Related papers: A generalization of quantum Lakshmibai-Seshadri pa…
Large Language Models (LLMs) typically rely on a large number of parameters for token embedding, leading to substantial storage requirements and memory footprints. In particular, LLMs deployed on edge devices are memory-bound, and reducing…
The rapid evolution of artificial intelligence has driven interest in Long Short-Term Memory (LSTM) networks for their effectiveness in processing sequential data. However, traditional LSTMs are limited by issues such as the vanishing…
We develop an abstract framework for the investigation of quantization and dequantization procedures based on orthogonality relations that do not necessarily involve group representations. To illustrate the usefulness of our abstract method…
Subsystems of entangled quantum systems are not traditionally described in a local way. This paper begins to address the issue by constructing an explicit local hidden variable theory for quantum subsystems. The interpretation is based on a…
Classification using variational quantum circuits is a promising frontier in quantum machine learning. Quantum supervised learning (QSL) applied to classical data using variational quantum circuits involves embedding the data into a quantum…
The path space of an inhomogeneous vertex model constructed from the vector representation of $U_q\bigl(gl(2|2)\bigr)$ and its dual is studied for various choices of composite vertices and assignments of $gl(2|2)$-weights. At $q=0$, the…
We consider the quantum Gelfand invariants which first appeared in a landmark paper by Reshetikhin, Takhtadzhyan and Faddeev (1989). We calculate the eigenvalues of the invariants acting in irreducible highest weight representations of the…
We introduce several probabilistic quantum algorithms that overcome the normal unitary restrictions in quantum machine learning by leveraging the Linear Combination of Unitaries (LCU) method. Among our investigations are quantum native…
A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…
A class of highest weight irreducible representations of the algebra $U_h(A_\infty)$, the quantum analogue of the completion and central extension $A_\infty$ of the Lie algebra $gl_\infty$, is constructed. It is considerably larger than the…
Missing data presents a critical challenge in real-world datasets, significantly degrading the performance of machine learning models. While Large Language Models (LLMs) have recently demonstrated remarkable capabilities in tabular data…
A recent article by Ivander, Lindoy and Lee [Nature Communications 15, 8087 (2024)] claims to discover the relationship between the generalized quantum master equation (GQME) and the path integral for a system coupled to a harmonic bath.…
Quantum algorithms can enhance machine learning in different aspects. In 2014, Rebentrost $et~al.$ constructed a least squares quantum support vector machine (LS-QSVM), in which the Swap Test plays a crucial role in realizing the…
We construct an Abel-Jacobi type map on the homologically trivial part of Lawson homology groups. It generalizes the Abel-Jacobi map constructed by Griffiths. By using a result of H. Clemens, we give some examples of smooth projective…
We study finite-rank left-translation invariant algebraic $D$-modules on complex affine algebraic groups. Using the standard description of these objects as left-invariant flat algebraic connections on the trivial vector bundle, modulo…
In the framework of algebraic supergeometry, we give a construction of the scheme-theoretic supergeometric analogue of Chevalley groups, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. In…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
Maximum a posteriori (MAP) inference is an important task for graphical models. Due to complex dependencies among variables in realistic model, finding an exact solution for MAP inference is often intractable. Thus, many approximation…
We aim to construct a non-commutative algebraic geometry by using generalised valuations. To this end, we introduce groupoid valuation rings and associate suitable value functions to them. We show that these objects behave rather like their…
We construct for each choice of a quiver $Q$, a cohomology theory $A$ and a poset $P$ a "loop Grassmannian" $\mathcal{G}^P(Q,A)$. This generalizes loop Grassmannians of semisimple groups and the loop Grassmannians of based quadratic forms.…