Related papers: Koopman-von Neumann Approach to Quantum Simulation…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
In loop quantum cosmology the quantum dynamics is well understood. We approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen…
It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schr\"odinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to…
An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon's path-integral expression of the reduced density matrix, is used to…
We discuss the simulation of a complex dynamical system, the so-called quantum sawtooth map model, on a quantum computer. We show that a quantum computer can be used to efficiently extract relevant physical information for this model. It is…
This paper investigates quantum simulation algorithms for the Liouville equation in geometrical optics with partial transmission and reflection at sharp interfaces, based on the Schr\"odingerization method. By means of a warped phase…
Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond…
We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular the quantum walks. Through this strategy, we obtain the quantum wave function from classical…
We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a…
We present a quantum-classical algorithm to study the dynamics of the two-spatial-site Schwinger model on IBM's quantum computers. Using rotational symmetries, total charge, and parity, the number of qubits needed to perform computation is…
In this paper we study the classical Hilbert space introduced by Koopman and von Neumann in their operatorial formulation of classical mechanics. In particular we show that the states of this Hilbert space do not spread, differently than…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
The problem of classical particle in linear potential is studied by using the formalism of Hilbert space and tomographic probability distribution. The Liouville equation for this problem is solved by finding the density matrix satisfying…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
The so called Driven Liouville-von Neumann equation is a dynamical formulation to simulate a voltage bias across a molecular system and to model a time-dependent current in a grand-canonical framework. This approach introduces a damping…
We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in…
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…
We develop an approach to quantum dynamics based on quantum phase space trajectories. The latter are built from a unitary irreducible representation of the symmetry group of the respective classical phase space. We use a quantum action…
Numerical simulation of turbulent fluid dynamics needs to either parameterize turbulence-which introduces large uncertainties-or explicitly resolve the smallest scales-which is prohibitively expensive. Here we provide evidence through…
A general method of quantum-to-classical reduction of quantum dynamics is described. The key aspect of our method is the similarity transformation of the Liouvillian, which provides a new perspective. In conventional studies of quantum…