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Quantum Computing offers an entirely new way of doing computation governed by the rules of quantum mechanics like Superposition and Entanglement. These rules allow us to do computation over all the possible states simultaneously. Hence,…

Quantum Physics · Physics 2021-07-08 Mohd. Hussain Mir , Harkirat Singh

Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well on…

Quantum Physics · Physics 2023-10-11 Chris Cade , Marten Folkertsma , Ido Niesen , Jordi Weggemans

Grover's algorithm for quantum search can also be applied to classical energy transfer. The procedure takes a system in which the total energy is equally distributed among $N$ subsystems and transfers most of the it to one marked subsystem.…

Quantum Physics · Physics 2011-01-25 Juan Carlos Garcia-Escartin Pedro Chamorro-Posada

A major problem in data augmentation is to ensure that the generated new samples cover the search space. This is a challenging problem and requires exploration for data augmentation policies to ensure their effectiveness in covering the…

Machine Learning · Computer Science 2020-10-08 Alireza Naghizadeh , Mohammadsajad Abavisani , Dimitris N. Metaxas

We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a…

Optimization and Control · Mathematics 2017-05-16 Figen Öztoprak , Ş. İlker Birbil

In April 2025 GMV announced a competition for finding the best method to solve a particular polynomial system over a finite field. In this paper we provide a method for solving the given equation system significantly faster than what is…

Computational Complexity · Computer Science 2026-03-06 Àngela Barbero , Ragnar Freij-Hollanti , Camilla Hollanti , Håvard Raddum , Øyvind Ytrehus , Morten Øygarden

Mini-batch algorithms have been proposed as a way to speed-up stochastic convex optimization problems. We study how such algorithms can be improved using accelerated gradient methods. We provide a novel analysis, which shows how standard…

Machine Learning · Computer Science 2011-06-24 Andrew Cotter , Ohad Shamir , Nathan Srebro , Karthik Sridharan

Grover's algorithm is normally presented as a method of searching a database, however it would be more accurately described as a method of identifying elements of an interval of the integers which satisfy some logical clause - an example…

Quantum Physics · Physics 2022-06-09 David Jones , Benjamin Varcoe

We review Grover's algorithm by means of a detailed geometrical interpretation and a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are also reviewed. This work is intended for non-specialists which have…

Quantum Physics · Physics 2007-05-23 C. Lavor , L. R. U. Manssur , R. Portugal

The augmentation scheme provides a nontraditional approach to nonlinear integer programming by iteratively refining incumbent solutions along objective-improving directions from the Graver basis. Its main computational bottleneck, however,…

Optimization and Control · Mathematics 2026-03-09 Wenbo Liu , Akang Wang , Wenguo Yang

This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…

Methodology · Statistics 2019-03-27 Maxime Vono , Nicolas Dobigeon , Pierre Chainais

Grover's search algorithm is one of the first quantum algorithms to exhibit a provable quantum advantage. It forms the backbone of numerous quantum applications and is widely used in benchmarking efforts. Here, we report…

Quantum Physics · Physics 2022-11-10 Bibek Pokharel , Daniel Lidar

We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…

Quantum Physics · Physics 2012-08-02 Ashley Montanaro

Data augmentation is an essential technique for improving generalization ability of deep learning models. Recently, AutoAugment has been proposed as an algorithm to automatically search for augmentation policies from a dataset and has…

Machine Learning · Computer Science 2020-01-09 Sungbin Lim , Ildoo Kim , Taesup Kim , Chiheon Kim , Sungwoong Kim

It is questionable that Grover algorithm may be more valuable than a classical one, when a partial information is given in a unstructured database. In this letter, to consider quantum search when a partial information is given, we replace…

Quantum Physics · Physics 2007-05-23 Sangwoong Park , Joonwoo Bae , Younghun Kwon

The original Grover's algorithm has a success probability to output a correct solution, while deterministic Grover's algorithms improve the success probability to 100%. However, the success probability of deterministic Grover's algorithm…

Quantum Physics · Physics 2023-05-23 Jian Leng , Fan Yang , Xiang-Bin Wang

The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It can be understood from the early invented quantum algorithms such as…

Quantum Physics · Physics 2017-11-17 Pulak Ranjan Giri , Vladimir E. Korepin

Acceleration of first order methods is mainly obtained via inertial techniques \`a la Nesterov, or via nonlinear extrapolation. The latter has known a recent surge of interest, with successful applications to gradient and proximal gradient…

Machine Learning · Statistics 2021-10-29 Quentin Bertrand , Mathurin Massias

We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This…

Quantum Physics · Physics 2015-09-17 A. H. Homid , Mahmoud Abdel-Aty , A. -S. F. Obada

One of the challenges in optimization of high dimensional problems is finding appropriate solutions in a way that are as close as possible to the global optima. In this regard, one of the most common phenomena that occurs is the curse of…

Optimization and Control · Mathematics 2021-12-22 Somayeh Seifi Shalamzari , Mojtaba Banifakhr