Related papers: The computational difficulty of finding MPS ground…

This paper introduces a Heisenberg picture approach to Matrix Product States (MPS), offering a rigorous yet intuitive framework to explore their structure and classification. MPS efficiently represent ground states of quantum many-body…

We prove that every injective Matrix Product State is the unique ground state of a simple hopping theory. We start by studying the low energy spectrum of parent Hamiltonians of injective Matrix Product States in a particular long range and…

Studies on quantum algorithms for ground state energy estimation often assume perfect ground state preparation; however, in reality the initial state will have imperfect overlap with the true ground state. Here we address that problem in…

For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can…

We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main new ingredient we introduce the superposed…

A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…

We investigate the ground states of 1D continuum models having short-range ferromagnetic type interactions and a wide class of competing longer-range antiferromagnetic type interactions. The model is defined in terms of an energy…

The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour…

We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement over the best…

Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While MPS are comprehensively understood, in…

Matrix Product States (MPS) and Operators (MPO) have been proven to be a powerful tool to study quantum many-body systems but are restricted to moderately entangled states as the number of parameters scales exponentially with the…

Nonstabilizerness, or `magic', is a critical quantum resource that, together with entanglement, characterizes the non-classical complexity of quantum states. Here, we address the problem of quantifying the average nonstabilizerness of…

Computing Gaussian ground states via variational optimization is challenging because the covariance matrices must satisfy the uncertainty principle, rendering constrained or Riemannian optimization costly, delicate, and thus difficult to…

We consider the computational complexity of Hamiltonians which are sums of commuting terms acting on plaquettes in a square lattice of qubits, and we show that deciding whether the ground state minimizes the energy of each local term…

Density Matrix Renormalization Group (DMRG) or Matrix Product States (MPS) are widely acknowledged as highly effective and accurate methods for solving one-dimensional quantum many-body systems. However, the direct application of DMRG to…

Working in a subspace with dimensionality much smaller than the dimension of the full Hilbert space, we deduce exact 4-particle ground states in 2D samples containing hexagonal repeat units and described by Hubbard type of models. The…

Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…

We study the problem of computing energy density in one-dimensional quantum systems. We show that the ground-state energy per site or per bond can be computed in time (i) independent of the system size and subexponential in the desired…

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…

Bosonic Gaussian states are ubiquitous in quantum optics and condensed matter physics. While they are efficiently handled within the Gaussian formalism, sampling requires calculating amplitudes in the boson occupation basis. This step,…