Related papers: A (simple) classical algorithm for estimating Bett…
In many physical problems it is not possible to find an exact solution. However, when some parameter in the problem is small, one can obtain an approximate solution by expanding in this parameter. This is the basis of perturbative methods,…
We present new classical and quantum algorithms for solving random subset-sum instances. First, we improve over the Becker-Coron-Joux algorithm (EUROCRYPT 2011) from $\tilde{\mathcal{O}}(2^{0.291 n})$ downto $\tilde{\mathcal{O}}(2^{0.283…
We consider the multi-parameter random simplicial complex as a higher dimensional extension of the classical Erd\"os-R\'enyi graph. We investigate appearance of "unusual" topological structures in the complex from the point of view of large…
We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature, 619, 282-287 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the…
We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…
Using quantum algorithms, we obtain, for accuracy $\epsilon>0$ and confidence $1-\delta,0<\delta<1,$ a new sample complexity upper bound of $O((\mbox{log}(\frac{1}{\delta}))/\epsilon)$ as $\epsilon,\delta\rightarrow 0$ for a general…
The graph Laplacian is a fundamental object in the analysis of and optimization on graphs. This operator can be extended to a simplicial complex $K$ and therefore offers a way to perform ``signal processing" on $p$-(co)chains of $K$.…
Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…
The quantum algorithms for Monte Carlo integration (QMCI), which are based on quantum amplitude estimation (QAE), speed up expected value calculation compared with classical counterparts, and have been widely investigated along with their…
This paper describes recent advances in the combinatorial method for computing $\pi(x)$, the number of primes $\leq x$. In particular, the memory usage has been reduced by a factor of $\log x$, and modifications for shared- and…
An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…
Sequential Monte Carlo samplers represent a compelling approach to posterior inference in Bayesian models, due to being parallelisable and providing an unbiased estimate of the posterior normalising constant. In this work, we significantly…
Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to…
We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis. The proposed strategy combines the superior sampling of the Hamiltonian Monte Carlo method with…
We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a $d$-sparse Hamiltonian $H$…
Perceptrons, which perform binary classification, are the fundamental building blocks of neural networks. Given a data set of size~$N$ and margin~$\gamma$ (how well the given data are separated), the query complexity of the best-known…
Quasi-Monte Carlo methods replaced classical Monte Carlo methods in many areas of numerical analysis over the last decades. The purpose of this paper is to extend quasi-Monte Carlo methods into a new direction. We construct and implement a…
We present an iterative algorithm for solving a class of \\nonlinear Laplacian system of equations in $\tilde{O}(k^2m \log(kn/\epsilon))$ iterations, where $k$ is a measure of nonlinearity, $n$ is the number of variables, $m$ is the number…
We investigate the performance of the hybrid Monte Carlo algorithm, the standard algorithm used for lattice QCD simulations involving fermions, in updating non-trivial global topological structures. We find that the hybrid Monte Carlo…
Quantum algorithms for topological data analysis (TDA) seem to provide an exponential advantage over the best classical approach while remaining immune to dequantization procedures and the data-loading problem. In this paper, we give…