Related papers: Quantum Factor Graphs

Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms…

The kernel trick in supervised learning signifies transformations of an inner product by a feature map, which then restructures training data in a larger Hilbert space according to an endowed inner product. A quantum feature map corresponds…

Modern cryptography is largely based on complexity assumptions, for example, the ubiquitous RSA is based on the supposed complexity of the prime factorization problem. Thus, it is of fundamental importance to understand how a quantum…

Data encoding plays a fundamental and distinctive role in Quantum Machine Learning (QML). While classical approaches process data directly as vectors, QML may require transforming classical data into quantum states through encoding…

The development of quantum computers has been the stimulus that enables the realization of Quantum Machine Learning (QML), an area that integrates the calculational framework of quantum mechanics with the adaptive properties of classical…

Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…

The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical…

Quantum machine learning (QML) is a promising early use case for quantum computing. There has been progress in the last five years from theoretical studies and numerical simulations to proof of concepts. Use cases demonstrated on…

Quantum feature maps are a key component of quantum machine learning, encoding classical data into quantum states to exploit the expressive power of high-dimensional Hilbert spaces. Despite their theoretical promise, designing quantum…

Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…

The application of near-term quantum devices to machine learning (ML) has attracted much attention. In one such attempt, Mitarai et al. (2018) proposed a framework to use a quantum circuit for supervised ML tasks, which is called quantum…

We formulate maximum likelihood (ML) channel decoding as a quadratic unconstraint binary optimization (QUBO) and simulate the decoding by the current commercial quantum annealing machine, D-Wave 2000Q. We prepared two implementations with…

According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…

In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large…

Quantum Annealing (QA) uses quantum fluctuations to search for a global minimum of an optimization-type problem faster than classical computers. To meet the demand for future internet traffic and mitigate the spectrum scarcity, this work…

Quantum-centric supercomputing presents a compelling framework for large-scale hybrid quantum-classical tasks. Although quantum machine learning (QML) offers theoretical benefits in various applications, challenges such as large-size data…

Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum, preserving coherence. Such settings include quantum purity amplification (QPA),…

Conventional decoding algorithms for polar codes strive to balance achievable performance and computational complexity in classical computing. While maximum likelihood (ML) decoding guarantees optimal performance, its NP-hard nature makes…

Quantum Machine Learning has the potential to improve traditional machine learning methods and overcome some of the main limitations imposed by the classical computing paradigm. However, the practical advantages of using quantum resources…

As in classical reversible computing, Quantum Arithmetic is typically seen as a set of tools that process binary data encoded into a quantum register to set the value of another quantum register. This article presents another approach to…