Related papers: Quantum Simulation of Nonlinear Dynamical Systems …

Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…

Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…

Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed…

We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in…

We present a variational algorithm for fault tolerant quantum computing to solve a system of linear equations which directly maximises the parameters of the target fidelity. This so-called measurement test algorithm can be applied to any…

A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference…

We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…

Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of…

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…

A pure frequency domain method for the computation of periodic solutions of nonlinear ordinary differential equations (ODEs) is proposed in this study. The method is particularly suitable for the analysis of systems that feature distinct…

This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential…

We propose a quantum algorithm to simulate the dynamics in quantum chemistry problems. It is based on adding fresh qubits at each Trotter step, which enables a simpler implementation of the dynamics in the extended system. After each step,…

Previous years researchers began to simulate open quantum system, taking into account the interaction between system and the environment. One approach to deal with this problem is to use the density matrix within the Liouville-von-Neumann…

We propose a framework for computing the structure and dynamics for second-quantized many-nucleon Hamiltonians on quantum computers. We develop an oracle-based Hamiltonian input model that computes the many-nucleon states and nonzero…

We propose and analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal target state, applicable to a wide class of analog quantum simulators without advanced sophisticated…

Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…

For noisy intermediate-scale quantum (NISQ) devices only a moderate number of qubits with a limited coherence is available thus enabling only shallow circuits and a few time evolution steps in the currently performed quantum computations.…

We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…

We develop randomized quantum algorithms to simulate quantum collision models, also known as repeated interaction schemes, which provide a rich framework to model various open-system dynamics. The underlying technique involves composing…

The efficient validation of quantum devices is critical for emerging technological applications. In a wide class of use-cases the precise engineering of a Hamiltonian is required both for the implementation of gate-based quantum information…