-metal atom and an alkaline-earth ion.

Simulating adiabatic quantum computing with parameterized quantum circuits

Abstract Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term devices, a number of hybrid approaches have been pursued in which a parameterized quantum circuit prepares and measures quantum states and a classical optimization algorithm minimizes an objective function that encompasses the solution to the problem of interest. In this work, we propose a different approach starting by analyzing how a small perturbation of a Hamiltonian affects the parameters that minimize the energy within a family of parameterized quantum states. We derive a set of equations that allow us to compute the new minimum by solving a constrained linear system of equations that is obtained from measuring a series of observables on the unperturbed system. We then propose a discrete version of adiabatic quantum computing that can be implemented in a near-term device while at the same time is insensitive to the initialization of the parameters and to other limitations hindered in the optimization part of variational quantum algorithms. We compare our proposed algorithm with the variational quantum eigensolver on two classical optimization problems, namely MaxCut and number partitioning, and on a quantum-spin configuration problem, the transverse-field ising chain model, and confirm that our approach demonstrates superior performance.

Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement

Calderbank-Shor-Steane (CSS) codes are a class of quantum error correction codes that contains the toric code and fracton models. A procedure called foliation defines a cluster state for a given CSS code. We use the CSS chain complex and its tensor product with other chain complexes to describe the topological structure in the foliated cluster state, and argue that it has a symmetry-protected topological order protected by generalized global symmetries supported on cycles in the foliated CSS chain complex. We demonstrate the so-called anomaly inflow between CSS codes and corresponding foliated cluster states by explicitly showing the equality of the gauge transformations of the bulk and boundary partition functions defined as functionals of defect world-volumes. We show that the bulk and boundary defects are related via measurement of the bulk system. Further, we provide a procedure to obtain statistical models associated with general CSS codes via the foliated cluster state, and derive a generalization of the Kramers-Wannier-Wegner duality for such statistical models with insertion of twist defects. We also study the measurement-assisted gauging method with cluster-state entanglers for CSS/fracton models based on recent proposals in the literature, and demonstrate a non-invertible fusion of duality operators. Using the cluster-state entanglers, we construct the so-called strange correlator for general CSS/fracton models. Finally, we introduce a new family of subsystem-symmetric quantum models each of which is self-dual under the generalized Kramers-Wannier-Wegner duality transformation, which becomes a non-invertible symmetry.

An inductive bias from quantum mechanics: learning order effects with non-commuting measurements

There are two major approaches to building good machine learning algorithms: feeding lots of data into large models or picking a model class with an “inductive bias” that suits the structure of the data. When taking the second approach as a starting point to design quantum algorithms for machine learning, it is important to understand how mathematical structures in quantum mechanics can lead to useful inductive biases in quantum models. In this work, we bring a collection of theoretical evidence from the quantum cognition literature to the field of quantum machine learning to investigate how non-commutativity of quantum observables can help to learn data with “order effects,” such as the changes in human answering patterns when swapping the order of questions in a survey. We design a multi-task learning setting in which a generative quantum model consisting of sequential learnable measurements can be adapted to a given task — or question order — by changing the order of observables, and we provide artificial datasets inspired by human psychology to carry out our investigation. Our first experimental simulations show that in some cases the quantum model learns more non-commutativity as the amount of order effect present in the data is increased and that the quantum model can learn to generate better samples for unseen question orders when trained on others — both signs that the model architecture suits the task.

Model and Energy Bounds for a Two-Dimensional System of Electrons Localized in Concentric Rings.

We study a two-dimensional system of interacting electrons confined in equidistant planar circular rings. The electrons are considered spinless and each of them is localized in one ring. While confined to such ring orbits, each electron interacts with the remaining ones by means of a standard Coulomb interaction potential. The classical version of this two-dimensional quantum model can be viewed as representing a system of electrons orbiting planar equidistant concentric rings where the kinetic energy may be discarded when one is searching for the lowest possible energy. Within this framework, the lowest possible energy of the system is the one that minimizes the total Coulomb interaction energy. This is the equilibrium energy that is numerically determined with high accuracy by using the simulated annealing method. This process allows us to obtain both the equilibrium energy and position configuration for different system sizes. The adopted semi-classical approach allows us to provide reliable approximations for the quantum ground state energy of the corresponding quantum system. The model considered in this work represents an interesting problem for studies of low-dimensional systems, with echoes that resonate with developments in nanoscience and nanomaterials.

Quantum lozenge tiling and entanglement phase transition

While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding ground state in higher dimensions, entangled in more than one direction, has been an open problem. Here we construct a 2D frustration-free Hamiltonian with maximal violation of the area law. We do so by building a quantum model of random surfaces with color degree of freedom that can be viewed as a collection of colored Dyck paths. The Hamiltonian may be viewed as a 2D generalization of the Fredkin spin chain. It relates all the colored random surface configurations subject to a Dirichlet boundary condition and hard wall constraint from below to one another, and the ground state is therefore a superposition of all such classical states and non-degenerate. Its entanglement entropy between subsystems undergoes a quantum phase transition as the deformation parameter is tuned. The area- and volume-law phases are similar to the one-dimensional model, while the critical point scales with the linear size of the system L as Llog⁡L. Further it is conjectured that similar models with entanglement phase transitions can be built in higher dimensions with even softer area law violations at the critical point.

Quantum Variational Autoencoders for Predictive Analytics in High Frequency Trading Enhancing Market Anomaly Detection

High-frequency trading (HFT) markets, characterized by high and frequent price fluctuations, necessitate the use of anomaly detection mechanisms to monitor the market and ensure the efficacy of the trading system. This paper aims to discuss the possibility of improving predictive analytics in HFT using quantum computing with the help of the Quantum Variational Autoencoder (QL-VAE). As a result, we propose a new direction for further research on quantum VAEs in HFT that involves their direct comparison with classical VAEs. The application of quantum models for mastering the intensive data flow of HFT is conditioned by the advantages of quantum computation in comparison to classical ones, which are more suitable for handling multidimensional data arrangements and intricate topologies. Our detailed study methodology involved examining various aspects of HFT data, such as order book features and stock price characteristics. We normalized all the data and reduced some of its dimensions. We established quantum VAEs using Pennylane, and configured the classical VAEs using TensorFlow. When it comes to market anomalies, the results of the comparative analysis showed higher accuracy, recall, and F1 rate in quantum VAEs compared to classical models when it comes to the analysis of market anomalies. Therefore, the quantum model's ability to handle high-dimensional data makes it a better fit for HFT than classical methods. These studies suggest that quantum VAEs could significantly improve anomaly detection in the financial market.

Optimizing $c$-sum BKW and Faster Quantum Variant for LWE

The Learning with Errors (LWE) problem has become one of the most prominent candidates of post-quantum cryptography, offering promising potential to meet the challenge of quantum computing. From a theoretical perspective, optimizing algorithms to solve LWE is a vital task for the analysis of this cryptographic primitive. In this paper, we propose a fine-grained time/memory trade-off method to analyze c-sum BKW variants for LWE in both classical and quantum models, then offer new complexity bounds for multiple BKW variants determined by modulus q, dimension k, error rate alpha, and stripe size b. Through our analysis, optimal parameters can be efficiently found for different settings, and the minimized complexities are lower than existing results. Furthermore, we enhance the performance of c-sum BKW in the quantum computing model by adopting the quantum Meet-in-the-Middle technique as c-sum solver instead of the naive c-sum technique. Our complexity trade-off formula also applies to the quantum version of BKW, and optimizes the theoretical quantum time and memory costs, which are exponentially lower than existing quantum c-sum BKW variants.

Towards quantum gravity with neural networks: solving quantum Hamilton constraints of 3d Euclidean gravity in the weak coupling limit

Abstract The aim of the present work is to demonstrate the applicability of machine learning techniques and in particular neural network quantum states in the context of loop quantum gravity, albeit for a simplified theory. We consider 3-dimensional Euclidean gravity in a gauge theoretical formulation in a certain weak coupling limit due to Smolin, and show that the gauge group becomes Abelian, resulting in U(1)3 BF- theory. The theory is quantised using loop quantum gravity methods. The kinematical degrees of freedom are truncated, on account of computational feasibility, by fixing a graph and deforming the algebra of the holonomies to impose a cutoff on the charge vectors. This leads to a quantum theory related to Uq(1)3 BF-theory. The effect of imposing the cutoff on the charges is examined. We also implement the quantum volume operator of 3d loop quantum gravity. Most importantly we compare two constraints for the quantum model obtained: a master constraint enforcing curvature and Gauß constraint, as well as a combination of a quantum Hamilton constraint constructed using Thiemann’s strategy and the Gauβ master constraint. The two constraints are solved using the neural network quantum state ansatz, demonstrating its ability to explore models which are out of reach for exact numerical methods. The solutions spaces are quantitatively compared and although the forms of the constraints are radically different, the solutions turn out to have a surprisingly large overlap. We also investigate the behavior of the quantum volume in solutions to the constraints.

Correction to: Two resonant quantum electrodynamics models of quantum measuring systems

Correction to: Two resonant quantum electrodynamics models of quantum measuring systems

Thirring universe model

In recent years, there has been a significant amount of research focused on Thirring instantons. This study aims to employ the Thirring quantum model as a theoretical Universe model to gain a more profound understanding of the beginning of the Universe. For this, we propose to analyze the entropy of the quantum states of zero energy Thirring instanton solutions and the transition to other quantum states. Our findings by also using Lyapunov exponents and the cyclic attractors as comparative nonlinear methods show that there is no entropy corresponding to instanton solutions with zero energy and that the sudden increase in entropy indicates the formation of the Universe. We evaluate the implications of this study in terms of the standard Universe model. Thus we anticipate that these results have the potential to contribute significantly to our understanding of the origin of the Universe and highlight the role of chaos and complexity in its evolution.

Quantum visual feature encoding revisited

Although quantum machine learning has been introduced for a while, its applications in computer vision are still limited. This paper, therefore, revisits the quantum visual encoding strategies, the initial step in quantum machine learning. Investigating the root cause, we uncover that the existing quantum encoding design fails to ensure information preservation of the visual features after the encoding process, thus complicating the learning process of the quantum machine learning models. In particular, the problem, termed the “Quantum Information Gap” (QIG), leads to an information gap between classical and corresponding quantum features. We provide theoretical proof and practical examples with visualization for that found and underscore the significance of QIG, as it directly impacts the performance of quantum machine learning algorithms. To tackle this challenge, we introduce a simple but efficient new loss function named Quantum Information Preserving (QIP) to minimize this gap, resulting in enhanced performance of quantum machine learning algorithms. Extensive experiments validate the effectiveness of our approach, showcasing superior performance compared to current methodologies and consistently achieving state-of-the-art results in quantum modeling.

Quantization, dequantization, and distinguished states

Abstract Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and — using techniques of geometric quantization — construct the quantum algebra and equip it with a distinguished state. We compare our result with the construction due to Sorkin — which starts from the same input data — and show that our distinguished state coincides with the Sorkin-Johnson state. Sorkin’s construction was originally applied to the free scalar field over a causal set (locally finite, partially ordered set). Our perspective suggests a natural generalization to less linear examples, such as an interacting field.

Quantum inspired kernel matrices: Exploring symmetry in machine learning

Quantum machine learning, an emerging field at the intersection of quantum computing and classical machine learning, has shown great promise in enhancing computational capabilities beyond classical bounds. A key element in this area of research is the utilization of Quantum Kernel Estimators, traditionally grounded in the symmetries of SU(2) groups associated with qubits. This study extends the conceptual framework of Quantum Kernel Estimators to incorporate a broader spectrum of symmetry groups. By harnessing the various structures of Lie groups, we develop novel quantum-inspired feature maps that offer more flexible and potentially powerful ways to encode and compress classical data into quantum states. We present a comprehensive theoretical introduction for this approach, followed by a methodology that integrates the developed feature maps into quantum-inspired kernel classifiers. Our results, derived from a series of computational experiments across various datasets, demonstrate the efficacy of this approach in comparison to traditional quantum and classical machine learning models. The findings not only underline the versatility of Lie-group theory in potentially enhancing quantum machine learning algorithms but also open new avenues for exploring complex symmetries in quantum information processing. This research bridges a gap between the study of symmetries and machine learning, paving the way for more sophisticated quantum algorithms capable of tackling complex, high-dimensional data in ways previously unattainable.

Prerelaxation in quantum, classical, and quantum-classical two-impurity models

We numerically study the relaxation dynamics of impurity-host systems, focusing on the presence of long-lived metastable states in the nonequilibrium dynamics after an initial excitation of the impurities. In generic systems, an excited impurity coupled to a large bath at zero temperature is expected to relax and approach its ground state over time. However, certain exceptional cases exhibit metastability, where the system remains in an excited state on timescales largely exceeding the typical relaxation time. We study this phenomenon for three prototypical impurity models: a tight-binding quantum model of independent spinless fermions on a lattice with two stub impurities, a classical-spin Heisenberg model with two weakly coupled classical impurity spins, and a tight-binding quantum model of independent electrons with two classical impurity spins. Through numerical integration of the fundamental equations of motion, we find that all three models exhibit similar qualitative behavior: complete relaxation for nearest-neighbor impurities and incomplete or strongly delayed relaxation for next-nearest-neighbor impurities. The underlying mechanisms leading to this behavior differ between models and include impurity-induced bound states, emergent approximately conserved local observables, and exact cancellation of local and nonlocal dissipation effects. Published by the American Physical Society 2024