相关论文: Virtual crystals and Kleber's algorithm

The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. These methods allow non-native problems to be adapted to the target annealer's architecture. The…

Using a finite-dimensional Clifford algebra a new combinatorial product formula for the small quantum cohomology ring of the complex Grassmannian is presented. In particular, Gromov-Witten invariants can be expressed through certain…

A systematic theory of product and diagonal states is developed for tensor products of $\mathbb Z_2$-graded $*$-algebras, as well as $\mathbb Z_2$-graded $C^*$-algebras. As a preliminary step to achieve this goal, we provide the…

Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…

In this paper we study a family of commutative algebras generated by two infinite sets of generators. These algebras are parametrized by Young diagrams. We explain a connection of these algebras with the fusion product of integrable…

This paper is about establishing a natural connection of quantum affine algebras with quantum vertex algebras. Among the main results, we establish $\hbar$-adic versions of the smash product construction of quantum vertex algebras and their…

In this paper we give a direct proof of the equality of certain generating function associated with tensor product multiplicities of Kirillov-Reshetikhin modules for each simple Lie algebra g. Together with the theorems of Nakajima and…

The X=M conjecture of Hatayama et al. asserts the equality between the one-dimensional configuration sum X expressed as the generating function of crystal paths with energy statistics and the fermionic formula M for all affine Kac--Moody…

We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to…

Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most…

In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads to so-called rack bialgebra. We construct canon-ical rack bialgebras (some kind of enveloping algebras) for any Leibniz algebra. Our motivation…

By means of contractions of Lie algebras, we obtain new classes of indecomposable quasi-classical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise…

Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of…

The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the…

Quantum simulation of fermionic systems is a promising application of quantum computers, but in order to program them, we need to map fermionic states and operators to qubit states and quantum gates. While quantum processors may be built as…

We construct the Fock space representations of classical quantum affine algebras using combinatorics of Young walls. We also show that the crystal graphs of the Fock space representations can be realized as the abstract crystal consisting…

For an affine algebra of nonexceptional type in the large rank we show the fermionic formula depends only on the attachment of the node 0 of the Dynkin diagram to the rest, and the fermionic formula of not type A can be expressed as a sum…

In proving the Fermionic formulae, combinatorial bijection called the Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a bijection between the set of highest paths and the set of rigged configurations. In this…

Verlinde's formula for rational vertex operator algebras computes the fusion rules from the modular transformations of characters. In the non semisimple and non finite case, a logarithmic Verlinde formula has been proposed together with…

Frenkel and Reshetikhin introduced q-characters to study finite dimensional representations of quantum affine algebras. In the simply laced case Nakajima defined deformations of q-characters called q,t-characters. The definition is…