Related papers: Matrix Product State applications for the ALPS pro…
I introduce a modification of continuous matrix product states (CMPS) that makes them adapted to relativistic quantum field theories (QFT). These relativistic CMPS can be used to solve genuine 1+1 dimensional QFT without UV cutoff and…
We review White's density matrix renormalisation group method, an increasingly popular method for the solution of low dimensional quantum Hamiltonians. We describe some applications to frustrated spin systems, quantum critical phenomena,…
We investigate the relation between the scaling of block entropies and the efficient simulability by Matrix Product States (MPS), and clarify the connection both for von Neumann and Renyi entropies (see Table I). Most notably, even states…
Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes…
The canonical form of Matrix Product States (MPS) and the associated fundamental theorem, which relates different MPS representations of a state, are the theoretical framework underlying many of the analytical results derived through MPS,…
Ultrafast dynamics in chemical systems provide a unique access to fundamental processes at the molecular scale. A proper description of such systems is often very challenging because of the quantum nature of the problem. The concept of…
Matrix Product States (MPS) are used for the simulation of the real-time dynamics induced by an electric quench on the vacuum state of the massive Schwinger model. For small quenches it is found that the obtained oscillatory behavior of…
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 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…
As in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is…
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…
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…
In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that…
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…
Ground-state preparation is a fundamental task in quantum simulation, because the overlap of the prepared state with the true ground state significantly affects the overall cost of subsequent quantum algorithms. We propose a three-stage…
Matrix Product States form the basis of powerful simulation methods for ground state problems in one dimension. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the "area law". In…
Theoretical understanding of strongly correlated systems in one spatial dimension (1D) has been greatly advanced by the density-matrix renormalization group (DMRG) algorithm, which is a variational approach using a class of…
We present the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models…
Data representation in quantum state space offers an alternative function space for machine learning tasks. However, benchmarking these algorithms at a practical scale has been limited by ineffective simulation methods. We develop a quantum…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamical…