Related papers: Quantum Distance Calculation for $\epsilon$-Graph …
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
We propose a new method to extend the size of a quantum computation beyond the number of physical qubits available on a single device. This is accomplished by randomly inserting measure-and-prepare channels to express the output state of a…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
We present a quantum theory of distances along a curve, based on a linear line element that is equal to the operator square root of the quadratic metric of Riemannian geometry. Since the linear line element is an operator, we treat it…
We give a new upper bound on the quantum query complexity of deciding $st$-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation…
Predicting new links in physical, biological, social, or technological networks has a significant scientific and societal impact. Path-based link prediction methods utilize explicit counting of even and odd-length paths between nodes to…
The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…
By using highly entangled states, quantum metrology guarantees precision impossible with classical measurements. Unfortunately such states can be very susceptible to noise, and it is a great challenge of the field to maintain quantum…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and…
We study a path-planning problem amid a set $\mathcal{O}$ of obstacles in $\mathbb{R}^2$, in which we wish to compute a short path between two points while also maintaining a high clearance from $\mathcal{O}$; the clearance of a point is…
Many applications in pattern recognition represent patterns as a geometric graph. The geometric graph distance (GGD) has recently been studied as a meaningful measure of similarity between two geometric graphs. Since computing the GGD is…
Entanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology, and life sciences. For arbitrary multiparticle…
With growing success in experimental implementations it is critical to identify a "gold standard" for quantum information processing, a single measure of distance that can be used to compare and contrast different experiments. We enumerate…
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
Scientists in quantum technology aspire to quantum advantage: a computational result unattainable with classical computers. Gaussian boson sampling experiment has been already claimed to achieve this goal. In this setup squeezed light…
We explore in this paper a novel approach that builds an overapproximation of the state space of preemptive real time systems. Our graph construction extends the expression of a class to the time distance system that encodes the…
Hyperbolicity is a graph parameter which indicates how much the shortest-path distance metric of a graph deviates from a tree metric. It is used in various fields such as networking, security, and bioinformatics for the classification of…
We survey the existing techniques for calculating code distances of classical codes and apply these techniques to generic quantum codes. For classical and quantum LDPC codes, we also present a new linked-cluster technique. It reduces…
Quantum communication between distant parties is based on suitable instances of shared entanglement. For efficiency reasons, in an anticipated quantum network beyond point-to-point communication, it is preferable that many parties can…