Related papers: Improved precision scaling for simulating coupled …
Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman-von Neumann formulation of classical mechanics. The Koopman-von Neumann formulation implies that the…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
The quantum-classical Liouville equation describes the dynamics of a quantum subsystem coupled to a classical environment. It has been simulated using various methods, notably, surface-hopping schemes. A representation of this equation in…
The Koopman-von Neumann (KvN) formalism recasts classical mechanics in a Hilbert space framework using complex wavefunctions and linear operators, akin to quantum mechanics. Instead of evolving probability densities in phase space (as in…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…
We propose a highly efficient mixed quantum-classical molecular dynamics scheme based on a solution of the quantum-classical Liouville equation (QCLE). By casting the equations of motion for the quantum subsystem and classical bath degrees…
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this…
We present a quantum algorithm for simulating the classical dynamics of $2^n$ coupled oscillators (e.g., $2^n$ masses coupled by springs). Our approach leverages a mapping between the Schr\"odinger equation and Newton's equation for…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…
A novel quantum algorithm for solving the Boltzmann-Maxwell equations of the 6D collisionless plasma is proposed. The equation describes the kinetic behavior of plasma particles in electromagnetic fields and is known for the classical…
We present an improved field-theoretic approach to the grand-canonical potential suitable for linear scaling molecular dynamics simulations using forces from self-consistent electronic structure calculations. It is based on an exact…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
Quantum computing has the potential to reduce the computational cost required for quantum dynamics simulations. However, existing quantum algorithms for coupled electron-nuclear dynamics simulation either require fault-tolerant devices, or…
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…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
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 simulate the center of mass motion of cold atoms in a standing, amplitude modulated, laser field as an example of a system that has a classical mixed phase-space. We show a simple model to explain the momentum distribution of the atoms…
A common approach to minimizing the cost of quantum computations is by transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations,…
We derive a "classical-quantum" approximation scheme for a broad class of bipartite quantum systems from fully quantum dynamics. In this approximation, one subsystem evolves via classical equations of motion with quantum corrections, and…