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MiS Preprint
38/2019

Uniform matrix product states from an algebraic geometer's point of view

Adam Czapliński, Mateusz Michałek and Tim Seynnaeve

Abstract

We apply methods from algebraic geometry to study uniform matrix product states. Our main results concern the topology of the locus of tensors expressed as uMPS, their defining equations and identifiability. By an interplay of theorems from algebra, geometry and quantum physics we answer several questions and conjectures posed by Critch, Morton and Hackbusch.

Received:
Apr 16, 2019
Published:
Apr 29, 2019
MSC Codes:
15A69, 15A90
Keywords:
uniform matrix product states, trace algebra, trace parametrization, W-state, injectivity radius

Related publications

inJournal
2023 Repository Open Access
Adam Czapliński, Mateusz Michałek and Tim Seynnaeve

Uniform matrix product states from an algebraic geometer's point of view

In: Advances in applied mathematics, 142 (2023), p. 102417