Related papers: Quantum dilogarithms and partition q-series
We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking orders. Our finding…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
Tilting mutation is a way of producing new tilting complexes from old ones replacing only one indecomposable summand. In this paper, we give a purely combinatorial procedure for performing tilting mutation of suitable algebras. As an…
Let $\Lambda$ be the set of partitions of length $\geq 0$. We introduce an $\mathbb{N}$-graded algebra $\mathbb{A}_q^d(\Lambda)$ associated to $\Lambda$, which can be viewed as a quantization of the algebra of partitions defined by Reineke.…
We consider the mixed states of the bipartite quantum system with the first party a qubit and the second a qutrit. The group of local unitary transformations of the system, ignoring the overall phase factor, is the direct product G of SU(2)…
In this note we review some of the uses of framed quivers to study BPS invariants of Donaldson-Thomas type. We will mostly focus on non-compact Calabi-Yau threefolds. In certain cases the study of these invariants can be approached as a…
In this paper, we extend past work done on the application of the mathematics of category theory to quantum information science. Specifically, we present a realization of a dagger-compact category that can model finite-dimensional quantum…
This paper introduces the quantum deep sets model, expanding the quantum machine learning tool-box by enabling the possibility of learning variadic functions using quantum systems. A couple of variants are presented for this model. The…
Machine learning has emerged as a promising approach to study the properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods$-$such as Monte Carlo$-$which…
We show that the refined Donaldson-Thomas invariants of C3, suitably normalized, have a Gaussian distribution as limit law. Combinatorially these numbers are given by weighted counts of 3D partitions. Our technique is to use the…
Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry and statistics. Traditional solution methods such as Gaussian elimination become very time…
We address the task of higher-order derivative evaluation of computer programs that contain QR decompositions and real symmetric eigenvalue decompositions. The approach is a combination of univariate Taylor polynomial arithmetic and matrix…
Although QR iterations dominate in eigenvalue computations, there are several important cases when alternative LR-type algorithms may be preferable. In particular, in the symmetric tridiagonal case where differential qd algorithm with…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
As part of our study of the $q$-tetrahedron algebra $\boxtimes_q$ we introduce the notion of a $q$-inverting pair. Roughly speaking, this is a pair of invertible semisimple linear transformations on a finite-dimensional vector space, each…
We define mutation on coloured quivers associated to tilting objects in higher cluster categories. We show that this operation is compatible with the mutation operation on the tilting objects. This gives a combinatorial approach to tilting…
A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert scheme-type) framed versions of quiver moduli is derived. This is applied to…
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09, arXiv:0811.3171] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical…
In this paper we give a geometric construction of the quantum group Ut(G) using Nakajima categories, which were developed in [29]. Our methods allow us to establish a direct connection between the algebraic realization of the quantum group…