Related papers: Constant-time Quantum Algorithm for Homology Detec…
Underwater object-level mapping requires incorporating visual foundation models to handle the uncommon and often previously unseen object classes encountered in marine scenarios. In this work, a metric of semantic uncertainty for open-set…
Persistent homology is a crucial invariant that is used in many areas to understand data. The $O(N^4)$ run time is a hindrance to its use on most large datasets. We give a parallelization method to utilize multi-core machines and clusters.…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Nguyen and Onak constructed the first constant-time algorithm for the approximation of the size of the maximum matching in bounded degree graphs. The Borel oracle machinery is a tool that can be used to convert some statements in Borel…
Given two rational, properly parametrized space curves ${\mathcal C}_1$ and ${\mathcal C}_2$, where $\CCC_2$ is contained in some plane $\Pi$, we provide an algorithm to check whether or not there exist perspective or parallel projections…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
The geometric Cauchy problem for a class of surfaces in a pseudo-Riemannian manifold of dimension 3 is to find the surface which contains a given curve with a prescribed tangent bundle along the curve. We consider this problem for constant…
We compute quantum cohomology ring of elliptic $\mathbb{P}^1$ orbifolds via orbi-curve counting. The main technique is the classification theorem which relates holomorphic orbi-curves with certain orbifold coverings. The countings of…
Distance geometry problem belongs to a class of hard problems in classical computation that can be understood in terms of a set of inputs processed according to a given transformation, and for which the number of possible outcomes grows…
We argue that in contrast to the classical physics, the measurements in the quantum mechanics should provide simultaneous information about all relevant relative amplitudes (pure states and the transitions between them) and all relevant…
The claw finding problem has been studied in terms of query complexity as one of the problems closely connected to cryptography. For given two functions, f and g, as an oracle which have domains of size N and M (N<=M), respectively, and the…
We make use of the complex implicit representation in order to provide a deterministic algorithm for checking whether or not two implicit algebraic curves are related by a similarity, a central question in Pattern Recognition and Computer…
Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit…
In the oracle identification problem we have oracle access to bits of an unknown string $x$ of length $n$, with the promise that it belongs to a known set $C\subseteq\{0,1\}^n$. The goal is to identify $x$ using as few queries to the oracle…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…
We give a quantum algorithm for a novel type of black-box problem: identifying a hidden $d$-regular base graph $G$ on $n$ vertices from oracle access to an obfuscated version of it, rather than traversing it. From $G$ we build the spired…
Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. A classic example is computing the edit distance of two strings of length $n$, which can be solved in…
Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition--------quantum coherence or quantum superposition. In this paper, we attempt to give an alternative…
Quantum Annealing (QA) is a computational framework where a quantum system's continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for…
We study a variant of the subgraph isomorphism problem that is of high interest to the quantum computing community. Our results give an algorithm to perform pattern matching in quantum circuits for many patterns simultaneously,…