Related papers: Geometric Algebra and Information Geometry for Qua…
Quantum multi-programming is a method utilizing contemporary noisy intermediate-scale quantum computers by executing multiple quantum circuits concurrently. Despite early research on it, the research remains on quantum gates or small-size…
We show that Grover's algorithm defines a geodesic in quantum Hilbert space with the Fubini-Study metric. From statistical point of view Grover's algorithm is characterized by constant Fisher's function. Quantum algorithms changing…
Algebraic multigrid (AMG) is conventionally applied in a black-box fashion, agnostic to the underlying geometry. In this work, we propose that using geometric information -- when available -- to assist with setting up the AMG hierarchy is…
Studies on Quantum Computing have been developed since the 1980s, motivating researches on quantum algorithms better than any classical algorithm possible. An example of such algorithms is Grover's algorithm, capable of finding $k$ (marked)…
Grover's quantum search algorithm provides a quadratic speedup over the classical one. The computational complexity is based on the number of queries to the oracle. However, depth is a more modern metric for noisy intermediate-scale quantum…
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle…
Grover's Search algorithm was a breakthrough at the time it was introduced, and its underlying procedure of amplitude amplification has been a building block of many other algorithms and patterns for extracting information encoded in…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical…
The research community has been actively working on the realization of quantum computer. But the large scale commercial quantum computers are not a reality yet quantum computing field has become richer by day with the advent of algorithms…
An adiabatic cyclic evolution of control parameters of a quantum system ends up with a holonomic operation on the system, determined entirely by the geometry in the parameter space. The operation is given either by a simple phase factor (a…
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose,…
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…
What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework…
A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed,…
Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…
Grover discovered a quantum algorithm for identifying a target element in an unstructured search universe of N items in approximately square-root of N queries to a quantum oracle, thus achieving a square-root speed-up over classical…
This book gives a geometry-first, hardware-aware route through quantum-information workflows, with one goal: connect states, circuits, and measurement to deterministic classical pipelines that make hybrid quantum systems run. Part 1…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
In this work, we develop a novel mathematical framework for universal digital quantum computation using algebraic probability theory. We rigorously define quantum circuits as finite sequences of elementary quantum gates and establish their…