Related papers: Simple Ways to improve Discrete Time Evolution
Here we provide a scheme of transforming the one-axis twisting Hamiltonian into the two-axis twisting one based on high order Trotter-Suzuki Approximation. Compared with the paper [Y. C. Liu et al., Phys. Rev. Lett. 107, 013601 (2011)], our…
In this work a general approach to compute a compressed representation of the exponential $\exp(h)$ of a high-dimensional function $h$ is presented. Such exponential functions play an important role in several problems in Uncertainty…
The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
We describe a new method to compute general cubature formulae. The problem is initially transformed into the computation of truncated Hankel operators with flat extensions. We then analyse the algebraic properties associated to flat…
A fourth-order multi-exponential scheme is proposed for the Zakharov-Shabat system. The scheme represents a product of 13 exponential operators. The construction of the scheme is based on a fourth-order three-exponential scheme, which…
Decomposing unitary operations into native gates is an essential step for implementing quantum algorithms. For qubit-based devices, where native gates are typically single- and two-qubit operations, a range of decomposition techniques have…
Recently double-bracket quantum algorithms have been proposed as a way to compile circuits for approximating eigenstates. Physically, they consist of appropriately composing evolutions under an input Hamiltonian together with diagonal…
This paper is devoted to the construction of exponential integrators of first and second order for the time discretization of constrained parabolic systems. For this extend, we combine well-known exponential integrators for unconstrained…
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…
The time integration of semilinear parabolic problems by exponential methods of different kinds is considered. A new algorithm for the implementation of these methods is proposed. The algorithm evaluates the operators required by the…
In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+D of…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
There exists the well known approximate expression describing the large time behaviour of matrix elements of the evolution operator in quantum theory: <U(t)>=exp(at)+... This expression plays the crucial role in considerations of problems…
Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical…
We provide three improvements to the product formula implementation of the ground state energy estimation algorithm via Trotter-Suzuki decomposition. These consist of smaller circuit templates for each Hamiltonian term, parallelization of…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…
This paper is a short introduction to numerical methods using the double exponential (DE) transformation, such as tanh-sinh quadrature and DE-Sinc approximation. The DE-based methods for numerical computation have been developed intensively…