Related papers: Towards structure-preserving quantum encodings
Complex quantum circuits are constituted by combinations of quantum subroutines. The computation is possible as long as the quantum data encoding is consistent throughout the circuit. Despite its fundamental importance, the formalization of…
Generalisation in machine learning often relies on the ability to encode structures present in data into an inductive bias of the model class. To understand the power of quantum machine learning, it is therefore crucial to identify the…
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…
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
Given a data set with a notion of distance, such as a point cloud in Euclidean space, topological data analysis (TDA) uses techniques from algebraic topology and metric geometry to infer the topology of a hypothetical manifold from which…
Quantum machine learning deals with leveraging quantum theory with classic machine learning algorithms. Current research efforts study the advantages of using quantum mechanics or quantum information theory to accelerate learning time or…
Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
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 rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
Geometric quantum machine learning uses the symmetries inherent in data to design tailored machine learning tasks with reduced search space dimension. The field has been well-studied recently in an effort to avoid barren plateau issues…
Leveraging the extraordinary phenomena of quantum superposition and quantum correlation, quantum computing offers unprecedented potential for addressing challenges beyond the reach of classical computers. This paper tackles two pivotal…
It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this…
When creating a quantum system whose natural dynamics provide useful computational operations, designers have two key tools at their disposal: the (constrained) choice of both the Hamiltonian and the the initial state of the system (an…
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…
Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…
Interest in quantum machine learning is increasingly growing due to its potential to offer more efficient solutions for problems that are difficult to tackle with classical methods. In this context, the research work presented here focuses…
We present a notion of geometry encoding suitable for machine learning-based numerical simulation. In particular, we delineate how this notion of encoding is different than other encoding algorithms commonly used in other disciplines such…
Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…