Related papers: The first-order Trotter decomposition in the dynam…
Known as no fast-forwarding theorem in quantum computing, the simulation time for the Hamiltonian evolution needs to be $O(\|H\| t)$ in the worst case, which essentially states that one can not go across the multiple scales as the…
The main topic of this present thesis is the study of the asymptotic behaviour of sequences modulo 1. In particular, by using ergodic and dynamical methods, a new insight to problems concerning the asymptotic behaviour of multidimensional…
Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The former reflects the suppression of the interference between the components of the current state while the latter reflects that within the initial…
A complex but important challenge in understanding quantum mechanical phenomena is the simulation of quantum many-body dynamics. Although quantum computers offer significant potential to accelerate these simulations, their practical…
The main subject of this work is the study of the problem of the Trojan orbits from a perturbative Hamiltonian perspective. We face this problem by introducing first a novel Hamiltonian formulation, exploiting the well-differentiated…
Stochastic methods offer an effective way to suppress coherent errors in quantum simulation. In particular, the randomized compilation protocol may reduce circuit depth by randomly sampling Hamiltonian terms rather than following the…
Dynamical phase transitions (DPTs) arise from qualitative changes in the long-time behavior of stochastic trajectories, often observed in systems with kinetic constraints or driven out of equilibrium. Here we demonstrate that first-order…
Many quantum many-body wavefunctions, such as Jastrow-Slater, tensor network, and neural quantum states, are studied with the variational Monte Carlo technique, where stochastic optimization is usually performed to obtain a faithful…
According to the adiabatic theorem of quantum mechanics, a system initially in the ground state of a Hamiltonian remains in the ground state if one slowly changes the Hamiltonian. This can be used in principle to solve hard problems on…
In this paper, we present a generic approach of a dynamical data-driven model order reduction technique for three-dimensional fluid-structure interaction problems. A low-order continuous linear differential system is identified from…
Fault-tolerant quantum computing is a promising tool for simulating molecules and materials, but frequently-considered applications require substantial resources, and the gap between hardware capabilities and requirements remains…
We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the Planar Circular Restricted Three-Body Problem (PCRTBP), by introducing a number of key new ideas in the…
The reliability and proper function of data-driven applications hinge on the data's continued conformance to the applications' initial design. When data deviates from this initial profile, system behavior becomes unpredictable. Data…
We present a comprehensive analysis of the emerging order and chaos and enduring symmetries, accompanying a generic (high-barrier) first-order quantum phase transition (QPT). The interacting boson model Hamiltonian employed, describes a QPT…
We present an explicit quantum circuit construction for Hamiltonian simulation of a first-order velocity--stress formulation of the three-dimensional elastic wave equation in homogeneous isotropic media. Previous studies have shown how…
A simple statistical model for the effects of dephasing on electron transport in one-dimensional quantum systems is introduced, which allows to adjust the degree of phase and momentum randomization independently. Hence, the model is able to…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
A short-time dynamic approach to weak first order phase transitions is proposed. Taking the 2-dimensional Potts models as examples, from short-time behaviour of non-equilibrium relaxational processes starting from high temperature and zero…
Convergence of path integral simulations requires a substantial number of beads when quantum effects are significant. Traditional Trotter scaling approaches estimate the continuum limit through extrapolation, however they are restricted to…
Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation…