Related papers: Quantum Simulation for Quantum Dynamics with Artif…
Hamiltonian simulation is a central task in quantum computing, with wide-ranging applications in quantum chemistry, condensed matter physics, and combinatorial optimization. A fundamental challenge lies in approximating the unitary…
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably…
We develop a quantum algorithm for linear algebraic equations $ A\bb{x} = \bb{b} $ from the perspective of Schr\"odingerization-form problems, which are characterized by a system of linear convection equations in one higher dimension. When…
In quantum mechanics, the time evolution of particles is given by the Schr\"odinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not…
An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This new method is based on a method we developed previously, but with an essential change in solving the Schrodinger's equation.…
We solve the time-dependent Schr\"odinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under…
To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational…
This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron…
Understanding the collective quantum dynamics of nonequilibrium many-body systems is an outstanding challenge in quantum science. In particular, dynamics driven by quantum fluctuations are important for the formation of exotic quantum…
Computational fluid dynamics (CFD) is a cornerstone of classical scientific computing, and there is growing interest in whether quantum computers can accelerate such simulations. To date, the existing proposals for fault-tolerant quantum…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
Simulations of chemical dynamics are a powerful means for understanding chemistry. However, classical computers struggle to simulate many chemical processes, especially non-adiabatic ones, where the Born-Oppenheimer approximation breaks…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
A classical computer simulating Schrodinger dynamics of a quantum system requires resources which scale exponentially with the size of the system, and is regarded as inefficient for such purposes. However, a quantum computer made up of a…
The theoretical investigation of non-adiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the…
It is not possible, using standard lattice techniques in Euclidean space, to calculate the complete fermionic spectrum of a quantum field theory. Algorithms running on quantum computers have the potential to access the theory with real-time…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
The advection-diffusion equation is simulated on a superconducting quantum computer via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive…
We propose quantum algorithms for complex-valued nonlinear partial differential equations in the strongly nonlinear regime, where the dynamics is governed by vortex cores, phase singularities, and nonlinear vortex interactions. Examples…
The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric…