Related papers: Matrix product states and first quantization
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…
In this work, we present a novel representation of matrix product states (MPS) within the framework of quasi-local algebras. By introducing an enhanced compatibility condition, we enable the extension of finite MPS to an infinite-volume…
Out-of-equilibrium dynamics of non-integrable Hamiltonian many-body quantum systems are characterized by highly entangled wave functions. Near-maximal entanglement arises in systems exhibiting thermalization or pre-thermalization, where the…
We analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with fixed number parity yet not necessarily fixed particle number. The "mode entanglement" between one single-particle level and its…
We show how to efficiently simulate pure quantum states in one dimensional systems that have both finite energy density and vanishingly small energy fluctuations. We do so by studying the performance of a tensor network algorithm that…
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…
We introduce Gaussian Matrix Product States (GMPS), a generalization of Matrix Product States (MPS) to lattices of harmonic oscillators. Our definition resembles the interpretation of MPS in terms of projected maximally entangled pairs,…
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 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…
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…
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…
We introduce a general bipartite-like representation and Schmidt decomposition of an arbitrary pure state of $N$ indistinguishable fermions, based on states of $M<N$ and $(N-M)$ fermions. It is directly connected with the reduced $M$- and…
Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical post-processing resources growing exponentially…
We propose an alternative to the infinite density-matrix renormalization approach for accessing quantum many-body states within a finite-size calculation that faithfully mimics the thermodynamic limit. Our method constructs environment…
We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term…
Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many-body systems. For instance, they are…
We obtain an exact matrix-product-state (MPS) representation of a large series of fractional quantum Hall (FQH) states in various geometries of genus 0. The states in question include all paired k=2 Jack polynomials, such as the Moore-Read…
Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for…
We investigate ensembles of Matrix Product States (MPSs) generated by quantum circuit evolution followed by projection onto MPSs with a fixed bond dimension $\chi$. Specifically, we consider ensembles produced by: (i) random sequential…
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…