Related papers: Unknot Recognition Through Quantifier Elimination
A textile structure is a periodic arrangement of threads in the thickened plane. A topological classification of textile structures is harder than for classical knots and links that are non-periodic and restricted to a bounded region. The…
We consider the entanglement entropy for a spacetime region and its spacelike complement in the framework of algebraic quantum field theory. For a M\"obius covariant local net satisfying a certain nuclearity property, we consider the von…
We prove that any arc-presentation of the unknot admits a monotonic simplification by elementary moves; this yields a simple algorithm for recognizing the unknot. We obtain similar results for split links and composite links.
We show that the genus problem for alternating knots with $n$ crossings has linear time complexity and is in Logspace$(n)$. Almost all alternating knots of given genus possess additional combinatorial structure, we call them standard. We…
We present a numerical method for solving the separability problem of Gaussian quantum states in continuous-variable quantum systems. We show that the separability problem can be cast as an equivalent problem of determining the feasibility…
In the classical knot theory there is a well-known notion of descending diagram. From an arbitrary diagram one can easily obtain, by some crossing changes, a descending diagram which is a diagram of the unknot or unlink. In this paper the…
We consider an atom-cavity system having long-range atomic interactions mediated by cavity modes. It has been shown that quantum simulations of spin models with this system can naturally be used to solve number partition problems. Here, we…
Processing qubit Hamiltonians derived from electronic-structure problems can become classically prohibitive because many downstream manipulations still rely on dense operator constructions whose cost grows exponentially with qubit number.…
We introduce a notion of intrinsic linking and knotting for virtual spatial graphs. Our theory gives two filtrations of the set of all graphs, allowing us to measure, in a sense, how intrinsically linked or knotted a graph is; we show that…
Smoothed analysis is a powerful paradigm in overcoming worst-case intractability in unsupervised learning and high-dimensional data analysis. While polynomial time smoothed analysis guarantees have been obtained for worst-case intractable…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…
A bottleneck for analyzing the interplay between magic and entanglement is the computation of these quantities in highly entangled quantum many-body magic states. Efficient extraction of entanglement can also inform our understanding of…
A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the knot. Knots are typically encoded by…
The impossibility of creating perfect identical copies of unknown quantum systems is a fundamental concept in quantum theory and one of the main non-classical properties of quantum information. This limitation imposed by quantum mechanics,…
As the demand for exercising the "right to be forgotten" grows, the need for verifiable machine unlearning has become increasingly evident to ensure both transparency and accountability. We present {\em zkUnlearner}, the first…
Zonotopes are becoming an increasingly popular set representation for formal verification techniques. This is mainly due to their efficient representation and their favorable computational complexity of important operations in…
Let $M_n$ be the topological moduli space of all parallel n-cables of long framed oriented knots in 3-space. We construct in a combinatorial way for each natural number $n>1$ a 1-cocycle $R_n$ which represents a non trivial class in…
We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
A computationally challenging classical elimination theory problem is to compute polynomials which vanish on the set of tensors of a given rank. By moving away from computing polynomials via elimination theory to computing pseudowitness…