Matrix-product unitaries: Beyond quantum cellular automata
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 repeated tensor are known to coincide with 1D quantum cellular...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-02-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-02-25-1645/pdf/ |
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| author | Georgios Styliaris Rahul Trivedi David Perez-Garcia J. Ignacio Cirac |
| author_facet | Georgios Styliaris Rahul Trivedi David Perez-Garcia J. Ignacio Cirac |
| author_sort | Georgios Styliaris |
| collection | DOAJ |
| description | 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 repeated tensor are known to coincide with 1D quantum cellular automata (QCA), i.e., unitaries with an exact light cone. However, this correspondence breaks down for MPU with open boundary conditions, even if the resulting operator is translation-invariant. Such unitaries can turn short- to long-range correlations and thus alter the underlying phase of matter. Here we make the first steps towards a theory of MPU with uniform bulk but arbitrary boundary. In particular, we study the structure of a subclass with a direct-sum form which maximally violates the QCA property. We also consider the general case of MPU formed by site-dependent (nonuniform) tensors and show a correspondence between MPU and locally maximally entanglable states. |
| format | Article |
| id | doaj-art-feb4c75b5d3e4c3b8a9ac2a29df12bc2 |
| institution | OA Journals |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-feb4c75b5d3e4c3b8a9ac2a29df12bc22025-08-20T02:04:09ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-02-019164510.22331/q-2025-02-25-164510.22331/q-2025-02-25-1645Matrix-product unitaries: Beyond quantum cellular automataGeorgios StyliarisRahul TrivediDavid Perez-GarciaJ. Ignacio CiracMatrix-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 repeated tensor are known to coincide with 1D quantum cellular automata (QCA), i.e., unitaries with an exact light cone. However, this correspondence breaks down for MPU with open boundary conditions, even if the resulting operator is translation-invariant. Such unitaries can turn short- to long-range correlations and thus alter the underlying phase of matter. Here we make the first steps towards a theory of MPU with uniform bulk but arbitrary boundary. In particular, we study the structure of a subclass with a direct-sum form which maximally violates the QCA property. We also consider the general case of MPU formed by site-dependent (nonuniform) tensors and show a correspondence between MPU and locally maximally entanglable states.https://quantum-journal.org/papers/q-2025-02-25-1645/pdf/ |
| spellingShingle | Georgios Styliaris Rahul Trivedi David Perez-Garcia J. Ignacio Cirac Matrix-product unitaries: Beyond quantum cellular automata Quantum |
| title | Matrix-product unitaries: Beyond quantum cellular automata |
| title_full | Matrix-product unitaries: Beyond quantum cellular automata |
| title_fullStr | Matrix-product unitaries: Beyond quantum cellular automata |
| title_full_unstemmed | Matrix-product unitaries: Beyond quantum cellular automata |
| title_short | Matrix-product unitaries: Beyond quantum cellular automata |
| title_sort | matrix product unitaries beyond quantum cellular automata |
| url | https://quantum-journal.org/papers/q-2025-02-25-1645/pdf/ |
| work_keys_str_mv | AT georgiosstyliaris matrixproductunitariesbeyondquantumcellularautomata AT rahultrivedi matrixproductunitariesbeyondquantumcellularautomata AT davidperezgarcia matrixproductunitariesbeyondquantumcellularautomata AT jignaciocirac matrixproductunitariesbeyondquantumcellularautomata |