Related papers: MPS Stability and the Intersection Property
Recently it was shown that continuous Matrix Product States (cMPS) cannot express the continuum limit state of any Matrix Product State (MPS), according to a certain natural definition of the latter. The missing element is a projector in…
We show how local bounded interactions in an unbounded Hamiltonian lead to eigenfunctions with favorable low-rank properties. To this end, we utilize ideas from quantum entanglement of multi-particle spin systems. We begin by analyzing the…
This note establishes the Exponential Input-to-State Stability (EISS) property for a clamped-free damped string with respect to distributed and boundary disturbances. While efficient methods for establishing ISS properties for distributed…
We will prove certain general relations in Matrix Product Ansatz for one dimensional stochastic systems, which are true in both random and sequential updates. We will derive general MPA expressions for the currents and current correlators…
We show that the BPS property is a generic feature of field theories in (1+1) dimensions, which does not put any restriction on the action. Here, by BPS solutions we understand static solutions which i) obey a lower-order Bogomolny-type…
While highly entangled ground states of gapless local Hamiltonians have been known to exist in one dimension, their two-dimensional counterparts were only recently found, with rather sophisticated interactions involving at least four…
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States…
We consider the simplest inhomogeneous Matrix-Product-State for an open chain of N quantum spins that involves only two angles per site and two angles per bond with the following direct physical meanings. The two angles associated to the…
Let $\{f_\mu\}_{\mu \in \mathbb{D}}$ be a family of automorphisms of $\mathbb{C}^2$ unfolding a generic homoclinic tangency associated to a fixed point $p$ belonging to a horseshoe. We prove that if the linearized versions of the Cantor…
A large, or even infinite, local Hilbert space dimension poses a significant computational challenge for simulating quantum systems. In this work, we present a matrix product state (MPS)-based method for simulating one-dimensional quantum…
The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that ensure closed-loop performance bounds and boundedness of the…
When the state of a system may remain bounded even if both the input amplitude and energy are unbounded, then the state bounds given by the standard input-to-state stability (ISS) and integral-ISS (iISS) properties may provide no useful…
We consider an initial-boundary value problem for the Maxwell's system in a bounded domain with a linear inhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver-Muller-type boundary feedback mechanism…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
A class of vector coherent states is derived with multiple of matrices as vectors in a Hilbert space, where the Hilbert space is taken to be the tensor product of several other Hilbert spaces. As examples vector coherent states with…
Suppose we would like to approximate all local properties of a quantum many-body state to accuracy $\delta$. In one dimension, we prove that an area law for the Renyi entanglement entropy $R_\alpha$ with index $\alpha<1$ implies a matrix…
The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
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…
Symmetry is central to how we classify phases of matter: solids break spatial translations, superfluids break particle-number conservation, and superconductors "break" gauge symmetry. Mixed anomalies involving higher-form symmetries,…