Related papers: Big data comparison of quantum invariants
We introduce a new class of quantum enhancements we call biquandle brackets, which are customized skein invariants for biquandle colored links.Quantum enhancements of biquandle counting invariants form a class of knot and link invariants…
In this paper we give a quantum statistical interpretation for the bracket polynomial state sum <K> and for the Jones polynomial. We use this quantum mechanical interpretation to give a new quantum algorithm for computing the Jones…
The quantification of the quantumness of a quantum ensemble has theoretical and practical significance in quantum information theory. We propose herein a class of measures of the quantumness of quantum ensembles using the unitary similarity…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
The usual way to reveal properties of an unknown quantum state, given many copies of a system in that state, is to perform measurements of different observables and to analyze the measurement results statistically. Here we show that the…
It has been argued based on electric-magnetic duality and other ingredients that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four dimensions. Here, we…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
We present a scalable method for the tomography of large multiqubit quantum registers. It acquires information about the permutationally invariant part of the density operator, which is a good approximation to the true state in many,…
Current quantum systems have significant limitations affecting the processing of large datasets with high dimensionality, typical of high energy physics. In the present paper, feature and data prototype selection techniques were studied to…
In an era where data underpins decision-making across science, politics, and economics, ensuring high data quality is of paramount importance. Conventional computing algorithms for enhancing data quality, including anomaly detection, demand…
Given any diagram of a link, we define on the cube of Kauffman's states a "2-complex" whose homology is an invariant of the associated framed links, and such that the graded Euler characteristic reproduces the unnormalized Kauffman bracket.…
We present networks for directly estimating the polynomial invariants of multi-party quantum states under local transformations. The structure of these networks is closely related to the structure of the invariants themselves and this lends…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
The pioneering work of Jones and Kauffman unveiled a fruitful relationship between statistical mechanics and knot theory. Recently, Jones introduced two subgroups $\vec{F}$ and $\vec{T}$ of the Thompson groups $F$ and $T$, respectively,…
Quantum machine learning has gained considerable attention as quantum technology advances, presenting a promising approach for efficiently learning complex data patterns. Despite this promise, most contemporary quantum methods require…
We provide a review of the experimental and theoretical research in the field of quantum tomography with an emphasis on recently developed adaptive protocols. Several statistical frameworks for adaptive experimental design are discussed. We…
We present an algorithm to determine topological invariants of inhomogeneous systems, such as alloys, disordered crystals, or amorphous systems. Based on the kernel polynomial method, our algorithm allows us to study samples with more than…
In this paper, we give a description of a recent quantum algorithm created by Aharonov, Jones, and Landau for approximating the values of the Jones polynomial at roots of unity of the form exp(2$\pi$i/k). This description is given with two…
In this paper we show that coloured Jones and coloured Alexander polynomials can both be read off from the same picture provided by two Lagrangians in a symmetric power of a surface. More specifically, the $N^{th}$ coloured Jones and…
Based on different views on the Jones polynomial we review representation theoretic categorified link and tangle invariants. We unify them in a common combinatorial framework and connect them via the theory of Soergel bimodules. The…