Related papers: Quantum algorithms to simulate quadratic classical…
The Fokker-Planck equation models rare events across sciences, but its high-dimensional nature challenges classical computers. Quantum algorithms for such non-unitary dynamics often suffer from exponential {decay in} success probability. We…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…
It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum…
We propose Quantum Riemannian Hamiltonian Descent (QRHD), a quantum algorithm for continuous optimization on Riemannian manifolds that extends Quantum Hamiltonian Descent (QHD) by incorporating geometric structure of the parameter space via…
We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of…
Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase…
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…
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…
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…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and…
Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such…
Simulating noninteracting fermion systems is a common task in computational many-body physics. In absence of translational symmetries, modeling free fermions on $N$ modes usually requires poly$(N)$ computational resources. While often…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…