Entropy corrected geometric Brownian motion.

The geometric Brownian motion (GBM) is widely used for modeling stochastic processes, particularly in finance. However, its solutions are constrained by the assumption that the underlying distribution of returns follows a log-normal distribution. This assumption limits the predictive power of GBM, especially in capturing the complexities of real-world data, where deviations from log-normality are common.

Time Resolved Quantum Tomography in Molecular Spectroscopy by the Maximal Entropy Approach.

Attosecond science offers unprecedented precision in probing the initial moments of chemical reactions, revealing the dynamics of molecular electrons that shape reaction pathways. A fundamental question emerges: what role, if any, do quantum coherences between molecular electron states play in photochemical reactions? Answering this question necessitates quantum tomography─the determination of the electronic density matrix from experimental data, where the off-diagonal elements represent these coherences. The Maximal Entropy (MaxEnt) based Quantum State Tomography (QST) approach offers unique advantages in studying molecular dynamics, particularly with partial tomographic data.

Simulation of Chemical Reactions on a Quantum Computer.

Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities. However, the intricate nature of quantum interactions poses challenges, necessitating the use of advanced mathematical models and computational approaches to tackle the inherent complexities.

Walking with the Atoms in a Chemical Bond: A Perspective Using Quantum Phase Transition.

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.

Physics-Inspired Quantum Simulation of Resonating Valence Bond States─A Prototypical Template for a Spin-Liquid Ground State.

Spin liquids─an emergent, exotic collective phase of matter─have garnered enormous attention in recent years. While experimentally many prospective candidates have been proposed and realized, theoretically modeling real materials that display such behavior may pose serious challenges due to the inherently high correlation content of such phases. Over the last few decades, the second-quantum revolution has been the harbinger of a novel computational paradigm capable of initiating a foundational evolution in computational physics.

Mapping Molecular Hamiltonians into Hamiltonians of Modular cQED Processors.

We introduce a general method based on the operators of the Dyson-Masleev transformation to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. Furthermore, we introduce a modular approach to programming a cQED processor with components corresponding to the mapping Hamiltonian. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson (FMO) complex and the spin-boson model of charge transfer.

Quantum Machine Learning Predicting ADME-Tox Properties in Drug Discovery.

In the drug discovery paradigm, the evaluation of absorption, distribution, metabolism, and excretion (ADME) and toxicity properties of new chemical entities is one of the most critical issues, which is a time-consuming process, immensely expensive, and poses formidable challenges in pharmaceutical R&D. In recent years, emerging technologies like artificial intelligence (AI), big data, and cloud technologies have garnered great attention to predict the ADME and toxicity of molecules. Currently, the blend of quantum computation and machine learning has attracted considerable attention in almost every field ranging from chemistry to biomedicine and several engineering disciplines as well.

Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations.

We present a quantum algorithm based on the generalized quantum master equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system-bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator.

Toward perturbation theory methods on a quantum computer.

Perturbation theory, used in a wide range of fields, is a powerful tool for approximate solutions to complex problems, starting from the exact solution of a related, simpler problem. Advances in quantum computing, especially over the past several years, provide opportunities for alternatives to classical methods. Here, we present a general quantum circuit estimating both the energy and eigenstates corrections that is far superior to the classical version when estimating second-order energy corrections.

Analogy between Boltzmann Machines and Feynman Path Integrals.

Machine learning has had a significant impact on multiple areas of science, technology, health, and computer and information sciences. Through the advent of quantum computing, quantum machine learning has developed as a new and important avenue for the study of complex learning problems. Yet there is substantial debate and uncertainty in regard to the foundations of machine learning.

Characterizing quantum circuits with qubit functional configurations.

We develop a systematic framework for characterizing all quantum circuits with qubit functional configurations. The qubit functional configuration is a mathematical structure that can classify the properties and behaviors of quantum circuits collectively. Major benefits of classifying quantum circuits in this way include: 1.

Hamiltonian Learning from Time Dynamics Using Variational Algorithms.

The Hamiltonian of a quantum system governs the dynamics of the system via the Schrodinger equation. In this paper, the Hamiltonian is reconstructed in the Pauli basis using measurables on random states forming a time series data set. The time propagation is implemented through Trotterization and optimized variationally with gradients computed on the quantum circuit.

Quantum Simulation of the Radical Pair Dynamics of the Avian Compass.

The simulation of open quantum dynamics on quantum circuits has attracted wide interests recently with a variety of quantum algorithms developed and demonstrated. Among these, one particular design of a unitary-dilation-based quantum algorithm is capable of simulating general and complex physical systems. In this paper, we apply this quantum algorithm to simulating the dynamics of the radical pair mechanism in the avian compass.

Magnetic phases of spatially modulated spin-1 chains in Rydberg excitons: Classical and quantum simulations.

In this work, we study the magnetic phases of a spatially modulated chain of spin-1 Rydberg excitons. Using the Density Matrix Renormalization Group (DMRG) technique, we study various magnetic and topologically nontrivial phases using both single-particle properties, such as local magnetization and quantum entropy, and many-body ones, such as pair-wise Néel and long-range string correlations. In particular, we investigate the emergence and robustness of the Haldane phase, a topological phase of anti-ferromagnetic spin-1 chains.

Variational approach to quantum state tomography based on maximal entropy formalism.

Quantum state tomography is an integral part of quantum computation and offers the starting point for the validation of various quantum devices. One of the central tasks in the field of state tomography is to reconstruct, with high fidelity, the quantum states of a quantum system. From an experiment on a real quantum device, one can obtain the mean measurement values of different operators.

Realization of Heisenberg models of spin systems with polar molecules in pendular states.

We show that ultra-cold polar diatomic or linear molecules, oriented in an external electric field and mutually coupled by dipole-dipole interactions, can be used to realize the exact Heisenberg XYZ, XXZ and XY models without invoking any approximation. The two lowest lying excited pendular states coupled by microwave or radio-frequency fields are used to encode the pseudo-spin. We map out the general features of the models by evaluating the models constants as functions of the molecular dipole moment, rotational constant, strength and direction of the external field as well as the distance between molecules.

Statistical Properties of Bit Strings Sampled from Sycamore Random Quantum Circuits.

Quantum supremacy has been recently reported for random circuit sampling on the Sycamore processor with 53 qubits. Here, we analyze the statistical properties of bit strings sampled from random quantum circuits. In contrast to classical random bit strings, bit strings sampled from Sycamore random circuits give rise to heat maps with stripe patterns at specific qubits, have more bit 1 than 0, and do not pass the NIST random number tests.

Quantum machine learning for chemistry and physics.

Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes.

Geometrical picture of the electron-electron correlation at the large- limit.

In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrödinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation.

A quantum encryption design featuring confusion, diffusion, and mode of operation.

Quantum cryptography-the application of quantum information processing and quantum computing techniques to cryptography has been extensively investigated. Two major directions of quantum cryptography are quantum key distribution (QKD) and quantum encryption, with the former focusing on secure key distribution and the latter focusing on encryption using quantum algorithms. In contrast to the success of the QKD, the development of quantum encryption algorithms is limited to designs of mostly one-time pads (OTP) that are unsuitable for most communication needs.

Constructive Quantum Interference in Photochemical Reactions.

Interferences emerge when multiple pathways coexist together, leading toward the same result. Here, we report a theoretical study for a reaction scheme that leads to constructive quantum interference in a photoassociation (PA) reaction of a Rb Bose-Einstein condensate where the reactant spin state is prepared in a coherent superposition of multiple bare spin states. This is achieved by changing the reactive scattering channel in the PA reaction.

Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials.

Quantum machine-learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However, the discussion in all these recipes focuses specifically on targeting the ground state.

Prime factorization using quantum variational imaginary time evolution.

The road to computing on quantum devices has been accelerated by the promises that come from using Shor's algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and lack of robust error correction schemes. Here we explore a promising, alternative method for prime factorization that uses well-established techniques from variational imaginary time evolution.