Application
Quantum simulation architectures in HPC systems
Quantic
Group description:
Quantum computation is becoming a reality. As a discipline combining multiple areas of research, it serves as a novel paradigm of computation and provides at the same time novel tools to understand physical phenomena. It brings novel techniques for solving problems in either a classical or Quantum description.
Around the world, several research laboratories and computer-based companies are developing the first prototypes of quantum computers using diverse physical systems. At this stage of development, Quantum Computation theory moves along the developments and limitations of novel Hardware to better exploit its current capabilities.
QUANTIC research focuses on the application of Quantum computers to hard scientific problems. These may be formulated from fundamental principles, or by an affective optimization function. Using novel algorithms they address these problems optimizing resources devoted to their slution. Additionally, they exploit the full power of current classical devices to develop novel simulation tools for Quantum systems in HPC systems.
The group is made up of the following researchers: Artur García Sáez, Alba Cervera-Lierta, Axel Pérez Obiol Castaneda, Berta Casas I Font, David López Nuñez, José Ignacio Latorre Sentis, María Cea Fernández, Sergi Masot I LLima and Sergio Sánchez Ramírez.
Activity description:
The activities of the Quantic group at BSC focus on two main areas: the design of new quantum algorithms and the implementation of quantum simulators on HPC systems. The subtasks to be carried out are as follows:
- Development of HPC simulators that allow the reproduction of the behaviour of quantum algorithms using the parallelized architecture of supercomputers. These simulators will facilitate the design of circuits and algorithms for developers, reproducing the operation of ideal computers (without noise), offering traceability of the steps to be executed, as well as a reference for experimental developments.
- Application of these simulators and other classical-quantum hybrid architectures to the development of algorithms with applications in finance, computational chemistry, industrial optimization, and fundamental physics.
Results
Casas, B.; Bonet-Monroig, X.; Pérez-Salinas, A.
The role of data-induced randomness in quantum machine learning classification tasks Unpublished
Preprint, 2025.
Abstract | Links | BibTeX | Tags: quantic
@unpublished{nokey,
title = {The role of data-induced randomness in quantum machine learning classification tasks},
author = {Casas, B. and Bonet-Monroig, X. and Pérez-Salinas, A. },
url = {https://arxiv.org/pdf/2411.19281},
doi = {doi.org/10.48550/arXiv.2411.19281},
year = {2025},
date = {2025-11-28},
abstract = {Quantum machine learning (QML) has surged as a prominent area of research with the objective to go beyond the capabilities of classical machine learning models. A critical aspect of any learning task is the process of data embedding, which directly impacts model performance. Poorly designed data-embedding strategies can significantly impact the success of a learning task. Despite its importance, rigorous analyses of data-embedding effects are limited, leaving many cases without effective assessment methods. In this work, we introduce a metric for binary classification tasks, the class margin, by merging the concepts of average randomness and classification margin. This metric analytically connects data-induced randomness with classification accuracy for a given data-embedding map. We benchmark a range of data-embedding strategies through class margin, demonstrating that data-induced randomness imposes a limit on classification performance. We expect this work to provide a new approach to evaluate QML models by their data-embedding processes, addressing gaps left by existing analytical tools.},
howpublished = {Preprint},
keywords = {quantic},
pubstate = {published},
tppubtype = {unpublished}
}
Quantum machine learning (QML) has surged as a prominent area of research with the objective to go beyond the capabilities of classical machine learning models. A critical aspect of any learning task is the process of data embedding, which directly impacts model performance. Poorly designed data-embedding strategies can significantly impact the success of a learning task. Despite its importance, rigorous analyses of data-embedding effects are limited, leaving many cases without effective assessment methods. In this work, we introduce a metric for binary classification tasks, the class margin, by merging the concepts of average randomness and classification margin. This metric analytically connects data-induced randomness with classification accuracy for a given data-embedding map. We benchmark a range of data-embedding strategies through class margin, demonstrating that data-induced randomness imposes a limit on classification performance. We expect this work to provide a new approach to evaluate QML models by their data-embedding processes, addressing gaps left by existing analytical tools.
Tejedor, M.; Casas, B.; Conejero, J.; Cervera-Lierta, A.; R Badia, M.
Distributed Quantum Circuit Cutting for Hybrid Quantum-Classical High-Performance Computing Unpublished
Preprint, 2025.
Abstract | Links | BibTeX | Tags: quantic
@unpublished{nokey,
title = {Distributed Quantum Circuit Cutting for Hybrid Quantum-Classical High-Performance Computing},
author = {Tejedor, M. and Casas, B. and Conejero, J. and Cervera-Lierta, A. and Badia, R,M. },
url = {https://arxiv.org/pdf/2505.01184},
doi = {doi.org/10.48550/arXiv.2505.01184},
year = {2025},
date = {2025-05-05},
abstract = {Most quantum computers today are constrained by hardware limitations, particularly the number of available qubits, causing significant challenges for executing large-scale quantum algorithms. Circuit cutting has emerged as a key technique to overcome these limitations by decomposing large quantum circuits into smaller subcircuits that can be executed independently and later reconstructed. In this work, we introduce Qdislib, a distributed and flexible library for quantum circuit cutting, designed to seamlessly integrate with hybrid quantum-classical high-performance computing (HPC) systems. Qdislib employs a graph-based representation of quantum circuits to enable efficient partitioning, manipulation and execution, supporting both wire cutting and gate cutting techniques. The library is compatible with multiple quantum computing libraries, including Qiskit and Qibo, and leverages distributed computing frameworks to execute subcircuits across CPUs, GPUs, and quantum processing units (QPUs) in a fully parallelized manner. We present a proof of concept demonstrating how Qdislib enables the distributed execution of quantum circuits across heterogeneous computing resources, showcasing its potential for scalable quantum-classical workflows.},
howpublished = {Preprint},
keywords = {quantic},
pubstate = {published},
tppubtype = {unpublished}
}
Most quantum computers today are constrained by hardware limitations, particularly the number of available qubits, causing significant challenges for executing large-scale quantum algorithms. Circuit cutting has emerged as a key technique to overcome these limitations by decomposing large quantum circuits into smaller subcircuits that can be executed independently and later reconstructed. In this work, we introduce Qdislib, a distributed and flexible library for quantum circuit cutting, designed to seamlessly integrate with hybrid quantum-classical high-performance computing (HPC) systems. Qdislib employs a graph-based representation of quantum circuits to enable efficient partitioning, manipulation and execution, supporting both wire cutting and gate cutting techniques. The library is compatible with multiple quantum computing libraries, including Qiskit and Qibo, and leverages distributed computing frameworks to execute subcircuits across CPUs, GPUs, and quantum processing units (QPUs) in a fully parallelized manner. We present a proof of concept demonstrating how Qdislib enables the distributed execution of quantum circuits across heterogeneous computing resources, showcasing its potential for scalable quantum-classical workflows.
Casas, B.; Mieldzioć, G. R.; Ahmad, S.; Płodzień, M.; Bruzda, W.; Cervera-Lierta, A.; Życzkowski, K.
Quantum Circuits for High-Dimensional Absolutely Maximally Entangled States Unpublished
Preprint, 2025.
Abstract | Links | BibTeX | Tags: quantic
@unpublished{nokey,
title = {Quantum Circuits for High-Dimensional Absolutely Maximally Entangled States},
author = {Casas, B. and Mieldzioć, G.R. and Ahmad, S. and Płodzień, M. and Bruzda, W. and Cervera-Lierta, A. and Życzkowski, K. },
url = {https://arxiv.org/pdf/2504.05394},
doi = {doi.org/10.48550/arXiv.2504.05394},
year = {2025},
date = {2025-04-07},
abstract = {Absolutely maximally entangled (AME) states of multipartite quantum systems exhibit maximal entanglement across all possible bipartitions. These states lead to teleportation protocols that surpass standard teleportation schemes, determine quantum error correction codes and can be used to test performance of current term quantum processors. Several AME states can be constructed from graph states using minimal quantum resources. However, there exist other constructions that depart from the stabilizer formalism. In this work, we present explicit quantum circuits to generate exemplary non-stabilizer AME states of four subsystems with four, six, and eight levels each and analyze their capabilities to perform quantum information tasks.},
howpublished = {Preprint},
keywords = {quantic},
pubstate = {published},
tppubtype = {unpublished}
}
Absolutely maximally entangled (AME) states of multipartite quantum systems exhibit maximal entanglement across all possible bipartitions. These states lead to teleportation protocols that surpass standard teleportation schemes, determine quantum error correction codes and can be used to test performance of current term quantum processors. Several AME states can be constructed from graph states using minimal quantum resources. However, there exist other constructions that depart from the stabilizer formalism. In this work, we present explicit quantum circuits to generate exemplary non-stabilizer AME states of four subsystems with four, six, and eight levels each and analyze their capabilities to perform quantum information tasks.
Farreras, M.; Cervera-Lierta, A.
Simulation of the 1d XY model on a quantum computer Unpublished
Preprint, 2024.
Links | BibTeX | Tags: quantic
@unpublished{nokey,
title = {Simulation of the 1d XY model on a quantum computer},
author = {Farreras, M. and Cervera-Lierta, A.},
url = {https://doi.org/10.48550/arXiv.2410.21143
},
doi = {doi.org/10.48550/arXiv.2410.21143},
year = {2024},
date = {2024-10-28},
howpublished = {Preprint},
keywords = {quantic},
pubstate = {published},
tppubtype = {unpublished}
}
Pérez-Obiol, A.; Romero, A. M.; Menéndez, J.; Rios, A.; García-Sáez, A.; Juliá-Díaz, B.
Nuclear shell-model simulation in digital quantum computers Journal Article
In: Scientific Reports, vol. 13, 2023.
Abstract | Links | BibTeX | Tags: algorithms, quantic, quantum computing, simulations
@article{nokey,
title = {Nuclear shell-model simulation in digital quantum computers},
author = {Pérez-Obiol, A. and Romero, A. M. and Menéndez, J. and Rios, A. and García-Sáez, A. and Juliá-Díaz, B. },
url = {https://www.nature.com/articles/s41598-023-39263-7},
doi = {doi.org/10.1038/s41598-023-39263-7},
year = {2023},
date = {2023-07-29},
urldate = {2023-02-07},
journal = {Scientific Reports},
volume = {13},
abstract = {The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum circuit design strategy to find nuclear ground states that circumvents this limitation by exploiting an adaptive variational quantum eigensolver algorithm. Our circuit implementation is in excellent agreement with classical shell-model simulations for a dozen of light and medium-mass nuclei, including neon and calcium isotopes. We quantify the circuit depth, width and number of gates to encode realistic shell-model wavefunctions. Our strategy also addresses explicitly energy measurements and the required number of circuits to perform them. Our simulated circuits approach the benchmark results exponentially with a polynomial scaling in quantum resources for each nucleus and configuration space. Our work paves the way for quantum computing shell-model studies across the nuclear chart.},
keywords = {algorithms, quantic, quantum computing, simulations},
pubstate = {published},
tppubtype = {article}
}
The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum circuit design strategy to find nuclear ground states that circumvents this limitation by exploiting an adaptive variational quantum eigensolver algorithm. Our circuit implementation is in excellent agreement with classical shell-model simulations for a dozen of light and medium-mass nuclei, including neon and calcium isotopes. We quantify the circuit depth, width and number of gates to encode realistic shell-model wavefunctions. Our strategy also addresses explicitly energy measurements and the required number of circuits to perform them. Our simulated circuits approach the benchmark results exponentially with a polynomial scaling in quantum resources for each nucleus and configuration space. Our work paves the way for quantum computing shell-model studies across the nuclear chart.
Pérez-Obiol, A.; Masot-Llima, S.; Romero, A. M.; Menéndez, J.; Rios, A.; García-Sáez, A.; Juliá-Díaz, B.
Quantum entanglement patterns in the structure of atomic nuclei within the nuclear shell model Journal Article
In: The European Physical Journal A, vol. 59, no. 240, 2023, ISBN: 1434-601X.
Abstract | Links | BibTeX | Tags: quantic
@article{nokey,
title = {Quantum entanglement patterns in the structure of atomic nuclei within the nuclear shell model},
author = {Pérez-Obiol, A. and Masot-Llima, S. and Romero, A. M. and Menéndez, J. and Rios, A. and García-Sáez, A. and Juliá-Díaz, B. },
url = {https://link.springer.com/article/10.1140/epja/s10050-023-01151-z},
doi = {doi.org/10.1140/epja/s10050-023-01151-z},
isbn = {1434-601X},
year = {2023},
date = {2023-07-11},
urldate = {2023-07-11},
journal = {The European Physical Journal A},
volume = {59},
number = {240},
abstract = {Quantum entanglement offers a unique perspective into the underlying structure of strongly-correlated systems such as atomic nuclei. In this paper, we use quantum information tools to analyze the structure of light and medium-mass berillyum, oxygen, neon and calcium isotopes within the nuclear shell model. We use different entanglement metrics, including single-orbital entanglement, mutual information, and von Neumann entropies for different equipartitions of the shell-model valence space and identify mode-entanglement patterns related to the energy, angular momentum and isospin of the nuclear single-particle orbitals. We observe that the single-orbital entanglement is directly related to the number of valence nucleons and the energy structure of the shell, while the mutual information highlights signatures of proton–proton and neutron–neutron pairing, as well as nuclear deformation. Proton and neutron orbitals are weakly entangled by all measures, and in fact have the lowest von Neumann entropies among all possible equipartitions of the valence space. In contrast, orbitals with opposite angular momentum projection have relatively large entropies, especially in spherical nuclei. This analysis provides a guide for designing more efficient quantum algorithms for the noisy intermediate-scale quantum era.},
keywords = {quantic},
pubstate = {published},
tppubtype = {article}
}
Quantum entanglement offers a unique perspective into the underlying structure of strongly-correlated systems such as atomic nuclei. In this paper, we use quantum information tools to analyze the structure of light and medium-mass berillyum, oxygen, neon and calcium isotopes within the nuclear shell model. We use different entanglement metrics, including single-orbital entanglement, mutual information, and von Neumann entropies for different equipartitions of the shell-model valence space and identify mode-entanglement patterns related to the energy, angular momentum and isospin of the nuclear single-particle orbitals. We observe that the single-orbital entanglement is directly related to the number of valence nucleons and the energy structure of the shell, while the mutual information highlights signatures of proton–proton and neutron–neutron pairing, as well as nuclear deformation. Proton and neutron orbitals are weakly entangled by all measures, and in fact have the lowest von Neumann entropies among all possible equipartitions of the valence space. In contrast, orbitals with opposite angular momentum projection have relatively large entropies, especially in spherical nuclei. This analysis provides a guide for designing more efficient quantum algorithms for the noisy intermediate-scale quantum era.
Casas, B.; Cervera-Lierta, A.
Multi-dimensional Fourier series with quantum circuits Journal Article
In: Physical Review A, vol. 107, iss. 5, pp. 15, 2023.
Abstract | Links | BibTeX | Tags: algorithms, quantic, quantumcircuits, quantumsimulation
@article{,
title = {Multi-dimensional Fourier series with quantum circuits},
author = {Casas, B. and Cervera-Lierta, A.},
url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.107.062612
Preprint version: https://arxiv.org/abs/2302.03389
},
doi = {10.1103/PhysRevA.107.062612},
year = {2023},
date = {2023-06-29},
urldate = {2023-06-29},
journal = {Physical Review A},
volume = {107},
issue = {5},
pages = {15},
abstract = {Quantum machine learning is the field that aims to integrate machine learning with quantum computation. In recent years, the field has emerged as an active research area with the potential to bring new insights to classical machine learning problems. One of the challenges in the field is to explore the expressibility of parametrized quantum circuits and their ability to be universal function approximators, as classical neural networks are. Recent works have shown that, with a quantum supervised learning model, we can fit any one-dimensional Fourier series, proving their universality. However, models for multidimensional functions have not been explored in the same level of detail. In this work, we study the expressibility of various types of circuit Ansätze that generate multidimensional Fourier series. We found that, for some Ansätze, the degrees of freedom required for fitting such functions grow faster than the available degrees in the Hilbert space generated by the circuits. For example, single-qudit models have limited power to represent arbitrary multidimensional Fourier series. Despite this, we show that we can enlarge the Hilbert space of the circuit by using more qudits or higher local dimensions to meet the degrees of freedom requirements, thus ensuring the universality of the models.},
keywords = {algorithms, quantic, quantumcircuits, quantumsimulation},
pubstate = {published},
tppubtype = {article}
}
Quantum machine learning is the field that aims to integrate machine learning with quantum computation. In recent years, the field has emerged as an active research area with the potential to bring new insights to classical machine learning problems. One of the challenges in the field is to explore the expressibility of parametrized quantum circuits and their ability to be universal function approximators, as classical neural networks are. Recent works have shown that, with a quantum supervised learning model, we can fit any one-dimensional Fourier series, proving their universality. However, models for multidimensional functions have not been explored in the same level of detail. In this work, we study the expressibility of various types of circuit Ansätze that generate multidimensional Fourier series. We found that, for some Ansätze, the degrees of freedom required for fitting such functions grow faster than the available degrees in the Hilbert space generated by the circuits. For example, single-qudit models have limited power to represent arbitrary multidimensional Fourier series. Despite this, we show that we can enlarge the Hilbert space of the circuit by using more qudits or higher local dimensions to meet the degrees of freedom requirements, thus ensuring the universality of the models.
Dawid, Anna; Arnold, Julian; Requena, Borja; Gresch, Alexander; Płodzień, Marcin; Donatella, Kaelan; Nicoli, Kim; Stornati, Paolo; Koch, Rouven; Büttner, Miriam; Okuła, Robert; Muñoz-Gil, Gorka; Vargas-Hernández, Rodrigo A.; Cervera-Lierta, Alba; Carrasquilla, Juan; Dunjko, Vedran; Gabrié, Marylou; Huembeli, Patrick; van Nieuwenburg, Evert; Vicentini, Filippo; Wang, Lei; Wetzel, Sebastian J.; Carleo, Giuseppe; Greplová, Eliška; Krems, Roman; Marquardt, Florian; Tomza, Michał; Lewenstein, Maciej; Dauphin, Alexandre
Modern applications of machine learning in quantum sciences pre-print
2022.
Abstract | Links | BibTeX | Tags: machine learning, quantic, quantum science, quantumsimulation
@pre-print{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, quantic, quantum science, quantumsimulation},
pubstate = {published},
tppubtype = {pre-print}
}
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.
