Related papers: Quantum Distance Calculation for $\epsilon$-Graph …
Quantum effects are known to provide an advantage in particle transfer across networks. In order to achieve this advantage, requirements on both a graph type and a quantum system coherence must be found. Here we show that the process of…
The scheduling problem consists of finding a common 1 in two remotely located N bit strings. Denote the number of 1s in the string with the fewer 1s by epsilon*N. Classically, it needs at least O(epsilon*N) bits of communication to find the…
We show that two parties far apart can use shared entangled states and classical communication to align their coordinate systems with a very high fidelity. Moreover compared with previous methods proposed for such a task, i.e. sending…
Graph states play an important role in quantum information theory through their connection to measurement-based computing and error correction. Prior work has revealed elegant connections between the graph structure of these states and…
We describe a $O(\log n )$-approximation algorithm for computing the homotopic \Frechet distance between two polygonal curves that lie on the boundary of a triangulated topological disk. Prior to this work, algorithms were known only for…
Let $T=t_0 ... t_{n-1}$ be a text and $P = p_0 ... p_{m-1}$ a pattern taken from some finite alphabet set $\Sigma$, and let $\dist$ be a metric on $\Sigma$. We consider the problem of calculating the sum of distances between the symbols of…
We consider the typical distance between vertices of the giant component of a random intersection graph having a power law (asymptotic) vertex degree distribution with infinite second moment. Given two vertices from the giant component we…
The Fr\'echet distance is a popular similarity measure between curves. For some applications, it is desirable to match the curves under translation before computing the Fr\'echet distance between them. This variant is called the Translation…
We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert…
Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…
We propose a quantum ranging protocol to determine the distance between an observer and a target at the line of sight in the near-Earth curved spacetime. Unlike the quantum illumination scheme, here we employ multiple quantum hypothesis…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. It has been discussed so far for small systems with only a few independent…
We give for the first time a diagrammatic calculational tool of quantum entanglement. We present a pedagogical and simple mechanical implementation of quantum entanglement or "spooky action at a distance" to give a tangible realization of…
We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of…
It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…
Distributed quantum computing is motivated by the difficulty in building large-scale, individual quantum computers. To solve that problem, a large quantum circuit is partitioned and distributed to small quantum computers for execution.…
We construct a theory for long-distance quantum communication based on sharing entanglement through a linear chain of $N$ elementary swapping segments of length~$L=Nl$ where $l$ is the length of each elementary swap setup. Entanglement…
The search for macroscopic quantum phenomena is a fundamental pursuit in quantum mechanics. It allows us to test the limits quantum physics and provides new avenues for exploring the interplay between quantum mechanics and relativity. In…