Related papers: Majorization in General Grover's Algorithms: Effic…
We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
The family of Groves mechanisms, which includes the well-known VCG mechanism (also known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms. Unfortunately, the Groves mechanisms are generally not budget…
Algorithmic generalization in machine learning refers to the ability to learn the underlying algorithm that generates data in a way that generalizes out-of-distribution. This is generally considered a difficult task for most machine…
When applying Grover's algorithm to an unordered database, the probability of obtaining correct results usually decreases as the quantity of target increases. To amend the limitation, numbers of improved schemes are proposed. In this paper,…
Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that…
As the engineering endeavour to realise quantum computers progresses, we consider that such machines need not rely on binary as their de facto unit of information. We investigate Grover's algorithm under a generalised quantum circuit model,…
The Majorization Principle is a fundamental statement governing the dynamics of information processing in optimal and efficient quantum algorithms. While quantum computation can be modeled to be reversible, due to the unitary evolution…
In this article we consider an experimental study showing the influence of emotion regulation strategies on human memory performance: part of such experimental results are difficult to explain within a classic cognitive allocation model. We…
Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to…
We introduce the concepts of Grover operators and Grover kernels to systematically analyse Grover's searching algorithms. Then, we investigate a one-parameter family of quantum searching algorithms of Grover's type and we show that the…
We study the problem of learning efficient algorithms that strongly generalize in the framework of neural program induction. By carefully designing the input / output interfaces of the neural model and through imitation, we are able to…
Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple…
In this work we study five Grovers algorithm modifications, where each iteration is constructed by two generalized Householder reflections, against inaccuracies in the phases. By using semi-empirical methods, we investigate various…
Grover's algorithm is a quantum search algorithm that proceeds by repeated applications of the Grover operator and the Oracle until the state evolves to one of the target states. In the standard version of the algorithm, the Grover operator…
We investigate the necessary and sufficient conditions in order that a unitary operator can amplify a pre-assigned component relative to a particular basis of a generic vector at the expense of the other components. This leads to a general…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
The Grover algorithm is a crucial solution for addressing unstructured search problems and has emerged as an essential quantum subroutine in various complex algorithms. By using a different approach with previous studies, this research…
This article demonstrates how an understanding of the geometry of a family of cost functions can be used to develop efficient numerical algorithms for real-time optimisation. Crucially, it is not the geometry of the individual functions…
We study the fully generalized Grover's algorithm to find the optimal phase changes for each step of the iteration to maximize gain in probability of observation of the target, and when phase matching is required. We find that classical…