Algebraic Geometry of Matrix Product States
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Algebraic Geometry of Matrix Product States
|
|
| Creator |
Critch, A.
Morton, J. |
|
| Description |
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix product state or a limit of such states. For systems with few qubits, we give these equations explicitly, considering both periodic and open boundary conditions. Using the classical theory of trace varieties and trace algebras, we explain the relationship between MPS and hidden Markov models and exploit this relationship to derive useful parameterizations of MPS. We make four conjectures on the identifiability of MPS parameters.
|
|
| Date |
2019-02-10T09:46:25Z
2019-02-10T09:46:25Z 2014 |
|
| Type |
Article
|
|
| Identifier |
Algebraic Geometry of Matrix Product States / A. Critch, J. Morton // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 18 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 14J81; 81Q80; 14Q15 DOI:10.3842/SIGMA.2014.095 http://dspace.nbuv.gov.ua/handle/123456789/146599 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|