Related papers: Product Formulas for Exponentials of Commutators
The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for…
Clinical machine learning applications are often plagued with confounders that are clinically irrelevant, but can still artificially boost the predictive performance of the algorithms. Confounding is especially problematic in mobile health…
Several asymptotic expansions and formulas for cubic exponential sums are derived. The expansions are most useful when the cubic coefficient is in a restricted range. This generalizes previous results in the quadratic case and helps to…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
Trotterization in quantum mechanics is an important theoretical concept in handling the exponential of noncommutative operators. In this communication, we give a mathematical formulation of the Trotter Product Formula, and apply it to basic…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
We present a fast algorithm for modular exponentiation when the factorization of the modulus is known. Let $a,n,m$ be positive integers and suppose $m$ factors canonically as $\prod_{i=1}^k p_i^{e_i}$. Choose integer parameters $t_i\in [1,…
Matrix product states provide a natural entanglement basis to represent a quantum register and operate quantum gates on it. This scheme can be materialized to simulate a quantum adiabatic algorithm solving hard instances of a NP-Complete…
Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…
In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the…
We develop operators for construction of proposals in probabilistic programs, which we refer to as inference combinators. Inference combinators define a grammar over importance samplers that compose primitive operations such as application…
In a previous paper, we described a computer program called Qubiter which can decompose an arbitrary unitary matrix into elementary operations of the type used in quantum computation. In this paper, we describe a method of reducing the…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
In designing quantum control, it is generally required to simulate the controlled system evolution with a classical computer. However, computing the time evolution operator can be quite resource-consuming since the total Hamiltonian is…
This work concerns the construction and characterization of product kernels for multivariate approximation from a finite set of discrete samples. To this end, we consider composing different component kernels, each acting on a…
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…
The paper is devoted to the efficient computation of high-order cubature formulas for volume potentials obtained within the framework of approximate approximations. We combine this approach with modern methods of structured tensor product…