Related papers: Implementing the Koopman-von Neumann approach on c…
We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have been useful in…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
How to introduce thermodynamics to quantum mechanics ? Among from numerous possibilities of solving this task, the simple choice is here: The conventional von Neumann equation deals with a density operator whose probability weights are time…
Accurately modeling quantum dissipative dynamics remains challenging due to environmental complexity and non-Markovian memory effects. Although machine learning provides a promising alternative to conventional simulation techniques, most…
In this paper, we introduce a quantum extension of classical DNN, QDNN. The QDNN consisting of quantum structured layers can uniformly approximate any continuous function and has more representation power than the classical DNN. It still…
Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schr\"odinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately…
We propose a new method for solving quantum mechanical problems, which combines the flexibility of Gaussian basis set methods with the numerical accuracy of the Fourier method. The method is based on the incorporation of periodic boundary…
State-of-the-art cosmological simulations on classical computers are limited by time, energy, and memory usage. Quantum computers can perform some calculations exponentially faster than classical computers, using exponentially less energy…
Quantum computing, leveraging principles of quantum mechanics, represents a transformative approach in computational methodologies, offering significant enhancements over traditional classical systems. This study tackles the complex and…
Quantum computational chemistry holds great promise for simulating molecular systems more efficiently than classical methods by leveraging quantum bits to represent molecular wavefunctions. However, current implementations face significant…
Non-equilibrium thermodynamics of the driven resonant level model is studied using numerical simulations based on the driven Liouville von-Neumann formalism. The approach is first validated against recently obtained analytical results for…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
Quantum mechanics has introduced a new theoretical framework for the study of molecules, enabling the prediction of properties and dynamics through the solution of the Schr\"odinger equation applied to these systems. However, solving this…
The photonic framework offers clues leading to a possible update of the foundations of quantum mechanics yet preserving its mathematical grounds. Reconsideration of quantum theoretic measurement theory warrants removal of ideological…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…