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In this work, we present a quantum query algorithm for searching a word of length $m$ in an unsorted dictionary of size $n$. The algorithm uses $O(\sqrt{n})$ queries (Grover operators), like previously known algorithms. What is new is that…
Quantum algorithms are conventionally formulated for implementation on a single system of qubits amenable to projective measurements. However, in expectation value quantum computation, such as nuclear magnetic resonance realizations, the…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity. Thus, upon measurement, there is a…
Consider the unstructured search of an unknown number l of items in a large unsorted database of size N. The multi-object quantum search algorithm consists of two parts. The first part of the algorithm is to generalize Grover's…
In this paper we combine concepts from Riemannian Optimization and the theory of Sobolev gradients to derive a new conjugate gradient method for direct minimization of the Gross-Pitaevskii energy functional with rotation. The conservation…
This work considers a generalization of Grover's search problem, viz., to find any one element in a set of acceptable choices which constitute a fraction f of the total number of choices in an unsorted data base. An infinite family of…
We exploit Grover operator of database search algorithm for weight decision algorithm. In this research, weight decision problem is to find an exact weight w from given two weights as w1 and w2 where w1+w2=1 and 0<w1<w2<1. Firstly, if a…
In recent years, stochastic variance reduction algorithms have attracted considerable attention for minimizing the average of a large but finite number of loss functions. This paper proposes a novel Riemannian extension of the Euclidean…
We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton's method and the linear conjugate gradient algorithm, with explicit detection and use of negative curvature directions for the…
We question whether the measurement based quantum computing algorithm is in fact Grover's algorithm or simply a similar oracular search method. The two algorithms share several qualitative features especially in the case of the trivial 4…
We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…
Optimization problems with access to only zeroth-order information of the objective function on Riemannian manifolds arise in various applications, spanning from statistical learning to robot learning. While various zeroth-order algorithms…
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to…
Grover's algorithm provides a quadratic speedup over classical algorithms to search for marked elements in an unstructured database. The original algorithm is probabilistic, returning a marked element with bounded error. There are several…
Many inverse problems and signal processing problems involve low-rank regularizers based on the nuclear norm. Commonly, proximal gradient methods (PGM) are adopted to solve this type of non-smooth problems as they can offer fast and…
Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a proximity operator comes with its structure at no additional cost, and…
In the Euclidean setting, the proximal gradient method and its accelerated variants are a class of efficient algorithms for optimization problems with decomposable objective. In this paper, we develop a Riemannian proximal gradient method…
In this paper, we propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization (HUBO) problem. This algorithm is based on the Grover adaptive search that originally supported HUBO with integer…
As large language models (LLMs) demonstrate outstanding performance across various tasks, attention-driven models have profoundly transformed the field of machine learning. Since attention computations account for the primary computational…