Related papers: Nonlinear-ancilla aided quantum algorithm for nonl…
Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a…
We present a novel approach to accelerate iterative methods to solve nonlinear Schr\"odinger eigenvalue problems using neural networks. Nonlinear eigenvector problems are fundamental in quantum mechanics and other fields, yet conventional…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
We present a quantum algorithm for simulating open quantum systems coupled to Gaussian environments valid for any configuration and coupling strength. The algorithm is applicable to problems with strongly coupled, or non-Markovian,…
Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear…
We have previously formulated a simple criterion for deducing the intervals of oscillations in the solutions of second-order linear homogeneous differential equations. In this work, we extend analytically the same criterion to the cubic…
We present a mapping between a Schr\"odinger equation with a shifted non-linear potential and the Navier-Stokes equation. Following a generalization of the Madelung transformations, we show that the inclusion of the Bohm quantum potential…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
In this paper, we are concerned with the existence of nonnegative solutions for a nonlinear elliptic system. Our results are obtained by an application of the Arzela--Ascoli theorem.
As a first approximation beyond linearity, the nonlinear Schr\"odinger equation (NLSE) reliably describes a broad class of physical systems. Though numerical solutions of this model are well-established, these methods can be computationally…
A novel algorithm for producing smooth nonlinearities on digital hardware is presented. The non-linearities are inherently quadratic and have both symmetrical and asymmetrical variants. The integer (and fixed point) implementation is highly…
The time-dependent one-dimensional nonlinear Schr\"odinger equation (NLSE) is solved numerically by a hybrid pseudospectral-variational quantum algorithm that connects a pseudospectral step for the Hamiltonian term with a variational step…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
A new non-perturbative method of solution of the nonlinear Heisenberg equations in the finite-dimensional subspace is illustrated. The method, being a counterpart of the traditional Schrodinger picture method, is based on a finite operator…