Related papers: Symplectic perspective to quantum computing for Ha…
We investigate the performance of various methods of symplectic integration, which are based on two part splitting of the integration operator, for the numerical integration of multidimensional Hamiltonian systems. We implement these…
We develop a Hamiltonian theory for 2D soliton equations. In particular, we identify the spaces of doubly periodic operators on which a full hierarchy of commuting flows can be introduced, and show that these flows are Hamiltonian with…
On general symplectic manifolds we describe a correspondence between symplectic transformations and their phase functions. On the quantum level, this is a correspondence between unitary operators and phase functions of the…
The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace…
We implement and investigate the numerical properties of a new family of integrators connecting both variants of the symplectic Euler schemes, and including an alternative to the classical symplectic mid-point scheme, with some additional…
Quantum computing is gaining increased attention as a potential way to speed up simulations of physical systems, and it is also of interest to apply it to simulations of classical plasmas. However, quantum information science is…
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…
We prove that the recently developed semiexplicit symplectic integrators for non-separable Hamiltonian systems preserve any linear and quadratic invariants possessed by the Hamiltonian systems. This is in addition to being symmetric and…
We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…
In this work we propose a new numerical approach to distinguish between regular and chaotic orbits in Hamiltonian systems, based on the simultaneous integration of both the orbit and the deviation vectors using a symplectic scheme, hereby…
Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps by predicting the…
We have developed an application and implemented parallel algorithms in order to provide a computational framework suitable for massively parallel supercomputers to study the unitary dynamics of quantum systems. We use renowned parallel…
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for…
A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…
Symplectic topology has become a thriving area of research in mathematics and physics since Gromov's discovery in 1985 of a surprising property of canonical transformations (and hence of hamiltonian flows),"the principle of the symplectic…
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…
Quantum chemistry and materials science are among the most promising areas for demonstrating algorithmic quantum advantage and quantum utility due to their inherent quantum mechanical nature. Still, large-scale simulations of quantum…