Related papers: The Bethe Ansatz as a Quantum Circuit
The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator…
The generic quantum $\tau_2$-model (also known as Baxter-Bazhanov-Stroganov (BBS) model) with periodic boundary condition is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix (solutions…
Consider a tensor product of finite-dimensional irreducible gl_{N+1}-modules and its decomposition into irreducible modules. The gl_{N+1} Gaudin model assigns to each multiplicity space of that decomposition a commutative (Bethe) algebra of…
I briefly review the recently proposed construction of the Bethe ansatz which diagonalizes the Hamiltonian for quantum strings on AdS_5\times S^5 at large tension and restricted to the large charge states from a closed su(2) subsector.
A class of $\mathfrak{o}_{2n+1}$-invariant quantum integrable models is investigated in the framework of algebraic Bethe ansatz method. A construction of the $\mathfrak{o}_{2n+1}$-invariant Bethe vector is proposed in terms of the Drinfeld…
This work presents a comprehensive benchmark and validation of a recently proposed method called Effective Bethe Ansatz (EBA). It is a variational method that deforms the exact Bethe wavefunctions of one-dimensional spin chains at…
The finite volume problem of O(2N) sigma models with integrable diagonal boundaries on a finite interval is investigated. The double row transfer matrix is diagonalized by Algebraic Bethe Ansatz. The boundary Bethe Yang equations for the…
Faults are stochastic by nature while most man-made systems, and especially computers, work deterministically. This necessitates the linking of probability theory with mathematical logics, automata, and switching circuit theory. This paper…
We present a quantum variational algorithm based on a novel circuit that generates all permutations that can be spanned by one- and two-qubits permutation gates. The construction of the circuits follows from group-theoretical results, most…
The variational quantum eigensolver (VQE) is an attracting possible application of near-term quantum computers. Originally, the aim of the VQE is to find a ground state for a given specific Hamiltonian. It is achieved by minimizing the…
Quantum computing is a new way of data processing based on the concept of quantum mechanics. Quantum circuit design is a process of converting a quantum gate to a series of basic gates and is divided into two general categories based on the…
In this work, we propose the first quantum Ans\"atze for the statistical relational learning on knowledge graphs using parametric quantum circuits. We introduce two types of variational quantum circuits for knowledge graph embedding.…
The process of translating a quantum algorithm into a form suitable for implementation on a quantum computing platform is crucial but yet challenging. This entails specifying quantum operations with precision, a typically intricate task. In…
The Bethe-Salpeter formalism in the instantaneous approximation for the interaction kernel entering into the Bethe-Salpeter equation represents a reasonable framework for the description of bound states within relativistic quantum field…
We set up a hydrodynamic description of the non-equilibrium dynamics of sine-Gordon quantum field theory for generic coupling. It is built upon an explicit form of the Bethe Ansatz description of general thermodynamic states, with the…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an…
One-loop corrections to the energy of semiclassical rotating strings contain both analytic and non-analytic terms in the 't Hooft coupling. Analytic contributions agree with the prediction from the string Bethe ansatz based on the classical…
Quantum circuit synthesis is the task of decomposing a given quantum operator into a sequence of elementary quantum gates. Since the finite target gate set cannot exactly implement any given operator, approximation is often necessary. Model…
We study an integrable vertex model with a periodic boundary condition associated with U_q(A_n^{(1)}) at the crystallizing point q=0. It is an (n+1)-state cellular automaton describing the factorized scattering of solitons. The dynamics…