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In more recent years, there has been increasing research interest in exploiting the use of application specific hardware for solving optimisation problems. Examples of solvers that use specialised hardware are IBM's Quantum System One and…
We present explicit methods for simulating diffusions whose generator is self-adjoint with respect to a known (but possibly not normalizable) density. These methods exploit this property and combine an optimized Runge-Kutta algorithm with a…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
Quantum Monte Carlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum Monte Carlo simulations can in principle be used to…
Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or QUBO (quadratic unconstrained binary optimization) form. Although such solutions are…
Recent advances in quantum hardware offer new approaches to solve various optimization problems that can be computationally expensive when classical algorithms are employed. We propose a hybrid quantum-classical algorithm to solve a dynamic…
We consider deployment of the particle filter on modern massively parallel hardware architectures, such as Graphics Processing Units (GPUs), with a focus on the resampling stage. While standard multinomial and stratified resamplers require…
I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm. Such protocols will have…
It was recently demonstrated that a simple Monte Carlo (MC) algorithm involving the swap of particle pairs dramatically accelerates the equilibrium sampling of simulated supercooled liquids. We propose two numerical schemes integrating the…
The Monte Carlo method is a powerful technique for computing thermodynamic magnetic states of otherwise unsolvable spin Hamiltonians, but the method becomes computationally prohibitive with increasing number of spins and the simulation of…
This paper studies the Hamiltonian Cycle Problem (HCP) and the Traveling Salesman Problem (TSP) on D-Wave's quantum systems. Initially, motivated by the fact that most libraries present their benchmark instances in terms of adjacency…
Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant…
Quantum annealing aims to provide a faster method for finding the minima of complicated functions, compared to classical computing, so there is an increasing interest in the relaxation dynamics of quantum spin systems. Moreover, it is known…
We benchmark current annealing-based optimization workflows on a greenhouse-inspired quadratic unconstrained binary optimization problem for binary heater scheduling, where the horizon H denotes the number of hourly control decisions. For…
We discuss an Ising spin glass where each $S=1/2$ spin is coupled antiferromagnetically to three other spins (3-regular graphs). Inducing quantum fluctuations by a time-dependent transverse field, we use out-of-equilibrium quantum Monte…
This work is a benchmark study for quantum-classical computing method with a real-world optimization problem from industry. The problem involves scheduling and balancing jobs on different machines, with a non-linear objective function. We…
We show that addition of Metropolis single spin-flips to the Wolff cluster flipping Monte Carlo procedure leads to a dramatic {\bf increase} in performance for the spin-1/2 Ising model. We also show that adding Wolff cluster flipping to the…
While real quantum devices have been increasingly used to conduct research focused on achieving quantum advantage or quantum utility in recent years, executing deep quantum circuits or performing quantum machine learning with large-scale…
We evaluate using programmable superconducting flux qubit D-Wave quantum annealers to approximate the partition function of Ising models. We propose the use of two distinct quantum annealer sampling methods: chains of Monte Carlo-like…
Competing phases or interactions in complex many-particle systems can result in free energy barriers that strongly suppress thermal equilibration. Here we discuss how extended ensemble Monte Carlo simulations can be used to study the…