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Quantum Phase Estimation is a crucial component of several front-running quantum algorithms. Improving the efficiency and accuracy of QPE is currently a very active field of research. In this work, we present a hybrid quantum-classical…
The Liouville equation for the q-deformed 1-D classical harmonic oscillator is derived for two definitions of q-deformation. This derivation is achieved by using two different representations for the q-deformed Hamiltonian of this…
A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which goes beyond the common secular…
In the case of quantum systems interacting with multiple environments, the time-evolution of the reduced density matrix is described by the Liouvillian. For a variety of physical observables, the long-time limit or steady state solution is…
Modern cyberattacks are increasingly complex, posing significant challenges to classical machine learning methods, particularly when labeled data is limited and feature interactions are highly non-linear. In this study we investigates the…
We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of L\'{e}vy-stable type and nonetheless admit a Boltzmannian (thermal) equilibrium to arise in the large time…
As industrial models and designs grow increasingly complex, the demand for optimal control of large-scale dynamical systems has significantly increased. However, traditional methods for optimal control incur significant overhead as problem…
We prove quantum-classical correspondence for bound conservative classically chaotic Hamiltonian systems. In particular, quantum Liouville spectral projection operators and spectral densities, and hence classical dynamics, are shown to…
We propose in this paper a gradient-type dynamical system to solve the problem of maximizing quantum observables for finite dimensional closed quantum ensembles governed by the controlled Liouville-von Neumann equation. The asymptotic…
We propose a nonperturbative quantum dissipation theory, in term of hierarchical quantum master equation. It may be used with a great degree of confidence to various dynamics systems in condensed phases. The theoretical development is…
Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…
A non-Markovian master equation for a molecule interacting with a heat bath is obtained using the cumulant expansion method. The equation is applied to the problem of molecular wave packet relaxtional dynamics. An exact solution is derived…
While real quantum devices have been increasingly used to conduct research focused on achieving quantum advantage or quantum utility in recent years, executing deep quantum circuits or performing quantum machine learning with large-scale…
We present a novel quantum-classical approach to non-adiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the…
The extent to which quantum computers can simulate physical phenomena and solve the partial differential equations (PDEs) that govern them remains a central open question. In this work, one of the most fundamental PDEs is addressed: the…
We develop an approach for understanding the dynamics of open quantum systems by analyzing individual quantum trajectories in the eigenbasis of the Liouvillian superoperator. From trajectory-eigenstate overlaps, we construct a…
An equation of motion for open quantum systems incorporating memory effects and initial correlations with the environment is presented in terms of an effective Liouville operator that solely acts on states of the system. The environment can…
Track finding can be considered as a complex optimization problem initially introduced in particle physics involving the reconstruction of particle trajectories. A track is typically composed of several consecutive segments (track segments)…
This work is a benchmark study for quantum-classical computing method with a real-world optimization problem from industry. The problem involves scheduling and balancing jobs on different machines, with a non-linear objective function. We…
We apply the large-deviation method to study trajectories in dissipative quantum systems. We show that in the long time limit the statistics of quantum jumps can be understood from thermodynamic arguments by exploiting the analogy between…