Related papers: Matrix product state approximations to quantum sta…

Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.

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…

The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which…

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 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…

The advent of quantum computers promises exponential speed ups in the execution of various computational tasks. While their capabilities are hindered by quantum decoherence, they can be exactly simulated on classical hardware at the cost of…

While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of non-interacting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of…

Extending corresponding results for matrix product states [Verstraete and Cirac, PRB 73, 094423 (2006); Schuch et al. PRL 100, 030504 (2008)], it is shown how the approximation error of tree tensor network states (TTNS) can be bounded using…

Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…

The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], provides a powerful variational ansatz for the ground state of…

We explore the relation between the entanglement of a pure state and its energy variance for a local one dimensional Hamiltonian, as the system size increases. In particular, we introduce a construction which creates a matrix product state…

The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well…

Simulating quantum many-body systems (QMBS) is one of the long-standing, highly non-trivial challenges in condensed matter physics and quantum information due to the exponentially growing size of the system's Hilbert space. To date, tensor…

A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for…

We propose a way to construct a thermal pure quantum matrix product state (TPQ-MPS) that can simulate finite temperature quantum many-body systems with a minimal numerical cost comparable to the matrix product algorithm for the ground…

This work presents a method for studying low-energy physics in highly correlated magnetic systems using the matrix product state (MPS) manifold. We adapt the spin-wave approach, which has been very successful in modeling certain…

The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional…

It is expected that the statistical fluctuations of local observables in large quantum systems obey the central limit theorem, and approximate a normal distribution as their size grows. Here, we prove a version of the Berry-Esseen theorem…

Solving quantum many-body systems is one of the most significant regimes where quantum computing applies. Currently, as a hardware-friendly computational paradigms, variational algorithms are often used for finding the ground energy of…