Related papers: The Problem with Grover-Rudolph State Preparation …
The recently introduced backward Monte-Carlo method [Johan Carlsson, arXiv:math.NA/0010118] is validated, benchmarked, and compared to the conventional, forward Monte-Carlo method by analyzing the error in the Monte-Carlo solutions to a…
A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speedup and, in particular, for fault-tolerant quantum computation. We establish a remarkable connection…
Overlap between two neural quantum states can be computed through Monte Carlo sampling by evaluating the unnormalized probability amplitudes on a subset of basis configurations. Due to the presence of probability amplitude ratios in the…
We study multiproposal Markov chain Monte Carlo algorithms, such as Multiple-try or generalised Metropolis-Hastings schemes, which have recently received renewed attention due to their amenability to parallel computing. First, we prove that…
We review the use of continuum quantum Monte Carlo (QMC) methods for the calculation of energy gaps from first principles, and present a broad set of excited-state calculations carried out with the variational and fixed-node diffusion QMC…
A Monte Carlo method is presented to evaluate quantum states with many particles moving in the continuum. The scattering state is generated at each time by a Monte Carlo random sampling algorithm. The same calculation are repeated until the…
This paper introduces the first quantum computing framework for Stochastic Quantum Power Flow (SQPF) analysis in power systems. The proposed method leverages quantum states to encode power flow distributions, enabling the use of Quantum…
Quantum simulators offer great potential for investigating dynamical properties of quantum field theories. However, preparing accurate non-trivial initial states for these simulations is challenging. Classical Euclidean-time Monte-Carlo…
The one clean qubit model of quantum computation (DQC1) efficiently implements a computational task that is not known to have a classical alternative. During the computation, there is never more than a small but finite amount of…
Variational Monte Carlo (VMC) methods are used to sample classically from distributions corresponding to quantum states which have an efficient classical description. VMC methods are based on performing a number of steps of a Markov chain…
Quantum Monte Carlo methods provide in principle an accurate treatment of the many-body problem of the ground and excited states of condensed systems. In practice, however, uncontrolled errors such as those arising from the fixed-node and…
The intermediate quantum states of multiple qubits, generated during the operation of Shor's factoring algorithm are analyzed. Their entanglement is evaluated using the Groverian measure. It is found that the entanglement is generated…
We describe how quantum Monte Carlo calculations using the CASINO software can be accelerated using graphics processing units (GPUs) and OpenACC. In particular we consider offloading Ewald summation, the evaluation of long-range two-body…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
According to the Gottesman-Knill theorem, any quantum algorithm utilising operations chosen exclusively from a particular restricted set are efficiently simulable by a classical computer. Since some of these algorithms involve entangled…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
Although the nonequilibrium relaxation (NER) method has been widely used in Monte Carlo studies on phase transitions in classical spin systems, such studies have been quite limited in quantum phase transitions. The reason is that relaxation…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
Standard Bayesian credible-region theory for constructing an error region on the unique estimator of an unknown state in general quantum-state tomography to calculate its size and credibility relies on heavy Monte~Carlo sampling of the…
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…