Related papers: Quantum character varieties
The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine…
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
We study the cohomology of $G$-representation varieties and $G$-character stacks by means of a topological quantum field theory (TQFT). This TQFT is constructed as the composite of a so-called field theory and the 6-functor formalism of…
This paper surveys the field of quantum communication complexity. Some interesting recent results are collected concerning relations to classical communication, lower bound methods, one-way communication, and applications of quantum…
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…
We first consider a method of centering and a change of variable formula for a quantum integral. We then present three types of quantum integrals. The first considers the expectation of the number of heads in $n$ flips of a "quantum coin".…
This is a short introduction to quantum computers, quantum algorithms and quantum error correcting codes. Familiarity with the principles of quantum theory is assumed. Emphasis is put on a concise presentation of the principles avoiding…
A new quantum cryptography protocol, based on all unselected states of a qubit as a sort of alphabet with continuous set of letters, is proposed. Its effectiveness is calculated and shown to be essentially higher than those of the other…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
We compute quantum character varieties of arbitrary closed surfaces with boundaries and marked points. These are categorical invariants $\int_S\mathcal A$ of a surface $S$, determined by the choice of a braided tensor category $\mathcal A$,…
The notion of quantized characters is introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for compact quantum groups. As in the case of ordinary groups, the…
We propose a theory of characterizing quantum circuits with qubit functional configurations. Any quantum circuit can be decomposed into alternating sequences of 1-qubit unitary gates and CNOT gates. Each CNOT sequence prepares the current…
A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.
Local unitary invariance and the notion of negativity fonts are used as the principle tools to construct four qubit invariants of degree 8, 12, and 24. A degree 8 polynomial invariant that is non-zero on pure four qubit states with…
In this paper I will investigate geometrical structures of multipartite quantum systems based on complex projective varieties. These varieties are important in characterization of quantum entangled states. In particular I will establish…
Quantum communication is an important application that derives from the burgeoning field of quantum information and quantum computation. Focusing on secure communication, quantum cryptography has two major directions of development, namely…
X states are a broad class of two-qubit density matrices that generalize many states of interest in the literature. In this work, we give a comprehensive account of various quantum properties of these states, such as entanglement,…
This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief…
This text aims to present and explain quantum machine learning algorithms to a data scientist in an accessible and consistent way. The algorithms and equations presented are not written in rigorous mathematical fashion, instead, the…
I provide an introduction to quantum computers, describing how they might be realized using language accessible to a solid state physicist. A listing of the minimal requirements for creating a quantum computer is given. I also discuss…