Related papers: Sequentially generated states for the study of two…
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…
Recently it has been shown that projected entangled-pair states can be considered as a (physically motivated) resource state for measurement-based quantum computation. Here we elaborate on how to construct a deterministic measurement-based…
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 (MPS) and Tensor Networks provide a general framework for the construction of solvable models. The best-known example is the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, which is the ground state of a 2-body…
Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…
We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs…
We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties.…
We define a new family of matrix product states which are exact ground states of spin 1/2 Hamiltonians on one dimensional lattices. This class of Hamiltonians contain both Heisenberg and Dzyaloshinskii-Moriya interactions but at specified…
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…
We introduce a new class of continuous matrix product (CMP) states and establish the stochastic master equations (quantum filters) for an arbitrary quantum system probed by a bosonic input field in this class of states. We show that this…
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem and characterize the set of effectively…
We find the nearest product states for arbitrary generalized W states of n qubits, and show that the nearest product state is essentially unique if the W state is highly entangled. It is specified by a unit vector in Euclidean n-dimensional…
Matrix models, as quantum mechanical systems without explicit spatial dependence, provide valuable insights into higher-dimensional gauge and gravitational theories, especially within the framework of string theory, where they can describe…
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…
Slater determinants are product states of filled quantum fermionic orbitals. When they are expressed in a configuration space basis chosen a priori, their entanglement is bound and controlled. This suggests that an exact representation of…
Stationary states of stochastic models, which have $N$ states per site, in matrix product form are considered. First we give a necessary condition for the existence of a finite $M$-dimensional matrix product state for any ${N,M}$. Second,…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…
Matrix-product unitaries (MPU) are 1D tensor networks describing time evolution and unitary symmetries of quantum systems, while their action on states by construction preserves the entanglement area law. MPU which are formed by a single…
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…
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…