Related papers: Quantum Geometry of Data
Quantum geometry characterizes the variation of wavefunctions in momentum space through their overlaps and relative phases, providing a general framework for understanding many transport and optical properties. It is generally formulated in…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
Machine Learning (ML) has been widely applied across numerous domains due to its ability to automatically identify informative patterns from data for various tasks. The availability of large-scale data and advanced computational power…
The rapid advancements in quantum computing (QC) and machine learning (ML) have sparked significant interest, driving extensive exploration of quantum machine learning (QML) algorithms to address a wide range of complex challenges. The…
One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of…
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…
Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials science, statistical mechanics, quantum information,…
Quantum kernels quantify similarity between data points by measuring the inner product between quantum states, computed through quantum circuit measurements. By embedding data into quantum systems, quantum kernel feature maps, that may be…
Machine learning and quantum computing are two technologies that are causing a paradigm shift in the performance and behavior of certain algorithms, achieving previously unattainable results. Machine learning (kernel classification) has…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
Quantum Machine Learning (QML) presents as a revolutionary approach to weather forecasting by using quantum computing to improve predictive modeling capabilities. In this study, we apply QML models, including Quantum Gated Recurrent Units…
I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…
Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum information processing. In the HQC strategy information is encoded in degenerate eigen-spaces of a parametric family of Hamiltonians. The computational network of…
In the last few years, quantum computing has experienced a growth spurt. One exciting avenue of quantum computing is quantum machine learning (QML) which can exploit the high dimensional Hilbert space to learn richer representations from…
We demonstrate how one can use machine learning techniques to bypass the technical difficulties of designing an experiment and translating its outcomes into concrete claims about fundamental features of quantum fields. In practice, all…
Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this Review, we provide a structured overview of recent advances that bridge foundational…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study of their quantum counterparts. These quantum graphical…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
Quantum machine learning (QML) has great potential for the analysis of chemical datasets. However, conventional quantum data-encoding schemes, such as fingerprint encoding, are generally unfeasible for the accurate representation of…