Related papers: Quantum algorithms and the power of forgetting
Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state…
The model of open quantum systems is adopted to describe the non-local dynamical behaviour of qubits processed by entangling gates. The analysis gets to the conclusion that a distinction between evaluation steps and task-oriented computing…
We propose a quantum algorithm for `extremal learning', which is the process of finding the input to a hidden function that extremizes the function output, without having direct access to the hidden function, given only partial input-output…
Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly…
Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…
Topological invariants of a dataset, such as the number of holes that survive from one length scale to another (persistent Betti numbers) can be used to analyze and classify data in machine learning applications. We present an improved…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…
Along with the development of quantum technology, finding useful applications of quantum computers has been a central pursuit. Despite various quantum algorithms have been developed, many of them often require strong input assumptions,…
One of the major application areas of interest for both near-term and fault-tolerant quantum computers is the optimization of classical objective functions. In this work, we develop intuitive constructions for a large class of these…
Fault tree analysis is a technique widely used in risk and reliability analysis of complex engineering systems given its deductive nature and relatively simple interpretation. In a fault tree, events are usually represented by a binary…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…
Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
Quantum algorithms have demonstrated promising speed-ups over classical algorithms in the context of computational learning theory - despite the presence of noise. In this work, we give an overview of recent quantum speed-ups, revisit the…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths…