Related papers: Notes on nonlinear quantum algorithms
Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…
Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…
How well can quantum computers simulate classical dynamical systems? There is increasing effort in developing quantum algorithms to efficiently simulate dynamics beyond Hamiltonian simulation, but so far exact resource estimates are not…
Fast-forwarding refers to the ability to simulate a system of time $t$ using significantly fewer than $t$ queries or circuit depth. While various Hamiltonian systems are known to circumvent the no fast-forwarding theorem, analogous results…
In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings, or to…
Big Data is characterized by Volume, Velocity, Veracity and Complexity. The interaction between this huge data is complex with an associated free will having dynamic and non linear nature. We reduced big data based on its characteristics,…
In this paper we consider deterministic nonlinear time evolutions satisfying so called convex quasi-linearity condition. Such evolutions preserve the equivalence of ensembles and therefore are free from problems with signaling. We show that…
We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
The simulation of quantum processes is a key goal for the grand programme aiming at grounding quantum technologies as the way to explore complex phenomena that are inaccessible through standard, classical calculators. Some interesting steps…
Fundamental questions in chemistry and physics may never be answered due to the exponential complexity of the underlying quantum phenomena. A desire to overcome this challenge has sparked a new industry of quantum technologies with the…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
In this paper, we consider a non-linear fourth-order evolution equation of Cahn-Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
We derive an explicit expressions for geometric description of state manifold obtained from evolution governed by a three parameter family of Hamiltonians covering most cases related to real interacting two-qubit systems. We discuss types…
We report a family of quantum speed limits (QSLs) that give evolution time lower bounds between an initial and a final state whose separation is described by a certain representation basis dependent norm derived from the weighted…
The real- and imaginary-time evolution of quantum states are powerful tools in physics, chemistry, and beyond, to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. On near-term devices, variational…
For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution…