Descubriendo el potencial de la computación cuántica

@workingpaper{nokey,

title = {Matrix-product unitaries: Beyond quantum cellular automata},

author = {Styliaris, G. and Trivedi, R. and Pérez-García, D. and Cirac, J. I. 

},

url = {https://arxiv.org/abs/2406.10195},

doi = {doi.org/10.22331/q-2025-02-25-1645},

year  = {2025},

date = {2025-02-20},

abstract = {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.},

keywords = {UCM-4.2},

pubstate = {published},

tppubtype = {workingpaper}

}

@workingpaper{nokey,

title = {The product structure of MPS-under-permutations},

author = {Florido-Llinàs, M. and Alhambra, A.M. and Trivedi, R. and Schuch, N. Pérez-García, D. and Cirac, J.I. },

url = {https://arxiv.org/abs/2410.19541},

doi = {doi.org/10.48550/arXiv.2410.19541},

year  = {2024},

date = {2024-10-25},

abstract = {Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak form of permutational symmetry, in the sense that entanglement behaves similarly across any arbitrary bipartition. In this paper, we show that translationally-invariant (TI) matrix product states (MPS) with this property are trivial, meaning that they are either product states or superpositions of a few of them. The results also apply to non-TI generic MPS, as well as further relevant examples of MPS including the W state and the Dicke states in an approximate sense. Our findings motivate the usage of ansätze simpler than tensor networks in systems whose structure is invariant under permutations.},

keywords = {UCM-4.2},

pubstate = {published},

tppubtype = {workingpaper}

}

@workingpaper{nokey,

title = {Regular language quantum states},

author = {Florido-Llinàs, M. and Alhambra, A.M. and Pérez-García, D. and Cirac, J.I. },

url = {https://arxiv.org/abs/2407.17641},

doi = {doi.org/10.48550/arXiv.2407.17641},

year  = {2024},

date = {2024-07-24},

urldate = {2024-07-24},

abstract = {We introduce regular language states, a family of quantum many-body states. They are built from a special class of formal languages, called regular, which has been thoroughly studied in the field of computer science. They can be understood as the superposition of all the words in a regular language and encompass physically relevant states such as the GHZ-, W- or Dicke-states. By leveraging the theory of regular languages, we develop a theoretical framework to describe them. First, we express them in terms of matrix product states, providing efficient criteria to recognize them. We then develop a canonical form which allows us to formulate a fundamental theorem for the equivalence of regular language states, including under local unitary operations. We also exploit the theory of tensor networks to find an efficient criterion to determine when regular languages are shift-invariant.

},

keywords = {UCM-4.2},

pubstate = {published},

tppubtype = {workingpaper}

}