Related papers: Quantum complexity of the Kronecker coefficients
We establish a general framework for developing approximation algorithms for a class of counting problems. Our framework is based on the cluster expansion of abstract polymer models formalism of Koteck\'y and Preiss. We apply our framework…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.
Kronecker products of unitary Fourier matrices play important role in solving multilevel circulant systems by a multidimensional Fast Fourier Transform. They are also special cases of complex Hadamard (Zeilinger) matrices arising in many…
Centered kernel alignment (CKA) is a popular metric for comparing representations, determining equivalence of networks, and neuroscience research. However, CKA does not account for the underlying manifold and relies on numerous heuristics…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac-Moody algebra. As byproducts, we obtain a geometric realization of Lusztig's canonical bases of these representations as well…
The pursuit of quantum advantage in simulating many-body quantum systems on quantum computers has gained momentum with advancements in quantum hardware. This work focuses on leveraging the symmetry properties of these systems, particularly…
We provide an affirmative answer to the question posed in the title. Our argument is based on a treatment of the Schroedinger dynamics of the composite of a quantum microsystem, S, and a macroscopic measuring apparatus, I, consisting of N…
Quantum contextuality takes an important place amongst the concepts of quantum computing that bring an advantage over its classical counterpart. For a large class of contextuality proofs, aka. observable-based proofs of the Kochen-Specker…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
For a root system R, a field K and a "choice of coefficients in K" we define a category of graded spaces with operators and study some of its properties. Then we assume that the coefficients are given by quantum binomials. We use basic…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale…
Quantum communication devices, such as quantum repeaters, quantum memories, or quantum channels, are unavoidably exposed to imperfections. However, the presence of imperfections can be tolerated, as long as we can verify such devices retain…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
In theoretical machine learning, the statistical complexity is a notion that measures the richness of a hypothesis space. In this work, we apply a particular measure of statistical complexity, namely the Rademacher complexity, to the…
Quantum Neural Networks (QNNs) are suggested as one of the quantum algorithms which can be efficiently simulated with a low depth on near-term quantum hardware in the presence of noises. However, their performance highly relies on choosing…
The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved…