Related papers: Quantum algorithms for general nonlinear dynamics …
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
In this paper, we propose efficient quantum algorithms for solving nonlinear stochastic differential equations (SDE) via the associated Fokker-Planck equation (FPE). We discretize the FPE in space and time using two well-known numerical…
Digital quantum simulation uses the capabilities of quantum computers to determine the dynamics of quantum systems, which are beyond the computability of modern classical computers. A notoriously challenging task in this field is the…
Quantum simulation of non-Markovian open quantum dynamics is essential but challenging for standard quantum computers due to their non-Hermitian nature, leading to non-unitary evolution, and the limitations of available quantum resources.…
This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…
Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…
The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model-predictive control, where rapid and reliable…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
The rapid development of machine learning and quantum computing has placed quantum machine learning at the forefront of research. However, existing quantum machine learning algorithms based on quantum variational algorithms face challenges…
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness…
While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of…
Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…
It has been recently realized that dissipative processes can be harnessed and exploited to the end of coherent quantum control and information processing. In this spirit we consider strongly dissipative quantum systems admitting a…
Digital quantum computers provide a computational framework for solving the Schr\"{o}dinger equation for a variety of many-particle systems. Quantum computing algorithms for the quantum simulation of these systems have recently witnessed…
Recent advancements of intermediate-scale quantum processors have triggered tremendous interest in the exploration of practical quantum advantage. The simulation of fluid dynamics, a highly challenging problem in classical physics but vital…
We present a quantum computing algorithm for fluid flows based on the Carleman-linearization of the Lattice Boltzmann (LB) method. First, we demonstrate the convergence of the classical Carleman procedure at moderate Reynolds numbers,…