Related papers: Algorithmic Cluster Expansions for Quantum Problem…
Analytic continuation of numerical data obtained in imaginary time or frequency has become an essential part of many branches of quantum computational physics. It is, however, an ill-conditioned procedure and thus a hard numerical problem.…
The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter…
$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…
We investigate the question if quantum algorithms exist that compute the maximum of a set of conjugated elements of a given number field in quantum polynomial time. We will relate the existence of these algorithms for a certain family of…
Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit…
Motivated by notions of quantum heuristics and by average-case rather than worst-case algorithmic analysis, we define quantum computational advantage in terms of individual problem instances. Inspired by the classical notions of Kolmogorov…
Understanding the capacity of quantum circuits through the lens of approximation theory is essential for evaluating the complexity of quantum circuits required to solve various problems in scientific computation. We design quantum circuits…
A new maximum approximate likelihood (ML) estimation algorithm for the mixture of Kent distribution is proposed. The new algorithm is constructed via the BSLM (block successive lower-bound maximization) framework and incorporates manifold…
Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. A natural question is how many clusters are appropriate…
We present a classically solvable model that leads to optimized low-depth quantum circuits leveraging separable pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the…
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…
We develop a unified approach to the problem of clustering in the three different fields of applications, as indicated in the title the paper. The approach is based on Khintchine's probabilistic method that grew out of the Darwin-Fawler…
Correlation clustering is a widely studied framework for clustering based on pairwise similarity and dissimilarity scores, but its best approximation algorithms rely on impractical linear programming relaxations. We present faster…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…
Quantum state preparation is an important class of quantum algorithms that is employed as a black-box subroutine in many algorithms, or used by itself to generate arbitrary probability distributions. We present a novel state preparation…
For $d \ge 2$ and all $q\geq q_{0}(d)$ we give an efficient algorithm to approximately sample from the $q$-state ferromagnetic Potts and random cluster models on finite tori $(\mathbb Z / n \mathbb Z )^d$ for any inverse temperature…
Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…
The article presents a method of cluster expansions for groups of operators associated with the von Neumann equations for states and the Heisenberg equations for observables, aiming to construct generating operators for nonperturbative…