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We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
Understanding the dynamics of quantum systems is crucial in many areas of physics, but simulating many-body systems presents significant challenges due to the large Hilbert space to navigate and the exponential growth of computational…
Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on…
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…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
A new efficient ensemble prediction strategy is developed for a general turbulent model framework with emphasis on the nonlinear interactions between large and small scale variables. The high computational cost in running large ensemble…
We propose an adaptive quantum algorithm to prepare accurate variational time evolved wave functions. The method is based on the projected Variational Quantum Dynamics (pVQD) algorithm, that performs a global optimization with linear…
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…
As first proposed for the adiabatic quantum information processing by Wu, Byrd and Lidar [ Phys. Rev. Lett. 89, 057904 (2002)], the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…
We introduce neural particle smoothing, a sequential Monte Carlo method for sampling annotations of an input string from a given probability model. In contrast to conventional particle filtering algorithms, we train a proposal distribution…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
Multi-fidelity Gaussian process is a common approach to address the extensive computationally demanding algorithms such as optimization, calibration and uncertainty quantification. Adaptive sampling for multi-fidelity Gaussian process is a…
Randomization has been applied to Hamiltonian simulation in a number of ways to improve the accuracy or efficiency of product formulas. Deterministic product formulas are often constructed in a symmetric way to provide accuracy of even…
Hamiltonian simulation is one of the most promising applications of quantum computers, and the product formula is one of the most important methods for this purpose. Previous related work has mainly focused on the worst$-$case or…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of…
In an experimental study of single enzyme reactions, it has been proposed that the rate constants of the enzymatic reactions fluctuate randomly, according to a given distribution. To quantify the uncertainty arising from random rate…
Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. This approach typically relies on deep circuits and is therefore hampered by the substantial…