Aplicación
Algoritmos de cadenas de Markov cuánticas
GICC + MATHQI
Descripción del grupo:
La Universidad Complutense de Madrid (UCM) cuenta con dos grupos de investigación expertos en computación cuántica, QICC y MATHQI, y le interesa colaborar con los demás socios del proyecto para el desarrollo, expansión y difusión de esta tecnología. Con el fin de progresar en la investigación de la computación cuántica en los campos de su interés científico, la UCM desarrollará las actividades descritas en el siguiente apartado, dentro del marco del proyecto Quantum Spain.
Los grupos QICC y MATHQI, liderados respectivamente por los profesores Miguel Ángel Martín-Delgado y David Pérez-García, cuentan con una amplia experiencia en el análisis matemático de conceptos relacionados con la computación cuántica, así como en la simulación de sistemas cuánticos con redes de tensores. Las tareas de estos grupos de investigación de la UCM se centrarán en el estudio de las redes de tensores y el uso de cadenas de Markov cuánticas en procesos relacionados con la inteligencia artificial.
Descripción de la actividad:
Los algoritmos de cadena de Markov cuánticos son métodos estocásticos para reproducir distribuciones de probabilidad, que presentan ventajas de convergencia sobre equivalentes clásicos. Estas cadenas han demostrado su utilidad en optimización de un problema complejo: el plegado de proteínas. El objetivo principal de esta actividad es desarrollar nuevos algoritmos cuánticos de optimización, muestreo y aprendizaje automático basados en cadenas de Markov cuánticas.
Resultados
Capel, A.; Alhambra, A. M.; Gondolf, P.; Ruiz-de-Alarcón, A.; Scalet, S. O.
Conditional Independence of 1D Gibbs States with Applications to Efficient Learning Working paper
2025.
Resumen | Enlaces | BibTeX | Etiquetas: UCM-4.3
@workingpaper{nokey,
title = {Conditional Independence of 1D Gibbs States with Applications to Efficient Learning},
author = {Capel, A. and Alhambra, A.M. and Gondolf, P. and Ruiz-de-Alarcón, A. and Scalet, S.O.},
url = {https://doi.org/10.48550/arXiv.2402.18500},
doi = {doi.org/10.48550/arXiv.2402.18500},
year = {2025},
date = {2025-12-02},
urldate = {2025-12-02},
abstract = {We show that spin chains in thermal equilibrium have a correlation structure in which individual regions are strongly correlated at most with their near vicinity. We quantify this with alternative notions of the conditional mutual information, defined through the so-called Belavkin-Staszewski relative entropy. We prove that these measures decay superexponentially at every positive temperature, under the assumption that the spin chain Hamiltonian is translation-invariant. Using a recovery map associated with these measures, we sequentially construct tensor network approximations in terms of marginals of small (sublogarithmic) size. As a main application, we show that classical representations of the states can be learned efficiently from local measurements with a polynomial sample complexity. We also prove an approximate factorization condition for the purity of the entire Gibbs state, which implies that it can be efficiently estimated to a small multiplicative error from a small number of local measurements. The results extend from strictly local to exponentially-decaying interactions above a threshold temperature, albeit only with exponential decay rates. As a technical step of independent interest, we show an upper bound to the decay of the Belavkin-Staszewski relative entropy upon the application of a conditional expectation.},
keywords = {UCM-4.3},
pubstate = {published},
tppubtype = {workingpaper}
}
Escrig, G.; Campos, R.; Qi, H.; Martin-Delgado, M. A.
Quantum Bayesian Inference with Renormalization for Gravitational Waves Artículo de revista
En: The Astrophysical Journal Letters, vol. 979, iss. 2, pp. L36, 2025.
Resumen | Enlaces | BibTeX | Etiquetas: UCM-4.3
@article{nokey,
title = {Quantum Bayesian Inference with Renormalization for Gravitational Waves},
author = {Escrig, G. and Campos, R. and Qi, H. and Martin-Delgado, M.A. },
url = {https://iopscience.iop.org/article/10.3847/2041-8213/ada6ae},
doi = {10.3847/2041-8213/ada6ae},
year = {2025},
date = {2025-01-28},
journal = {The Astrophysical Journal Letters},
volume = {979},
issue = {2},
pages = {L36},
abstract = {Advancements in gravitational-wave (GW) interferometers, particularly the next generation, are poised to enable the detections of orders of magnitude more GWs from compact binary coalescences. While the surge in detections will profoundly advance GW astronomy and multimessenger astrophysics, it also poses significant computational challenges in parameter estimation. In this work, we introduce a hybrid quantum algorithm qBIRD, which performs quantum Bayesian inference with renormalization and downsampling to infer GW parameters. We validate the algorithm using both simulated and observed GWs from binary black hole mergers on quantum simulators, demonstrating that its accuracy is comparable to classical Markov Chain Monte Carlo methods. Currently, our analyses focus on a subset of parameters, including chirp mass and mass ratio, due to the limitations from classical hardware in simulating quantum algorithms. However, qBIRD can accommodate a broader parameter space when the constraints are eliminated with a small-scale quantum computer of sufficient logical qubits.},
keywords = {UCM-4.3},
pubstate = {published},
tppubtype = {article}
}
Giordano, S.; Martin-Delgado, M. A.
Quantum Algorithm for Testing Graph Completeness Working paper
2024.
Resumen | Enlaces | BibTeX | Etiquetas: UCM-4.3
@workingpaper{nokey,
title = {Quantum Algorithm for Testing Graph Completeness},
author = {Giordano, S. and Martin-Delgado, M.A.
},
url = {https://arxiv.org/abs/2407.20069},
doi = {doi.org/10.48550/arXiv.2407.20069},
year = {2024},
date = {2024-08-16},
urldate = {2024-08-16},
abstract = {Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm, which takes the number of nodes and the adjacency matrix as input, constructs a quantum walk operator and applies QPE to estimate its eigenvalues. These eigenvalues reveal the graph's structural properties, enabling us to determine its completeness. We establish a relationship between the number of nodes in a complete graph and the number of marked nodes, optimizing the success probability and running time. The time complexity of our algorithm is , where is the number of nodes of the graph. offering a clear quantum advantage over classical methods. This approach is useful in network structure analysis, evaluating classical routing algorithms, and assessing systems based on pairwise comparisons.},
keywords = {UCM-4.3},
pubstate = {published},
tppubtype = {workingpaper}
}
D., Pérez-García; Santilli, L.; Tierz, M
Hawking-Page transition on a spin chain Artículo de revista
En: Physical Review Research, vol. 6, iss. 3, pp. 033007, 2024.
Resumen | Enlaces | BibTeX | Etiquetas: UCM-4.3
@article{nokey,
title = {Hawking-Page transition on a spin chain},
author = {Pérez-García D. and Santilli, L. and Tierz, M
},
url = {https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.033007},
doi = {doi.org/10.1103/PhysRevResearch.6.033007},
year = {2024},
date = {2024-07-01},
urldate = {2024-07-01},
journal = {Physical Review Research},
volume = {6},
issue = {3},
pages = {033007},
abstract = {The accessibility of the Hawking-Page transition in AdS5 through a one-dimensional (1D) Heisenberg spin chain is demonstrated. We use the random matrix formulation of the Loschmidt echo for a set of spin chains, and randomize the ferromagnetic spin interaction. It is shown that the thermal Loschmidt echo, when averaged, detects the predicted increase in entropy across the Hawking-Page transition. This suggests that a 1D spin chain exhibits characteristics of black hole physics in 4+1 dimensions. We show that this approach is equally applicable to free fermion systems with a general dispersion relation.},
keywords = {UCM-4.3},
pubstate = {published},
tppubtype = {article}
}
Pérez-García, D.; Santilli, L.; Tierz, M.
Dynamical quantum phase transitions from random matrix theory Artículo de revista
En: Quantum, vol. 8, pp. 1271, 2024.
Resumen | Enlaces | BibTeX | Etiquetas: UCM-4.3
@article{nokey,
title = {Dynamical quantum phase transitions from random matrix theory},
author = {Pérez-García, D. and Santilli, L. and Tierz, M.},
url = {https://quantum-journal.org/papers/q-2024-02-29-1271/},
doi = {doi.org/10.22331/q-2024-02-29-1271},
year = {2024},
date = {2024-02-29},
journal = {Quantum},
volume = {8},
pages = {1271},
abstract = {We uncover a novel dynamical quantum phase transition, using random matrix theory and its associated notion of planar limit. We study it for the isotropic XY Heisenberg spin chain. For this, we probe its real-time dynamics through the Loschmidt echo. This leads to the study of a random matrix ensemble with a complex weight, whose analysis requires novel technical considerations, that we develop. We obtain three main results: 1) There is a third order phase transition at a rescaled critical time, that we determine. 2) The third order phase transition persists away from the thermodynamic limit. 3) For times below the critical value, the difference between the thermodynamic limit and a finite chain decreases exponentially with the system size. All these results depend in a rich manner on the parity of the number of flipped spins of the quantum state conforming the fidelity.},
keywords = {UCM-4.3},
pubstate = {published},
tppubtype = {article}
}