Related papers: Quantum Summation with an Application to Integrati…
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…
The last two decades have seen an explosive growth in the theory and practice of both quantum computing and machine learning. Modern machine learning systems process huge volumes of data and demand massive computational power. As silicon…
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…
We introduce a local concept of speed-up applicable to intermediate stages of a quantum algorithm. We use it to analyse the complementary roles played by quantum parallel computation and quantum measurement in yielding the speed-up. A…
We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
We consider arithmetic sequences, here defined as ordered lists of positive integers. Any such a sequence can be cast onto a quantum state, enabling the quantification of its `surprise' through von Neumann entropy. We identify typical…
In polynomial optimization problems, nonnegativity constraints are typically handled using the sum of squares condition. This can be efficiently enforced using semidefinite programming formulations, or as more recently proposed by Papp and…
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring…
In this study, a distinctive feature of quantum computation (QC) is characterized. To this end, a seemingly-powerful classical computing model, called "stochastic ensemble machine (SEnM)," is considered. The SEnM runs with an ensemble…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied…
Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) can potentially demonstrate…
We use Poisson summation formula to calculate integrals of producs of sinc functions (cf. [4]) and related integrals as in [5] and [3]. We also generalize the one in [5] and introduce other remarkable integrals. Finally we give a sum…
Quantum Bayesian Computation (QBC) is an emerging field that levers the computational gains available from quantum computers to provide an exponential speed-up in Bayesian computation. Our paper adds to the literature in two ways. First, we…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…
We discuss how quantum computation can be applied to financial problems, providing an overview of current approaches and potential prospects. We review quantum optimization algorithms, and expose how quantum annealers can be used to…
This paper develops a generalization of the line-search sequential quadratic programming (SQP) algorithm with $\ell_1$-merit function that uses objective and constraint function approximations with tunable accuracy to solve smooth…