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Pérez-Obiol, A.; Romero, A. M.; Menéndez, J.; Rios, A.; García-Sáez, A.; Juliá-Díaz, B.
Nuclear shell-model simulation in digital quantum computers Artículo de revista
En: Scientific Reports, vol. 13, 2023.
Resumen | Enlaces | BibTeX | Etiquetas: 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.
Etxezarreta Martinez, J.; Fuentes, P.; deMarti iOlius, A.; Garcia-Frias, J.; Rodríguez Fonollosa, J.; Crespo, P. M.
Multiqubit time-varying quantum channels for NISQ-era superconducting quantum processors Artículo de revista
En: Physical Review Research, vol. 5, iss. 3, 2023, ISBN: 2643-1564.
Resumen | Enlaces | BibTeX | Etiquetas: tecnun
@article{nokey,
title = {Multiqubit time-varying quantum channels for NISQ-era superconducting quantum processors},
author = {Etxezarreta Martinez, J. and Fuentes, P. and deMarti iOlius, A. and Garcia-Frias, J. and Rodríguez Fonollosa, J. and Crespo, P.M.},
url = {https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.5.033055},
doi = {doi.org/10.1103/PhysRevResearch.5.033055},
isbn = {2643-1564},
year = {2023},
date = {2023-07-26},
journal = {Physical Review Research},
volume = {5},
issue = {3},
abstract = {Time-varying quantum channels (TVQCs) have been proposed as a model to include fluctuations of the relaxation (𝑇1) and dephasing times (𝑇2). In previous works, realizations of multiqubit TVQCs have been assumed to be equal for all the qubits of an error correction block, implying that the random variables that describe the fluctuations of 𝑇1 and 𝑇2 are block-to-block uncorrelated but qubit-wise perfectly correlated for the same block. In this article, we perform a correlation analysis of the fluctuations of the relaxation times of five multiqubit quantum processors. Our results show that it is reasonable to assume that the fluctuations of the relaxation and dephasing times of superconducting qubits are local to each of the qubits of the system. Based on these results, we discuss the multiqubit TVQCs when the fluctuations of the decoherence parameters for an error correction block are qubit-wise uncorrelated (as well as from block-to-block), a scenario we have named the fast time-varying quantum channel (FTVQC). Furthermore, we lower-bound the quantum capacity of general FTVQCs based on a quantity we refer to as the ergodic quantum capacity. Finally, we use numerical simulations to study the performance of quantum error correction codes when they operate over FTVQCs.},
keywords = {tecnun},
pubstate = {published},
tppubtype = {article}
}
Time-varying quantum channels (TVQCs) have been proposed as a model to include fluctuations of the relaxation (𝑇1) and dephasing times (𝑇2). In previous works, realizations of multiqubit TVQCs have been assumed to be equal for all the qubits of an error correction block, implying that the random variables that describe the fluctuations of 𝑇1 and 𝑇2 are block-to-block uncorrelated but qubit-wise perfectly correlated for the same block. In this article, we perform a correlation analysis of the fluctuations of the relaxation times of five multiqubit quantum processors. Our results show that it is reasonable to assume that the fluctuations of the relaxation and dephasing times of superconducting qubits are local to each of the qubits of the system. Based on these results, we discuss the multiqubit TVQCs when the fluctuations of the decoherence parameters for an error correction block are qubit-wise uncorrelated (as well as from block-to-block), a scenario we have named the fast time-varying quantum channel (FTVQC). Furthermore, we lower-bound the quantum capacity of general FTVQCs based on a quantity we refer to as the ergodic quantum capacity. Finally, we use numerical simulations to study the performance of quantum error correction codes when they operate over FTVQCs.
Combarro, E. F.; Pérez-Fernández, R.; Ranilla, J.; De Baets, B.
Solving the Kemeny ranking aggregation problem with quantum optimization algorithms Artículo de revista
En: Mathematical Methods in the Applied Sciences, vol. 46, iss. 16, 2023, ISBN: 0170-4214.
Resumen | Enlaces | BibTeX | Etiquetas: UNIOVI
@article{nokey,
title = {Solving the Kemeny ranking aggregation problem with quantum optimization algorithms},
author = {Combarro, E.F. and Pérez-Fernández, R. and Ranilla, J. and De Baets, B. },
url = {https://onlinelibrary.wiley.com/doi/full/10.1002/mma.9489},
doi = {doi.org/10.1002/mma.9489},
isbn = {0170-4214},
year = {2023},
date = {2023-07-13},
journal = {Mathematical Methods in the Applied Sciences},
volume = {46},
issue = {16},
abstract = {The aim of a ranking aggregation problem is to combine several rankings into a single one that best represents them. A common method for solving this problem is due to Kemeny and selects as the aggregated ranking the one that minimizes the sum of the Kendall distances to the rankings to be aggregated. Unfortunately, the identification of the said ranking—called the Kemeny ranking—is known to be a computationally expensive task. In this paper, we study different ways of computing the Kemeny ranking with quantum optimization algorithms, and in particular, we provide some alternative formulations for the search for the Kemeny ranking as an optimization problem. To the best of our knowledge, this is the first time that this problem is addressed with quantum techniques. We propose four different ways of formulating the problem, one novel to this work. Two different quantum optimization algorithms—Quantum Approximate Optimization Algorithm and Quantum Adiabatic Computing—are used to evaluate each of the different formulations. The experimental results show that the choice of the formulation plays a big role on the performance of the quantum optimization algorithms.},
keywords = {UNIOVI},
pubstate = {published},
tppubtype = {article}
}
The aim of a ranking aggregation problem is to combine several rankings into a single one that best represents them. A common method for solving this problem is due to Kemeny and selects as the aggregated ranking the one that minimizes the sum of the Kendall distances to the rankings to be aggregated. Unfortunately, the identification of the said ranking—called the Kemeny ranking—is known to be a computationally expensive task. In this paper, we study different ways of computing the Kemeny ranking with quantum optimization algorithms, and in particular, we provide some alternative formulations for the search for the Kemeny ranking as an optimization problem. To the best of our knowledge, this is the first time that this problem is addressed with quantum techniques. We propose four different ways of formulating the problem, one novel to this work. Two different quantum optimization algorithms—Quantum Approximate Optimization Algorithm and Quantum Adiabatic Computing—are used to evaluate each of the different formulations. The experimental results show that the choice of the formulation plays a big role on the performance of the quantum optimization algorithms.
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 Artículo de revista
En: The European Physical Journal A, vol. 59, no 240, 2023, ISBN: 1434-601X.
Resumen | Enlaces | BibTeX | Etiquetas: 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.
Nzongani, U.; Zylberman, J.; Doncecchi, C. E.; Pérez, A.; Debbasch, F.; Arnault, P.
Quantum circuits for discrete-time quantum walks with position-dependent coin operator Artículo de revista
En: 2023.
Resumen | Enlaces | BibTeX | Etiquetas: UV
@article{nokey,
title = {Quantum circuits for discrete-time quantum walks with position-dependent coin operator},
author = {Nzongani, U. and Zylberman, J. and Doncecchi, C.E. and Pérez, A. and Debbasch, F. and Arnault, P. },
url = {https://link.springer.com/article/10.1007/s11128-023-03957-8},
doi = {doi.org/10.1007/s11128-023-03957-8},
year = {2023},
date = {2023-07-01},
abstract = {The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with n wires, each corresponding to one qubit, we encode position states. The data necessary to define an arbitrary position-dependent coin operator is therefore exponential in n. Hence, the exponentiality will necessarily appear somewhere in our circuits. We first propose a circuit implementing the position-dependent coin operator, that is naive, in the sense that it has exponential depth and implements sequentially all appropriate position-dependent coin operators. We then propose a circuit that “transfers” all the depth into ancillae, yielding a final depth that is linear in n at the cost of an exponential number of ancillae. The main idea of this linear-depth circuit is to implement in parallel all coin operators at the different positions. Reducing the depth exponentially at the cost of having an exponential number of ancillae is a goal which has already been achieved for the problem of loading classical data on a quantum circuit (Araujo in Sci Rep 11:6329, 2021) (notice that such a circuit can be used to load the initial state of the walker). Here, we achieve this goal for the problem of applying a position-dependent coin operator in a discrete-time quantum walk. Finally, we extend the result of Welch (New J Phys 16:033040, 2014) from position-dependent unitaries which are diagonal in the position basis to position-dependent -block-diagonal unitaries: indeed, we show that for a position dependence of the coin operator (the block-diagonal unitary) which is smooth enough, one can find an efficient quantum-circuit implementation approximating the coin operator up to an error (in terms of the spectral norm), the depth and size of which scale as. A typical application of the efficient implementation would be the quantum simulation of a relativistic spin-1/2 particle on a lattice, coupled to a smooth external gauge field; notice that recently, quantum spatial-search schemes have been developed which use gauge fields as the oracle, to mark the vertex to be found (Zylberman in Entropy 23:1441, 2021), (Fredon arXiv:2210.13920). A typical application of the linear-depth circuit would be when there is spatial noise on the coin operator (and hence a non-smooth dependence in the position).},
keywords = {UV},
pubstate = {published},
tppubtype = {article}
}
The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with n wires, each corresponding to one qubit, we encode position states. The data necessary to define an arbitrary position-dependent coin operator is therefore exponential in n. Hence, the exponentiality will necessarily appear somewhere in our circuits. We first propose a circuit implementing the position-dependent coin operator, that is naive, in the sense that it has exponential depth and implements sequentially all appropriate position-dependent coin operators. We then propose a circuit that “transfers” all the depth into ancillae, yielding a final depth that is linear in n at the cost of an exponential number of ancillae. The main idea of this linear-depth circuit is to implement in parallel all coin operators at the different positions. Reducing the depth exponentially at the cost of having an exponential number of ancillae is a goal which has already been achieved for the problem of loading classical data on a quantum circuit (Araujo in Sci Rep 11:6329, 2021) (notice that such a circuit can be used to load the initial state of the walker). Here, we achieve this goal for the problem of applying a position-dependent coin operator in a discrete-time quantum walk. Finally, we extend the result of Welch (New J Phys 16:033040, 2014) from position-dependent unitaries which are diagonal in the position basis to position-dependent -block-diagonal unitaries: indeed, we show that for a position dependence of the coin operator (the block-diagonal unitary) which is smooth enough, one can find an efficient quantum-circuit implementation approximating the coin operator up to an error (in terms of the spectral norm), the depth and size of which scale as. A typical application of the efficient implementation would be the quantum simulation of a relativistic spin-1/2 particle on a lattice, coupled to a smooth external gauge field; notice that recently, quantum spatial-search schemes have been developed which use gauge fields as the oracle, to mark the vertex to be found (Zylberman in Entropy 23:1441, 2021), (Fredon arXiv:2210.13920). A typical application of the linear-depth circuit would be when there is spatial noise on the coin operator (and hence a non-smooth dependence in the position).
Casas, B.; Cervera-Lierta, A.
Multi-dimensional Fourier series with quantum circuits Artículo de revista
En: Physical Review A, vol. 107, iss. 5, pp. 15, 2023.
Resumen | Enlaces | BibTeX | Etiquetas: 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.
Ding, Y.; Chen, X.; Magdalena-Benedito, R.; Martín-Guerrero, J. D.
Closed-loop control of a noisy qubit with reinforcement learning Bachelor Thesis
2023, ISBN: 2632-2153.
Resumen | Enlaces | BibTeX | Etiquetas: UPV/EHU
@bachelorthesis{nokey,
title = {Closed-loop control of a noisy qubit with reinforcement learning},
author = {Ding, Y. and Chen, X. and Magdalena-Benedito, R. and Martín-Guerrero, J.D.},
url = {https://iopscience.iop.org/article/10.1088/2632-2153/acd048},
doi = {10.1088/2632-2153/acd048},
isbn = {2632-2153},
year = {2023},
date = {2023-05-05},
journal = {Machine Learning: Science and Technology},
volume = {4},
number = {2},
abstract = {The exotic nature of quantum mechanics differentiates machine learning applications in the quantum realm from classical ones. Stream learning is a powerful approach that can be applied to extract knowledge continuously from quantum systems in a wide range of tasks. In this paper, we propose a deep reinforcement learning method that uses streaming data from a continuously measured qubit in the presence of detuning, dephasing, and relaxation. The model receives streaming quantum information for learning and decision-making, providing instant feedback on the quantum system. We also explore the agent's adaptability to other quantum noise patterns through transfer learning. Our protocol offers insights into closed-loop quantum control, potentially advancing the development of quantum technologies.},
keywords = {UPV/EHU},
pubstate = {published},
tppubtype = {bachelorthesis}
}
The exotic nature of quantum mechanics differentiates machine learning applications in the quantum realm from classical ones. Stream learning is a powerful approach that can be applied to extract knowledge continuously from quantum systems in a wide range of tasks. In this paper, we propose a deep reinforcement learning method that uses streaming data from a continuously measured qubit in the presence of detuning, dephasing, and relaxation. The model receives streaming quantum information for learning and decision-making, providing instant feedback on the quantum system. We also explore the agent's adaptability to other quantum noise patterns through transfer learning. Our protocol offers insights into closed-loop quantum control, potentially advancing the development of quantum technologies.
Ding, Y.; Chen, Xi.; Magdalena-Benedito, R.; J Martín-Guerrero, D.
Closed-loop control of a noisy qubit with reinforcement learning Artículo de revista
En: Machine Learning: Science and Technology, vol. 4, iss. 2, 2023, ISBN: 2632-2153.
Resumen | Enlaces | BibTeX | Etiquetas:
@article{nokey,
title = {Closed-loop control of a noisy qubit with reinforcement learning},
author = {Ding, Y. and Chen, Xi. and Magdalena-Benedito, R. and Martín-Guerrero, J,D.
},
url = {https://iopscience.iop.org/article/10.1088/2632-2153/acd048},
doi = {10.1088/2632-2153/acd048},
isbn = {2632-2153},
year = {2023},
date = {2023-05-05},
journal = {Machine Learning: Science and Technology},
volume = {4},
issue = {2},
abstract = {The exotic nature of quantum mechanics differentiates machine learning applications in the quantum realm from classical ones. Stream learning is a powerful approach that can be applied to extract knowledge continuously from quantum systems in a wide range of tasks. In this paper, we propose a deep reinforcement learning method that uses streaming data from a continuously measured qubit in the presence of detuning, dephasing, and relaxation. The model receives streaming quantum information for learning and decision-making, providing instant feedback on the quantum system. We also explore the agent's adaptability to other quantum noise patterns through transfer learning. Our protocol offers insights into closed-loop quantum control, potentially advancing the development of quantum technologies.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The exotic nature of quantum mechanics differentiates machine learning applications in the quantum realm from classical ones. Stream learning is a powerful approach that can be applied to extract knowledge continuously from quantum systems in a wide range of tasks. In this paper, we propose a deep reinforcement learning method that uses streaming data from a continuously measured qubit in the presence of detuning, dephasing, and relaxation. The model receives streaming quantum information for learning and decision-making, providing instant feedback on the quantum system. We also explore the agent's adaptability to other quantum noise patterns through transfer learning. Our protocol offers insights into closed-loop quantum control, potentially advancing the development of quantum technologies.
Ding, Y.; Gonzalez-Conde, J.; Lamata, L.; Martín-Guerrero, J. D.; Lizaso, E.; Mugel, S.; Chen, X.; Orús, R.; Solano, E.; Sanz, M.
Toward Prediction of Financial Crashes with a D-Wave Quantum Annealer Artículo de revista
En: Entropy, vol. 25, no 2, pp. 323, 2023, ISBN: 1099-4300.
Resumen | Enlaces | BibTeX | Etiquetas: UPV/EHU
@article{nokey,
title = {Toward Prediction of Financial Crashes with a D-Wave Quantum Annealer},
author = {Ding, Y. and Gonzalez-Conde, J. and Lamata, L. and Martín-Guerrero, J.D. and Lizaso, E. and Mugel, S. and Chen, X. and Orús, R. and Solano, E. and Sanz, M. },
url = {https://www.mdpi.com/1099-4300/25/2/323},
doi = {doi.org/10.3390/e25020323},
isbn = {1099-4300},
year = {2023},
date = {2023-02-10},
journal = {Entropy},
volume = {25},
number = {2},
pages = {323},
abstract = {The prediction of financial crashes in a complex financial network is known to be an NP-hard problem, which means that no known algorithm can efficiently find optimal solutions. We experimentally explore a novel approach to this problem by using a D-Wave quantum annealer, benchmarking its performance for attaining a financial equilibrium. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed into a spin-1/2 Hamiltonian with at most, two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. The size of the simulation is mainly constrained by the necessity of a large number of physical qubits representing a logical qubit with the correct connectivity. Our experiment paves the way for the codification of this quantitative macroeconomics problem in quantum annealers.},
keywords = {UPV/EHU},
pubstate = {published},
tppubtype = {article}
}
The prediction of financial crashes in a complex financial network is known to be an NP-hard problem, which means that no known algorithm can efficiently find optimal solutions. We experimentally explore a novel approach to this problem by using a D-Wave quantum annealer, benchmarking its performance for attaining a financial equilibrium. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed into a spin-1/2 Hamiltonian with at most, two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. The size of the simulation is mainly constrained by the necessity of a large number of physical qubits representing a logical qubit with the correct connectivity. Our experiment paves the way for the codification of this quantitative macroeconomics problem in quantum annealers.
S.; Sancho-Lorente Roca-Jerat, T. ; Román-Roche
Circuit Complexity through phase transitions: consequences in quantum state preparation pre-print
2023.
Resumen | Enlaces | BibTeX | Etiquetas: adiabatic algorithms, algorithms, quantia, quantum, quantum computing
@pre-print{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 di erent de nitions of complexity, namely the one following the Fubini-
Study metric or the Nielsen complexity. We also explore di erent models: Ising, ZZXZ or Dicke.
In addition, di erent 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 di erent phases, for
VQE the algorithm can nd a way to avoid criticality.},
keywords = {adiabatic algorithms, algorithms, quantia, quantum, quantum computing},
pubstate = {published},
tppubtype = {pre-print}
}
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 di erent de nitions of complexity, namely the one following the Fubini-
Study metric or the Nielsen complexity. We also explore di erent models: Ising, ZZXZ or Dicke.
In addition, di erent 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 di erent phases, for
VQE the algorithm can nd a way to avoid criticality.
systems. In particular, how this complexity grows as the ground state approaches a quantum
phase transition. We discuss di erent de nitions of complexity, namely the one following the Fubini-
Study metric or the Nielsen complexity. We also explore di erent models: Ising, ZZXZ or Dicke.
In addition, di erent 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 di erent phases, for
VQE the algorithm can nd a way to avoid criticality.
Miranda, E. R.; Martín-Guerrero, J. D.; Venkatesh, S.; Hernani-Morales, C.; Lamata, L.; Solano, E.
Quantum Brain Networks: A Perspective Artículo de revista
En: Electronics , vol. 11, no 10, pp. 1528, 2022.
Resumen | Enlaces | BibTeX | Etiquetas: artificial intelligence, quantum computing, UV
@article{nokey,
title = {Quantum Brain Networks: A Perspective},
author = {Miranda, E. R. and Martín-Guerrero, J. D. and Venkatesh, S. and Hernani-Morales, C. and Lamata, L. and Solano, E. },
editor = {Durdu Guney},
url = {https://www.mdpi.com/2079-9292/11/10/1528/htm},
doi = {10.3390/electronics11101528},
year = {2022},
date = {2022-05-11},
urldate = {2022-05-11},
journal = {Electronics },
volume = {11},
number = {10},
pages = {1528},
abstract = {We propose Quantum Brain Networks (QBraiNs) as a new interdisciplinary field integrating knowledge and methods from neurotechnology, artificial intelligence, and quantum computing. The objective is to develop an enhanced connectivity between the human brain and quantum computers for a variety of disruptive applications. We foresee the emergence of hybrid classical-quantum networks of wetware and hardware nodes, mediated by machine learning techniques and brain–machine interfaces. QBraiNs will harness and transform in unprecedented ways arts, science, technologies, and entrepreneurship, in particular activities related to medicine, Internet of Humans, intelligent devices, sensorial experience, gaming, Internet of Things, crypto trading, and business. },
keywords = {artificial intelligence, quantum computing, UV},
pubstate = {published},
tppubtype = {article}
}
We propose Quantum Brain Networks (QBraiNs) as a new interdisciplinary field integrating knowledge and methods from neurotechnology, artificial intelligence, and quantum computing. The objective is to develop an enhanced connectivity between the human brain and quantum computers for a variety of disruptive applications. We foresee the emergence of hybrid classical-quantum networks of wetware and hardware nodes, mediated by machine learning techniques and brain–machine interfaces. QBraiNs will harness and transform in unprecedented ways arts, science, technologies, and entrepreneurship, in particular activities related to medicine, Internet of Humans, intelligent devices, sensorial experience, gaming, Internet of Things, crypto trading, and business.
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.
Resumen | Enlaces | BibTeX | Etiquetas: 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.
Ding, Y.; Gonzalez-Conde, J.; L. Lamata, Martín-Guerrero; Lizaso, E.; Mugel, S.; Chen, X.; Orús, R.; Solano, E.; Sanz, M.
Toward Prediction of Financial Crashes with a D-Wave Quantum Annealer Artículo de revista
En: Entropy, vol. 25, iss. 2, pp. 323, 0000, ISBN: 1099-4300.
Resumen | Enlaces | BibTeX | Etiquetas: quantum, quantum annealer, UV
@article{nokey,
title = {Toward Prediction of Financial Crashes with a D-Wave Quantum Annealer},
author = {Ding, Y. and Gonzalez-Conde, J. and Lamata, L., Martín-Guerrero, J. D. and Lizaso, E. and Mugel, S. and Chen, X. and Orús, R. and Solano, E. and Sanz, M.
},
url = {https://quantumspain-project.es/wp-content/uploads/2023/05/entropy-25-00323-v2-1.pdf},
doi = {doi.org/10.3390/e25020323},
isbn = {1099-4300},
journal = {Entropy},
volume = {25},
issue = {2},
pages = {323},
abstract = {The prediction of financial crashes in a complex financial network is known to be an NP-hard problem, which means that no known algorithm can efficiently find optimal solutions. We experimentally explore a novel approach to this problem by using a D-Wave quantum annealer, benchmarking its performance for attaining a financial equilibrium. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed into a spin-1/2
Hamiltonian with at most, two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. The size of the simulation is mainly constrained by the necessity of a large number of physical qubits representing a logical qubit with the correct connectivity. Our experiment paves the way for the codification of this quantitative macroeconomics problem in quantum annealers.},
keywords = {quantum, quantum annealer, UV},
pubstate = {published},
tppubtype = {article}
}
The prediction of financial crashes in a complex financial network is known to be an NP-hard problem, which means that no known algorithm can efficiently find optimal solutions. We experimentally explore a novel approach to this problem by using a D-Wave quantum annealer, benchmarking its performance for attaining a financial equilibrium. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed into a spin-1/2
Hamiltonian with at most, two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. The size of the simulation is mainly constrained by the necessity of a large number of physical qubits representing a logical qubit with the correct connectivity. Our experiment paves the way for the codification of this quantitative macroeconomics problem in quantum annealers.
Hamiltonian with at most, two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. The size of the simulation is mainly constrained by the necessity of a large number of physical qubits representing a logical qubit with the correct connectivity. Our experiment paves the way for the codification of this quantitative macroeconomics problem in quantum annealers.
deMarti iOlius, A.; Etxezarreta Martinez, J.
The closed-branch decoder for quantum LDPC codes Sin publicar
Preprint, 0000.
Resumen | Enlaces | BibTeX | Etiquetas: tecnun
@unpublished{nokey,
title = {The closed-branch decoder for quantum LDPC codes},
author = {deMarti iOlius, A. and Etxezarreta Martinez, J.},
url = {https://arxiv.org/pdf/2402.01532},
doi = {doi.org/10.48550/arXiv.2402.01532},
abstract = {Quantum error correction is the building block for constructing fault-tolerant quantum processors that can operate reliably even if its constituting elements are corrupted by decoherence. In this context, real-time decoding is a necessity for implementing arbitrary quantum computations on the logical level. In this work, we present a new decoder for Quantum Low Density Parity Check (QLDPC) codes, named the closed-branch decoder, with a worst-case complexity loosely upper bounded by O(nmaxgrmaxbr), where maxgr and maxbr are tunable parameters that pose the accuracy versus speed trade-off of decoding algorithms. For the best precision, the maxgrmaxbr product increases exponentially as ∝djd, where d indicates the distance of the code and j indicates the average row weight of its parity check matrix. Nevertheless, we numerically show that considering small values that are polynomials of the code distance are enough for good error correction performance. The decoder is described to great extent and compared with the Belief Propagation Ordered Statistics Decoder (BPOSD) operating over data qubit, phenomenological and circuit-level noise models for the class of Bivariate Bicycle (BB) codes. The results showcase a promising performance of the decoder, obtaining similar results with much lower complexity than BPOSD when considering the smallest distance codes, but experiencing some logical error probability degradation for the larger ones. Ultimately, the performance and complexity of the decoder depends on the product maxgrmaxbr, which can be considered taking into account benefiting one of the two aspects at the expense of the other.},
howpublished = {Preprint},
keywords = {tecnun},
pubstate = {published},
tppubtype = {unpublished}
}
Quantum error correction is the building block for constructing fault-tolerant quantum processors that can operate reliably even if its constituting elements are corrupted by decoherence. In this context, real-time decoding is a necessity for implementing arbitrary quantum computations on the logical level. In this work, we present a new decoder for Quantum Low Density Parity Check (QLDPC) codes, named the closed-branch decoder, with a worst-case complexity loosely upper bounded by O(nmaxgrmaxbr), where maxgr and maxbr are tunable parameters that pose the accuracy versus speed trade-off of decoding algorithms. For the best precision, the maxgrmaxbr product increases exponentially as ∝djd, where d indicates the distance of the code and j indicates the average row weight of its parity check matrix. Nevertheless, we numerically show that considering small values that are polynomials of the code distance are enough for good error correction performance. The decoder is described to great extent and compared with the Belief Propagation Ordered Statistics Decoder (BPOSD) operating over data qubit, phenomenological and circuit-level noise models for the class of Bivariate Bicycle (BB) codes. The results showcase a promising performance of the decoder, obtaining similar results with much lower complexity than BPOSD when considering the smallest distance codes, but experiencing some logical error probability degradation for the larger ones. Ultimately, the performance and complexity of the decoder depends on the product maxgrmaxbr, which can be considered taking into account benefiting one of the two aspects at the expense of the other.
Mehrabankar, S.; García-March, M. A.; Almudéver, C. G.; Pérez, A.
Reducing the number of qubits in quantum simulations of one dimensional many-body Hamiltonians Sin publicar
Preprint, 0000.
Resumen | Enlaces | BibTeX | Etiquetas: UV
@unpublished{nokey,
title = {Reducing the number of qubits in quantum simulations of one dimensional many-body Hamiltonians},
author = {Mehrabankar, S. and García-March, M.A. and Almudéver, C.G. and Pérez, A. },
url = {https://arxiv.org/abs/2308.01545},
doi = {doi.org/10.48550/arXiv.2308.01545},
abstract = {We investigate the Ising and Heisenberg models using the Block Renormalization Group Method (BRGM), focusing on its behavior across different system sizes. The BRGM reduces the number of spins by a factor of 1/2 (1/3) for the Ising (Heisenberg) model, effectively preserving essential physical features of the model while using only a fraction of the spins. Through a comparative analysis, we demonstrate that as the system size increases, there is an exponential convergence between results obtained from the original and renormalized Ising Hamiltonians, provided the coupling constants are redefined accordingly. Remarkably, for a spin chain with 24 spins, all physical features, including magnetization, correlation function, and entanglement entropy, exhibit an exact correspondence with the results from the original Hamiltonian. The study of the Heisenberg model also shows this tendency, although complete convergence may appear for a size much larger than 24 spins, and is therefore beyond our computational capabilities. The success of BRGM in accurately characterizing the Ising model, even with a relatively small number of spins, underscores its robustness and utility in studying complex physical systems, and facilitates its simulation on current NISQ computers, where the available number of qubits is largely constrained.},
howpublished = {Preprint},
keywords = {UV},
pubstate = {published},
tppubtype = {unpublished}
}
We investigate the Ising and Heisenberg models using the Block Renormalization Group Method (BRGM), focusing on its behavior across different system sizes. The BRGM reduces the number of spins by a factor of 1/2 (1/3) for the Ising (Heisenberg) model, effectively preserving essential physical features of the model while using only a fraction of the spins. Through a comparative analysis, we demonstrate that as the system size increases, there is an exponential convergence between results obtained from the original and renormalized Ising Hamiltonians, provided the coupling constants are redefined accordingly. Remarkably, for a spin chain with 24 spins, all physical features, including magnetization, correlation function, and entanglement entropy, exhibit an exact correspondence with the results from the original Hamiltonian. The study of the Heisenberg model also shows this tendency, although complete convergence may appear for a size much larger than 24 spins, and is therefore beyond our computational capabilities. The success of BRGM in accurately characterizing the Ising model, even with a relatively small number of spins, underscores its robustness and utility in studying complex physical systems, and facilitates its simulation on current NISQ computers, where the available number of qubits is largely constrained.
Palacios, A.; Martínez-Pena, R.; Soriano, M. C.; Giorgi, G. L.; Zambrini, R.
Role of coherence in many-body Quantum Reservoir Computing Sin publicar
Preprint, 0000.
Resumen | Enlaces | BibTeX | Etiquetas: uib
@unpublished{nokey,
title = {Role of coherence in many-body Quantum Reservoir Computing},
author = {Palacios, A. and Martínez-Pena, R. and Soriano, M.C. and Giorgi, G.L. and Zambrini, R. },
url = {https://arxiv.org/pdf/2409.17734},
doi = {doi.org/10.48550/arXiv.2409.17734},
abstract = {Quantum Reservoir Computing (QRC) offers potential advantages over classical reservoir computing, including inherent processing of quantum inputs and a vast Hilbert space for state exploration. Yet, the relation between the performance of reservoirs based on complex and many-body quantum systems and non-classical state features is not established. Through an extensive analysis of QRC based on a transverse-field Ising model we show how different quantum effects, such as quantum
coherence and correlations, contribute to improving the performance in temporal tasks, as measured by the Information Processing Capacity. Additionally, we critically assess the impact of finite measurement resources and noise on the reservoir’s dynamics in different regimes, quantifying the limited ability to exploit quantum effects for increasing damping and noise strengths. Our results reveal a monotonic relationship between reservoir performance and coherence, along with the importance of quantum effects in the ergodic regime.},
howpublished = {Preprint},
keywords = {uib},
pubstate = {published},
tppubtype = {unpublished}
}
Quantum Reservoir Computing (QRC) offers potential advantages over classical reservoir computing, including inherent processing of quantum inputs and a vast Hilbert space for state exploration. Yet, the relation between the performance of reservoirs based on complex and many-body quantum systems and non-classical state features is not established. Through an extensive analysis of QRC based on a transverse-field Ising model we show how different quantum effects, such as quantum
coherence and correlations, contribute to improving the performance in temporal tasks, as measured by the Information Processing Capacity. Additionally, we critically assess the impact of finite measurement resources and noise on the reservoir’s dynamics in different regimes, quantifying the limited ability to exploit quantum effects for increasing damping and noise strengths. Our results reveal a monotonic relationship between reservoir performance and coherence, along with the importance of quantum effects in the ergodic regime.
coherence and correlations, contribute to improving the performance in temporal tasks, as measured by the Information Processing Capacity. Additionally, we critically assess the impact of finite measurement resources and noise on the reservoir’s dynamics in different regimes, quantifying the limited ability to exploit quantum effects for increasing damping and noise strengths. Our results reveal a monotonic relationship between reservoir performance and coherence, along with the importance of quantum effects in the ergodic regime.
Rout, S.; Sakharwade, N.; Bhattacharya, S. S.; Ramanathan, R.; Horodecki, P.
Unbounded Quantum Advantage in Communication with Minimal Input Scaling Sin publicar
Preprint, 0000.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@unpublished{nokey,
title = {Unbounded Quantum Advantage in Communication with Minimal Input Scaling},
author = {Rout, S. and Sakharwade, N. and Bhattacharya, S.S. and Ramanathan, R. and Horodecki, P.},
url = {https://arxiv.org/pdf/2305.10372},
doi = {doi.org/10.48550/arXiv.2305.10372},
abstract = {In communication complexity-like problems, previous studies have shown either an exponential quantum advantage or an unbounded quantum advantage with an exponentially large input set Θ(2n) bits with respect to classical communication Θ(n) bits. In the former, the quantum and classical separation grows exponentially in input while the latter's quantum communication resource is a constant. Remarkably, it was still open whether an unbounded quantum advantage exists while the inputs do not scale exponentially. Here we answer this question affirmatively using an input size of optimal order. Considering two variants as tasks: 1) distributed computation of relation and 2) {it relation reconstruction}, we study the one-way zero-error communication complexity of a relation induced by a distributed clique labelling problem for orthogonality graphs. While we prove no quantum advantage in the first task, we show an {it unbounded quantum advantage} in relation reconstruction without public coins. Specifically, for a class of graphs with order m, the quantum complexity is Θ(1) while the classical complexity is Θ(logm). Remarkably, the input size is Θ(logm) bits and the order of its scaling with respect to classical communication is {it minimal}. This is exponentially better compared to previous works. Additionally, we prove a lower bound (linear in the number of maximum cliques) on the amount of classical public coin necessary to overcome the separation in the scenario of restricted communication and connect this to the existence of Orthogonal Arrays. Finally, we highlight some applications of this task to semi-device-independent dimension witnessing as well as to the detection of Mutually Unbiased Bases.},
howpublished = {Preprint},
keywords = {UAB},
pubstate = {published},
tppubtype = {unpublished}
}
In communication complexity-like problems, previous studies have shown either an exponential quantum advantage or an unbounded quantum advantage with an exponentially large input set Θ(2n) bits with respect to classical communication Θ(n) bits. In the former, the quantum and classical separation grows exponentially in input while the latter's quantum communication resource is a constant. Remarkably, it was still open whether an unbounded quantum advantage exists while the inputs do not scale exponentially. Here we answer this question affirmatively using an input size of optimal order. Considering two variants as tasks: 1) distributed computation of relation and 2) {it relation reconstruction}, we study the one-way zero-error communication complexity of a relation induced by a distributed clique labelling problem for orthogonality graphs. While we prove no quantum advantage in the first task, we show an {it unbounded quantum advantage} in relation reconstruction without public coins. Specifically, for a class of graphs with order m, the quantum complexity is Θ(1) while the classical complexity is Θ(logm). Remarkably, the input size is Θ(logm) bits and the order of its scaling with respect to classical communication is {it minimal}. This is exponentially better compared to previous works. Additionally, we prove a lower bound (linear in the number of maximum cliques) on the amount of classical public coin necessary to overcome the separation in the scenario of restricted communication and connect this to the existence of Orthogonal Arrays. Finally, we highlight some applications of this task to semi-device-independent dimension witnessing as well as to the detection of Mutually Unbiased Bases.
