Related papers: Matrix Product States for Quantum Many-Fermion Sys…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum…
We study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the…
We demonstrate how to simulate both discrete and continuous stochastic evolution of a quantum many body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a…
The variational determination of the two-fermion reduced density matrix is described for harmonically trapped, ultracold few-fermion systems in one dimension with equal spin populations. This is accomplished by formulating the problem as a…
Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…
The possibility of a matrix product representation for eigenstates with energy and momentum zero of a general m-state quantum spin Hamiltonian with nearest neighbour interaction and periodic boundary condition is considered. The quadratic…
We derive analytically the full distribution of the ground-state energy of $K$ non-interacting fermions in a disordered environment, modelled by a Hamiltonian whose spectrum consists of $N$ i.i.d.~random energy levels with distribution…
The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states can have broad impacts. Variational quantum algorithms are one…
The DMRG method is very effective at finding ground states of 1D quantum systems in practice, but it is a heuristic method, and there is no known proof for when it works. In this paper we describe an efficient classical algorithm which…
Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial…
We investigate the application of matrix product states to the Hubbard model in one spatial dimension with both of open and periodic boundary conditions. We develop the variatinal method that the optimization of the variational parameters…
Significant effort in applied quantum computing has been devoted to the problem of ground state energy estimation for molecules and materials. Yet, for many applications of practical value, additional properties of the ground state must be…
We propose a new version of the matrix product (MP) states approach to the description of quantum spin chains, which allows one to construct MP states with certain total spin and its z-projection. We show that previously known MP…
We introduce a generic method for computing groundstates that is applicable to a wide range of spatially anisotropic 2D many-body quantum systems. By representing the 2D system using a low-energy 1D basis set, we obtain an effective 1D…
By combining the continuous matrix product state (cMPS) representation for quantum fields in the continuum with standard optimization techniques for matrix product states (MPS) on the lattice, we obtain an approximation $|\Psi\rangle$,…
We present lattice results for the ground state energy of a spin-1/2 fermion system in the unitary limit, where the effective range of the interaction is zero and the scattering length is infinite. We compute the ground state energy for a…
We quantify how well matrix product states approximate exact ground states of 1-D quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density…
We investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low energy excitations using the formalism of tensor network…
We investigate the existence and the properties of fully separable (fully factorized) ground states in quantum spin systems. Exploiting techniques of quantum information and entanglement theory we extend a recently introduced method and…
We develop a numerical method based on matrix product states for simulating quantum many-body systems at finite temperatures without importance sampling and evaluate its performance in spin 1/2 systems. Our method is an extension of the…