Related papers: Quantum Algorithm for Jaccard Similarity
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and…
We consider the problem of encoding a set of vectors into a minimal number of bits while preserving information on their Euclidean geometry. We show that this task can be accomplished by applying a Johnson-Lindenstrauss embedding and…
Correspondence identifies relationships among objects via similarities among their components; it is ubiquitous in the analysis of spatial datasets, including images, weather maps, and computational simulations. This paper develops a novel…
According to the Bell theorem, local hidden variable theories cannot reproduce all the predictions of quantum mechanics. An important consequence is that under physically reasonable assumptions quantum mechanics predicts correlations that…
We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
We introduce a connection between a near-term quantum computing device, specifically a Gaussian boson sampler, and the graph isomorphism problem. We propose a scheme where graphs are encoded into quantum states of light, whose properties…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
We construct a hybrid quantum-classical approach for the $K$-Nearest Neighbour algorithm, where the information is embedded in a phase-distributed multimode coherent state with the assistance of a single photon. The task of finding the…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
Many datasets take the form of a bipartite graph where two types of nodes are connected by relationships, like the movies watched by a user or the tags associated with a file. The partitioning of the bipartite graph could be used to fasten…
Quantum algorithms are touted as a way around some classically intractable problems such as the simulation of quantum mechanics. At the end of all quantum algorithms is a quantum measurement whereby classical data is extracted and utilized.…
Checking whether two quantum circuits are equivalent is important for the design and optimization of quantum-computer applications with real-world devices. We consider quantum circuits consisting of Clifford gates, a practically-relevant…
We put forward and demonstrate experimentally a {\it quantum-inspired} protocol that allows to quantify the degree of similarity between two spatial shapes embedded in two optical beams without the need to measure the amplitude and phase…
In the current NISQ (Noisy Intermediate-Scale Quantum) era, simulating and verifying noisy quantum circuits is crucial but faces challenges such as quantum state explosion and complex noise representations, constraining simulation and…
Calculating and categorizing the similarity of curves is a fundamental problem which has generated much recent interest. However, to date there are no implementations of these algorithms for curves on surfaces with provable guarantees on…
Quantum decoherence refers to the phenomenon when the interaction of a quantum system with its environment results in the degradation of quantum coherence. Decoherence is considered to be the most popular mechanism responsible for the…
As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can…
The purpose of this short tutorial paper is to review various criteria that have been used to characterize the quantum character of correlations in optical systems, such as "gemellity", QND correlation, intrication, EPR correlation and Bell…