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We describe a simple method to find the ground state energy without calculating the expectation value of the Hamiltonian in the time-evolving block decimation algorithm with tensor network states. For example, we consider quantum…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
For an interacting spatio-temporal lattice system we introduce a formal way of expressing multi-time correlation functions of local observables located at the same spatial point with a time state, i.e. a statistical distribution of…
The matrix product state (MPS) belongs to the most important mathematical models in, for example, condensed matter physics and quantum information sciences. However, to realize an $N$-qubit MPS with large $N$ and large entanglement on a…
Determining the low-energy eigenspectra of quantum many-body systems is a long-standing challenge in physics. In this work, we solve this problem by introducing two novel algorithms to determine low-energy eigenstates based on a compact…
Matrix product states (MPS) are a central language for one-dimensional quantum matter and a practical target for near-term quantum simulators and variational algorithms. Yet, while substantial effort has focused on preparing MPS with…
We present a new subspace iteration method for computing low-lying eigenpairs (excited states) of high-dimensional quantum many-body Hamiltonians with nearest neighbor interactions on two-dimensional lattices. The method is based on a new…
With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the…
Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors of the local effective Hamiltonian that is constructed from…
We derive an exact formula for a matrix product state (MPS) representation (or a PEPS in higher number of dimensions) of the ground state of translationally invariant bosonic lattice systems in terms of a single one-dimensional Euclidean…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in…
Matrix-product states (MPS) have proven to be a versatile ansatz for modeling quantum many-body physics. For many applications, and particularly in one-dimension, they capture relevant quantum correlations in many-body wavefunctions while…
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…
Resolving unsteady transport phenomena in geometrically complex domains is traditionally constrained by polynomial scaling of computational cost with spatial resolution. While methods based on tensor-network data representations or…
We present a variational matrix product state (vMPS) for the ground state of the spin-1/2 Heisenberg model. The MPS effectively organizes the various dimer configurations, in faithful reflection of the resonating valence bond (RVB) picture…
We propose a multireference linearized coupled cluster theory using matrix product states (MPS-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration…
Motivated by the existence of exact many-body quantum scars in the AKLT chain, we explore the connection between Matrix Product State (MPS) wavefunctions and many-body quantum scarred Hamiltonians. We provide a method to systematically…
While much is known about the entanglement characteristics of ground states, the properties of reduced thermal density matrices have received significantly less attention. Here we investigate the entanglement content of reduced thermal…