Related papers: Targeted Fibonacci Exponentiation
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…
We propose a distributed algorithm based on Alternating Direction Method of Multipliers (ADMM) to minimize the sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
We propose a conversion scheme that turns regret minimizing algorithms into fixed point iterations, with convergence guarantees following from regret bounds. The resulting iterations can be seen as a grand extension of the classical…
This work presents a novel method for task optimization in industrial plants using quantum-inspired tensor network technology. This method obtains the best possible combination of tasks on a set of machines with directed constraints while…
Fixed-point equations with Lipschitz operators have been studied for more than a century, and are central to problems in mathematical optimization, game theory, economics, and dynamical systems, among others. When the Lipschitz constant of…
One of the most promising applications of near-term quantum computing is the simulation of quantum systems, a classically intractable task. Quantum simulation requires computationally expensive matrix exponentiation; Trotter-Suzuki…
Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of…
We provide a method, based on automata theory, to mechanically prove the correctness of many numeration systems based on Fibonacci numbers. With it, long case-based and induction-based proofs of correctness can be replaced by simply…
Regularized factorization is proposed to simulate time evolution for quantum lattice systems. Transcending the Trotter decomposition, the resulting compact structure of the propagator indicates a high-order Baker-Campbell-Hausdorff series.…
Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…
In this paper we consider the sequence of Kakutani's $\alpha$-refinements corresponding to the inverse of golden ratio (which we call Kakutani-Fibonacci sequence of partitions) and associate to it an ergodic interval exchange (which we call…
For a positive integer sequence $\boldsymbol{a}=(a_1, \dots, a_{N+1})$, Sylvester's denumerant $E(\boldsymbol{a}; t)$ counts the number of nonnegative integer solutions to $\sum_{i=1}^{N+1} a_i x_i = t$ for a nonnegative integer $t$. It has…
Immense interest in quantum computing has prompted development of electronic structure methods that are suitable for quantum hardware. However, the slow pace at which quantum hardware progresses, forces researchers to implement their ideas…
Nature rarely reveals her secrets bluntly, yet in the Fibonacci sequence she grants us a glimpse of her quiet architecture of growth, harmony, and recursive stability \citep{Koshy2001Fibonacci, Livio2002GoldenRatio}. From spiral galaxies to…
In this paper we have considered a finite unitary matrix group with exact elements being unknown and only approximate elements available. Such a group becomes inconsistent with its own multiplication table. We found simple correction…
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point…
A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations $|Ax|^2=y$. The algorithms are developed by exploiting the inherent low rank structure of the problem based on the…
We develop a fixed-point iterative algorithm that computes the matrix projection with respect to the Bures distance on the set of positive definite matrices that are invariant under some symmetry. We prove that the fixed-point iteration…
We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…