Related papers: Adaptive Quantum Simulated Annealing for Bayesian …
The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…
Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic…
We analyze the performance of quantum annealing as a heuristic optimization method to find the absolute minimum of various continuous models, including landscapes with only two wells and also models with many competing minima and with…
In a recent study (Ref. [1]), quantum annealing was reported to exhibit a scaling advantage for approximately solving Quadratic Unconstrained Binary Optimization (QUBO). However, this claim critically depends on the choice of classical…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
Sampling problems are widely regarded as the task for which quantum computers can most readily provide a quantum advantage. Leveraging this feature, the quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287…
Quantum simulation with adiabatic annealing can provide insight into difficult problems that are impossible to study with classical computers. However, it deteriorates when the systems scale up due to the shrinkage of the excitation gap and…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
Quantum computers theoretically promise computational advantage in many tasks, but it is much less clear how such advantage can be maintained when using existing and near-term hardware that has limitations in the number and quality of its…
We study from a theoretical viewpoint the fundamental problem of efficiently computing the stationary distribution of general classes of structured Markov processes. In strong contrast with previous work, we consider this fundamental…
Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…
While quantum computing proposes promising solutions to computational problems not accessible with classical approaches, due to current hardware constraints, most quantum algorithms are not yet capable of computing systems of practical…
The mean of a random variable can be understood as a linear functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this…
We present classical and quantum algorithms for approximating partition functions of classical Hamiltonians at a given temperature. Our work has two main contributions: first, we modify the classical algorithm of \v{S}tefankovi\v{c},…
The standard quantum annealing algorithm tries to approach the ground state of a classical system by slowly decreasing the hopping rates of a quantum random walk in the configuration space of the problem, where the on-site energies are…
As one of the most robust global optimization methods, simulated annealing has received considerable attention, with many variations that attempt to improve the cooling schedule. This paper introduces a variant of simulated annealing that…
Quantum computing is a promising way to systematically solve the longstanding computational problem, the ground state of a many-body fermion system. Many efforts have been made to realise certain forms of quantum advantage in this problem,…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
Relations of simulated annealing and quantum annealing are studied by a mapping from the transition matrix of classical Markovian dynamics of the Ising model to a quantum Hamiltonian and vice versa. It is shown that these two operators, the…