Related papers: High order schemes for solving partial differentia…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
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…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
The solution of large systems of nonlinear differential equations is needed for many applications in science and engineering. In this study, we present three main improvements to existing quantum algorithms based on the Carleman…
We provide an explicit recursive divide and conquer approach for simulating quantum dynamics and derive a discrete first quantized non-relativistic QED Hamiltonian based on the many-particle Pauli Fierz Hamiltonian. We apply this recursive…
We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
Dissipation and irreversibility are central to most physical processes, yet they lead to non-unitary dynamics that are challenging to realise on quantum processors. High-order operator splitting is an attractive approach for simulating…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
In this paper, we propose a tensor type of discretization and optimization process for solving high dimensional partial differential equations. First, we design the tensor type of trial function for the high dimensional partial differential…
In quantum computing, the efficient optimization of Pauli string decompositions is a crucial aspect for the compilation of quantum circuits for many applications, such as chemistry simulations and quantum machine learning. In this paper, we…
We propose a general strategy to discretize the Dyson series without applying direct numerical quadrature to high-dimensional integrals, and extend this framework to open quantum systems. The resulting discretization can also be interpreted…
Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this…
Many numerical techniques for the description of quantum systems that are coupled to a continuous bath require the discretization of the latter. To this end, a wealth of methods has been developed in the literature, which we classify as (i)…
Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via…
To efficiently implement many-qubit gates for use in quantum simulations on quantum computers we develop and present methods reexpressing exp[-i (H_1 + H_2 + ...) \Delta t] as a product of factors exp[-i H_1 \Delta t], exp[-i H_2 \Delta t],…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
The first order by time partial differential equations are used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and others. In this paper we propose the new numerical method to solve a…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis…