Related papers: Learning and Inference in Hilbert Space with Quant…
Hidden Markov models (HMM) are commonly used in generation tasks and have demonstrated strong capabilities in neuro-symbolic applications for the Markov property. These applications leverage the strengths of neural networks and symbolic…
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…
The discrepancy between quantum distinguishability in Hilbert space and classical distinguishability in probability space is expressed by the gap between the quantum and classical Fisher information matrices (QFIM and CFIM, respectively).…
Accurate amine property prediction is essential for optimizing CO2 capture efficiency in post-combustion processes. Quantum machine learning (QML) can enhance predictive modeling by leveraging superposition, entanglement, and interference…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
Determining the ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and combinatorial optimization, yet it is often classically intractable due to the exponential growth of Hilbert space with system size.…
Quantum kernel methods are a promising method in quantum machine learning thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their…
Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this…
The importance of analyzing nontrivial datasets when testing quantum machine learning (QML) models is becoming increasingly prominent in literature, yet a cohesive framework for understanding dataset characteristics remains elusive. In this…
Quantum computers offer the potential for efficiently sampling from complex probability distributions, attracting increasing interest in generative modeling within quantum machine learning. This surge in interest has driven the development…
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…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
A non-Hermitian operator $H$ defined in a Hilbert space with inner product $\langle\cdot|\cdot\rangle$ may serve as the Hamiltonian for a unitary quantum system, if it is $\eta$-pseudo-Hermitian for a metric operator (positive-definite…
The problem of knowledge graph (KG) reasoning has been widely explored by traditional rule-based systems and more recently by knowledge graph embedding methods. While logical rules can capture deterministic behavior in a KG they are brittle…
Quantum Computing (QC) offers outstanding potential for molecular characterization and drug discovery, particularly in solving complex properties like the Ground State Energy (GSE) of biomolecules. However, QC faces challenges due to…
Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike. Its extension into the quantum regime has been the object of several recent works. These quantum versions of Bayes' rule have been expressed…
The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective…
Machine learning algorithms based on parametrized quantum circuits are prime candidates for near-term applications on noisy quantum computers. In this direction, various types of quantum machine learning models have been introduced and…
To accelerate the process of materials design, materials science has increasingly used data driven techniques to extract information from collected data. Specially, machine learning (ML) algorithms, which span the ML discipline, have…
Hidden Markov Models are widely used in classical computer science to model stochastic processes with a wide range of applications. This paper concerns the quantum analogues of these machines --- so-called Hidden Quantum Markov Models…