Related papers: Quantum Pattern Recognition of Classical Signal

It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity $O(\sqrt{GT})$ where $T$ is…

We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…

The classical knot recognition problem is the problem of determining whether the virtual knot represented by a given diagram is classical. We prove that this problem is in NP, and we give an exponential time algorithm for the problem.

Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…

The theory of decoherent histories is an attempt to derive classical physics from positing only quantum laws at the fundamental level without notions of a classical apparatus or collapse of the wave-function. Searching for a marked target…

Markov random fields (MRFs) appear in many problems in machine learning and statistics. From a computational learning theory point of view, a natural problem of learning MRFs arises: given samples from an MRF from a restricted class, learn…

This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…

Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a…

We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…

In this work, we consider the performance of using a quantum algorithm to predict a result for a binary classification problem if a machine learning model is an ensemble from any simple classifiers. Such an approach is faster than classical…

Over decades traditional information theory of source and channel coding advances toward learning and effective extraction of information from data. We propose to go one step further and offer a theoretical foundation for learning classical…

We present an algorithm for the generalized search problem (searching $k$ marked items among $N$ items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity $O(\sqrt{N/k})$ as the…

We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…

Grover's quantum search algorithm is considered as one of the milestone in the field of quantum computing. The algorithm can search for a single match in a database with $N$ records in $O(\sqrt{N})$ assuming that the item must exist in the…

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…

This note presents a quantum protocol for private information retrieval, in the single-server case and with information-theoretical privacy, that has O(\sqrt{n})-qubit communication complexity, where n denotes the size of the database. In…

Extracting useful signals is key to both classical and quantum technologies. Conventional noise filtering methods rely on different patterns of signal and noise in frequency or time domains, thus limiting their scope of application,…

We show how to determine whether a given pattern p of length m occurs in a given text t of length n in ${\tilde O}(\sqrt{n}+\sqrt{m})$\footnote{${\tilde O}$ allows for logarithmic factors in m and $n/m$} time, with inverse polynomial…

The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an…

We introduces the Quantum-Train(QT) framework, a novel approach that integrates quantum computing with classical machine learning algorithms to address significant challenges in data encoding, model compression, and inference hardware…