Related papers: Quantum complexity of the Kronecker coefficients
Kostka numbers and Littlewood-Richardson coefficients play an essential role in the representation theory of the symmetric groups and the special linear groups. There has been a significant amount of interest in their computation. The issue…
Important quantum algorithm routines allow the implementation of specific quantum operations (a.k.a. gates) by combining basic quantum circuits with an iterative structure. In this structure, the number of repetitions of the basic circuit…
We discuss symmetric quantum measurements and the associated covariant observables modelled, respectively, as instruments and positive-operator-valued measures. The emphasis of this work are the optimality properties of the measurements,…
In recent years, quantum computers have emerged as promising candidates for implementing kernels. Quantum Embedding Kernels embed data points into quantum states and calculate their inner product in a high-dimensional Hilbert Space by…
Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…
Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in…
Approximating convex bodies succinctly by convex polytopes is a fundamental problem in discrete geometry. A convex body $K$ of diameter $\mathrm{diam}(K)$ is given in Euclidean $d$-dimensional space, where $d$ is a constant. Given an error…
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…
We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries…
We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…
We study how efficiently a $k$-element set $S\subseteq[n]$ can be learned from a uniform superposition $|S\rangle$ of its elements. One can think of $|S\rangle=\sum_{i\in S}|i\rangle/\sqrt{|S|}$ as the quantum version of a uniformly random…
Let $\mathbb{X}_{\boldsymbol{p},\boldsymbol{\lambda}}$ be a weighted projective line. We define the quantum cluster algebra of $\mathbb{X}_{\boldsymbol{p},\boldsymbol{\lambda}}$ and realize its specialized version as the subquotient of the…
In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. The truncated Wigner…
The learnable, linear neural network layers between tensor power spaces of $\mathbb{R}^{n}$ that are equivariant to the orthogonal group, $O(n)$, the special orthogonal group, $SO(n)$, and the symplectic group, $Sp(n)$, were characterised…
The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is…
Kernel quadratures and other kernel-based approximation methods typically suffer from prohibitive cubic time and quadratic space complexity in the number of function evaluations. The problem arises because a system of linear equations needs…
Performing efficient quantum computer tuneup and calibration is essential for growth in system complexity. In this work we explore the link between facilitating such capabilities and the underlying architecture of the physical hardware. We…
We show that the Kronecker coefficients (the Clebsch-Gordan coefficients of the symmetric group) indexed by two two-row shapes are given by quadratic quasipolynomial formulas whose domains are the maximal cells of a fan. Simple calculations…
In a celebrated paper, Valiant and Vazirani raised the question of whether the difficulty of NP-complete problems was due to the wide variation of the number of witnesses of their instances. They gave a strong negative answer by showing…
In this paper we consider a problem of the similarity of complex symmetric operators to perturbations of restrictions of normal operators. For a subclass of cyclic complex symmetric operators in a finite-dimensional Hilbert space we prove…