Related papers: An Exact Bitwise Reversible Integrator
It is widely known that the recursion operator is a very important component of integrability. It allows one to describe in a compact form both hierarchies of the generalized symmetries and infinite series of the local conservation laws. In…
We apply a flexible numerical integrator to the simulation of adiabatic quantum computation with nonlinear paths. We find that a nonlinear path may significantly improve the performance of adiabatic algorithms versus the conventional…
Rational exponential integrators (REXI) are a class of numerical methods that are well suited for the time integration of linear partial differential equations with imaginary eigenvalues. Since these methods can be parallelized in time (in…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We present new almost time-reversible integrators for solution of planetary systems consisting of "planets" and a dominant mass ("star"). The algorithms can be considered adaptive generalizations of the Wisdom--Holman method, in which all…
Reversible computing basically means computation with less or not at all electrical power. Since the standard binary gates are not usually reversible we use the Fredkin gate in order to achieve reversibility. An algorithm for designing…
We propose a novel exact algorithm for the transportation problem, one of the paradigmatic network optimization problems. The algorithm, denoted Iterated Inside Out, requires in input a basic feasible solution and is composed by two main…
We revisit adaptive time stepping, one of the classical topics of numerical analysis and computational engineering. While widely used in application and subject of many theoretical works, a complete understanding is still missing. Apart…
Many applications in computational physics that use numerical integrators based on splitting and composition can benefit from the development of optimized algorithms and from choosing the best ordering of terms. The cost in programming and…
Recently, a generalization of the standard optical multiport was proposed [Phys. Rev. A 93, 043845 (2016)]. These directionally unbiased multiports allow photons to reverse direction and exit backwards from the input port, providing a…
In this paper, we introduce a new iterative method which we call one step back approach: the main idea is to anticipate the consequence of the iterative computation per coordinate and to optimize on the choice of the sequence of the…
It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here…
End-to-end optimization, which simultaneously optimizes optics and algorithms, has emerged as a powerful data-driven method for computational imaging system design. This method achieves joint optimization through backpropagation by…
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…
Modern computer vision algorithms have brought significant advancement to 3D geometry reconstruction. However, illumination and material reconstruction remain less studied, with current approaches assuming very simplified models for…
We introduce a quantum extension of dynamic programming, a fundamental computational method that efficiently solves recursive problems using memory. Our innovation lies in showing how to coherently generate recursion step unitaries by using…
We survey results of a quarter century of work on computation by reversible general-purpose computers (in this setting Turing machines), and general reversible simulation of irreversible computations, with respect to energy-, time- and…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
We establish a direct link between the time-reversal technique and the so-called adjoint method for imaging. Using this relationship, we derive new solution strategies for an inverse problem which arises in telecommunication. These…
Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…