相关论文: Spectral gaps of AKLT Hamiltonians using Tensor Ne…

In these lecture notes, we present a pedagogical review of a number of related {\it numerically exact} approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix…

In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement…

We propose a tensor-network algorithm for discrete-time stochastic dynamics of a homogeneous system in the thermodynamic limit. We map a $d$-dimensional nonequilibrium Markov process to a $(d+1)$-dimensional infinite tensor network by using…

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…

We reconstruct entanglement thermodynamics by means of Hessian geometry, since this method exactly generalizes thermodynamics into much wider exponential family cases including quantum entanglement. Starting with the correct first law of…

In this paper, we consider the network latency estimation, which has been an important metric for network performance. However, a large scale of network latency estimation requires a lot of computing time. Therefore, we propose a new method…

The mapping between gate voltages applied to a double quantum dot, and the parameters of a Hubbard-like Hamiltonian, is of utmost importance for understanding and operating spin qubits. State-of-the-art techniques for measuring Hamiltonian…

Network structures are reconstructed from dynamical data by respectively naive mean field (nMF) and Thouless-Anderson-Palmer (TAP) approximations. For TAP approximation, we use two methods to reconstruct the network: a) iteration method; b)…

We give a new proof for the area law for general 1D gapped systems, which exponentially improves Hastings' famous result \cite{ref:Has07}. Specifically, we show that for a chain of d-dimensional spins, governed by a 1D local Hamiltonian…

We devise a quantum-circuit algorithm to solve the ground state and ground energy of artificial graphene. The algorithm implements a Trotterized adiabatic evolution from a purely tight-binding Hamiltonian to one including kinetic,…

Generalized network tomography (GNT) deals with estimation of link performance parameters for networks with arbitrary topologies using only end-to-end path measurements of pure unicast probe packets. In this paper, by taking advantage of…

The algebraic Bethe Ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations.…

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the…

We study discounted Hamilton Jacobi equations on networks, without putting any restriction on their geometry. Assuming the Hamiltonians continuous and coercive, we establish a comparison principle and provide representation formulae for…

Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair…

Formulating non-Abelian gauge theories as a tensor network is known to be challenging due to the internal degrees of freedom that result in the degeneracy in the singular value spectrum. In two dimensions, it is straightforward to 'trace…

Thermalization and its breakdown in interacting quantum many-body systems are governed by mid-spectrum eigenstates, which are typically accessible only in small system sizes amenable to exact diagonalization. Here we demonstrate that the…

Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states…

Symmetry protected topological (SPT) phases with gapless edge excitations have been shown to exist in principle in strongly interacting bosonic/fermionic systems and it is highly desirable to find practical systems to realize such phases…

We study the Riemannian geometry of the Deep Linear Network (DLN) as a foundation for a thermodynamic description of the learning process. The main tools are the use of group actions to analyze overparametrization and the use of Riemannian…