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Uniform matrix product states from an algebraic geometer's point of view
- Publication Year :
- 2023
- Publisher :
- ACADEMIC PRESS INC ELSEVIER SCIENCE, 2023.
-
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.<br />Comment: 24 pages
- Subjects :
- Science & Technology
QUANTUM VERSION
Applied Mathematics
Mathematics, Applied
FOS: Physical sciences
Mathematical Physics (math-ph)
Trace algebra
Mathematics - Algebraic Geometry
510 Mathematics
Injectivity radius
15A69, 15A90
Trace parametrization
Physical Sciences
FOS: Mathematics
W-state
Uniform matrix product states
Algebraic Geometry (math.AG)
Constructible set
TENSOR
Mathematical Physics
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....9fe8c4f7faee1804685c4fa460156f94