Discovering the potential of quantum computing

@unpublished{nokey,

title = {Multi-dimensional Fourier series with quantum circuits},

author = {Casas, B., & Cervera-Lierta, A. (2023). },

url = {https://quantumspain-project.es/wp-content/uploads/2023/02/Multi-dimensional-Fourier-series-with-quantum-circuits.pdf},

doi = { https://doi.org/10.48550/arXiv.2302.03389},

year  = {2023},

date = {2023-02-07},

urldate = {2023-02-07},

abstract = {Quantum Machine Learning is the field that aims to integrate Machine Learning into quantum computation. Recently, some works have shown that we can naturally generate one-dimensional Fourier series with a supervised quantum machine learning model. However, models used for multi-dimensional Fourier series have not been explored with the same level of detail. In this work, we study different quantum strategies for fitting arbitrary multi-dimensional Fourier series. Using different types of circuit ansatzes, we found that the degrees of freedom required for fitting such functions grow faster than the degrees disposed of in the Hilbert space generated by the circuit. These results exhibit that, for these types of problems, the model does not have enough freedom to achieve any arbitrary Fourier series. Our work contributes to the study of multi-feature quantum machine learning algorithms with classical data and concludes that new encoding strategies beyond Fourier series formalism could be more convenient.},

keywords = {algorithms, quantumcircuits, quantumsimulation},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{nokey,

title = {Circuit Complexity through phase transitions: consequences in quantum state preparation},

author = {Roca-Jerat, S.; Sancho-Lorente, T.; Román-Roche, J.; & Zueco, D. (2023). },

url = {https://quantumspain-project.es/wp-content/uploads/2023/01/Circuit-Complexity-through-phase-transitions_UNIZAR-1.pdf},

doi = { https://doi.org/10.48550/arXiv.2301.04671},

year  = {2023},

date = {2023-01-11},

urldate = {2023-01-11},

abstract = {In this paper, we analyze the circuit complexity for preparing ground states of quantum manybody

systems. In particular, how this complexity grows as the ground state approaches a quantum

phase transition. We discuss dierent denitions of complexity, namely the one following the Fubini-

Study metric or the Nielsen complexity. We also explore dierent models: Ising, ZZXZ or Dicke.

In addition, dierent forms of state preparation are investigated: analytic or exact diagonalization

techniques, adiabatic algorithms (with and without shortcuts), and Quantum Variational Eigensolvers.

We nd that the divergence (or lack thereof) of the complexity near a phase transition depends on

the non-local character of the operations used to reach the ground state. For Fubini-Study based

complexity, we extract the universal properties and their critical exponents.

In practical algorithms, we nd that the complexity depends crucially on whether or not the system

passes close to a quantum critical point when preparing the state. While in the adiabatic case it is

dicult not to cross a critical point when the reference and target states are in dierent phases, for

VQE the algorithm can nd a way to avoid criticality.},

keywords = {adiabatic algorithms, algorithms, quantia, quantum, quantum computing},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{nokey,

title = {Modern applications of machine learning in quantum sciences},

author = {Anna Dawid and Julian Arnold and Borja Requena and Alexander Gresch and Marcin Płodzień and Kaelan Donatella and Kim Nicoli and Paolo Stornati and Rouven Koch and Miriam Büttner and Robert Okuła and Gorka Muñoz-Gil and Rodrigo A. Vargas-Hernández and Alba Cervera-Lierta and Juan Carrasquilla and Vedran Dunjko and Marylou Gabrié and Patrick Huembeli and Evert van Nieuwenburg and Filippo Vicentini and Lei Wang and Sebastian J. Wetzel and Giuseppe Carleo and Eliška Greplová and Roman Krems and Florian Marquardt and Michał Tomza and Maciej Lewenstein and Alexandre Dauphin},

url = {https://arxiv.org/abs/2204.04198},

doi = {10.48550/arXiv.2204.04198},

year  = {2022},

date = {2022-04-08},

urldate = {2022-04-08},

journal = {Arxiv},

pages = {268},

abstract = {In these Lecture Notes, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning.},

keywords = {machine learning, quantum science, quantumsimulation},

pubstate = {published},

tppubtype = {unpublished}

}