Aplicación
Técnicas de IA y quantum machine learning para la identificación de procesos cuánticos
Información Cuántica y Óptica Cuántica
Descripción del grupo:
Los grupos de Información Cuántica y Óptica Cuántica del departamento de Física de la UAB trabajan desde hace años en temas afines al uso de AI y machine learning para la optimización de los recursos cuánticos y dar solución a algunas de las preguntas abiertas en la física de altas energías y materia condensada. En la página web del grupo (https://grupsderecerca.uab.cat/giq/publications) se pueden encontrar más de 400 publicaciones científicas en el ámbito de la información cuántica, varias de ellas centradas en el uso de AI y machine learning para entender mejor los sistemas cuánticos, es decir, entre otras cosas, métodos de certificación y verificación de estados cuánticos. Esta experiencia será fundamental para poder discernir si lo generado en un ordenador cuántico es realmente el estado que queremos estudiar y no otro que se haya generado por error.
Descripción de la actividad:
El objetivo de esta tarea es estudiar de la frontera entre la algoritmia cuántica y la inteligencia artificial, y su aplicación a la mejora de tareas específicamente cuánticas.
En concreto, se abordarán los siguientes aspectos:
1. Clasificación de estados cuánticos a partir de datos experimentales.
2. Discriminación de mapas o procesos cuánticos mediante técnicas de IA.
3. Certificación y verificación de los recursos cuánticos mediante aprendizaje cuántico.
4. Desarrollo de algoritmos con utilidad para la física de altas energías y evaluación de los mismos en diversas plataformas cuánticas y clásicas.
Resultados
Fanizza, M.; Rouzé, C.; Stilck França, D.
Efficient Hamiltonian, structure and trace distance learning of Gaussian states Working paper
2026.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@workingpaper{nokey,
title = {Efficient Hamiltonian, structure and trace distance learning of Gaussian states},
author = {Fanizza, M. and Rouzé, C. and Stilck França, D.},
url = {https://arxiv.org/abs/2411.03163},
doi = {doi.org/10.48550/arXiv.2411.03163},
year = {2026},
date = {2026-06-01},
urldate = {2025-04-07},
abstract = {In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models. We obtain efficient protocols, both in sample and computational complexity, for the task of inferring the parameters of their underlying quadratic Hamiltonian under the assumption of bounded temperature, squeezing, displacement and maximal degree of the interaction graph. Our protocol only requires heterodyne measurements, which are often experimentally feasible, and has a sample complexity that scales logarithmically with the number of modes. Furthermore, we show that it is possible to learn the underlying interaction graph in a similar setting and sample complexity. Taken together, our results put the status of the quantum Hamiltonian learning problem for continuous variable systems in a more advanced state when compared to spins, where state-of-the-art results are either unavailable or quantitatively inferior to ours. In addition, we use our techniques to obtain the first results on learning Gaussian states in trace distance with a quadratic scaling in precision and polynomial in the number of modes, albeit imposing certain restrictions on the Gaussian states. Our main technical innovations are several continuity bounds for the covariance and Hamiltonian matrix of a Gaussian state, which are of independent interest, combined with what we call the local inversion technique. In essence, the local inversion technique allows us to reliably infer the Hamiltonian of a Gaussian state by only estimating in parallel submatrices of the covariance matrix whose size scales with the desired precision, but not the number of modes. This way we bypass the need to obtain precise global estimates of the covariance matrix, controlling the sample complexity.},
keywords = {UAB},
pubstate = {published},
tppubtype = {workingpaper}
}
In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models. We obtain efficient protocols, both in sample and computational complexity, for the task of inferring the parameters of their underlying quadratic Hamiltonian under the assumption of bounded temperature, squeezing, displacement and maximal degree of the interaction graph. Our protocol only requires heterodyne measurements, which are often experimentally feasible, and has a sample complexity that scales logarithmically with the number of modes. Furthermore, we show that it is possible to learn the underlying interaction graph in a similar setting and sample complexity. Taken together, our results put the status of the quantum Hamiltonian learning problem for continuous variable systems in a more advanced state when compared to spins, where state-of-the-art results are either unavailable or quantitatively inferior to ours. In addition, we use our techniques to obtain the first results on learning Gaussian states in trace distance with a quadratic scaling in precision and polynomial in the number of modes, albeit imposing certain restrictions on the Gaussian states. Our main technical innovations are several continuity bounds for the covariance and Hamiltonian matrix of a Gaussian state, which are of independent interest, combined with what we call the local inversion technique. In essence, the local inversion technique allows us to reliably infer the Hamiltonian of a Gaussian state by only estimating in parallel submatrices of the covariance matrix whose size scales with the desired precision, but not the number of modes. This way we bypass the need to obtain precise global estimates of the covariance matrix, controlling the sample complexity.
Baghali Khanian, Z.; Winter, A.
A Rate-Distortion Perspective on Quantum State Redistribution Artículo de revista
En: IEEE Transactions on Information Theory, 2026.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {A Rate-Distortion Perspective on Quantum State Redistribution},
author = {Baghali Khanian, Z. and Winter, A. },
url = {https://ieeexplore.ieee.org/document/10795756},
doi = {10.1109/TIT.2024.3516505},
year = {2026},
date = {2026-04-01},
urldate = {2025-12-12},
journal = {IEEE Transactions on Information Theory},
abstract = {We consider a rate-distortion version of the quantum state redistribution task, where the error of the decoded state is judged via an additive distortion measure; it thus constitutes a quantum generalisation of the classical Wyner-Ziv problem. The quantum source is described by a tripartite pure state shared between Alice (A, encoder), Bob (B, decoder) and a reference (R). Both Alice and Bob are required to output a system (Ã and B̃, respectively), and the distortion measure is encoded in an observable on ÃB̃R. It includes as special cases most quantum rate-distortion problems considered in the past, and in particular quantum data compression with the fidelity measured per copy; furthermore, it generalises the well-known state merging and quantum state redistribution tasks for a pure state source, with per-copy fidelity, and a variant recently considered by us, where the source is an ensemble of pure states [ZBK & AW, Proc. ISIT 2020, pp. 1858-1863 and ZBK, PhD thesis, UAB 2020, arXiv:2012.14143]. We derive a single-letter formula for the rate-distortion function of compression schemes assisted by free entanglement. A peculiarity of the formula is that in general it requires optimisation over an unbounded auxiliary register, so the rate-distortion function is not readily computable from our result, and there is a continuity issue at zero distortion. However, we show how to overcome these difficulties in certain situations.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
We consider a rate-distortion version of the quantum state redistribution task, where the error of the decoded state is judged via an additive distortion measure; it thus constitutes a quantum generalisation of the classical Wyner-Ziv problem. The quantum source is described by a tripartite pure state shared between Alice (A, encoder), Bob (B, decoder) and a reference (R). Both Alice and Bob are required to output a system (Ã and B̃, respectively), and the distortion measure is encoded in an observable on ÃB̃R. It includes as special cases most quantum rate-distortion problems considered in the past, and in particular quantum data compression with the fidelity measured per copy; furthermore, it generalises the well-known state merging and quantum state redistribution tasks for a pure state source, with per-copy fidelity, and a variant recently considered by us, where the source is an ensemble of pure states [ZBK & AW, Proc. ISIT 2020, pp. 1858-1863 and ZBK, PhD thesis, UAB 2020, arXiv:2012.14143]. We derive a single-letter formula for the rate-distortion function of compression schemes assisted by free entanglement. A peculiarity of the formula is that in general it requires optimisation over an unbounded auxiliary register, so the rate-distortion function is not readily computable from our result, and there is a continuity issue at zero distortion. However, we show how to overcome these difficulties in certain situations.
Gopalkrishna Naik, S.; Zartab, M.; Gisin, N.; Banik, M.
No-Go Theorem for Generic Simulation of Qubit Channels with Finite Classical Resources Artículo de revista
En: The Royal Society, 2026.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {No-Go Theorem for Generic Simulation of Qubit Channels with Finite Classical Resources},
author = {Gopalkrishna Naik, S. and Zartab, M. and Gisin, N. and Banik, M. },
url = {https://royalsocietypublishing.org/rspa/article/482/2333/20250831/480860/No-go-theorem-for-generic-simulation-of-qubit},
doi = {doi.org/10.1098/rspa.2025.0831},
year = {2026},
date = {2026-03-11},
urldate = {2025-07-16},
journal = {The Royal Society},
abstract = {Can quantum processes be simulated using only classical resources? This question delineates the boundary between classical and quantum models and clarifies the origin of quantum advantage in information processing. We address this question through the task of quantum channel simulation, where a sender (Alice) holds the classical description of a quantum state and wishes to transmit it to a receiver (Bob) for measurement. Prior work has shown that, for qubit channels, 2 bits of forward communication with shared randomness suffice to reproduce the statistics of any single-qubit measurement. We argue, however, that true channel simulation requires reproducing statistics of joint measurements—including entangled effects—on Alice’s state and an auxiliary system held by Bob. Such scenarios naturally arise in network communication, where some nodes know the state, while others do not. We prove that a perfect qubit channel cannot be simulated with any finite amount of classical communication, even using the most general multi-round, bidirectional protocols. We further show that this no-go result is rooted in the necessity of reproducing statistics associated with entangled effects. On the other hand, we show that noisy qubit channels, such as depolarizing channels, admit classical simulation, though the required communication diverges as noise decreases.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
Can quantum processes be simulated using only classical resources? This question delineates the boundary between classical and quantum models and clarifies the origin of quantum advantage in information processing. We address this question through the task of quantum channel simulation, where a sender (Alice) holds the classical description of a quantum state and wishes to transmit it to a receiver (Bob) for measurement. Prior work has shown that, for qubit channels, 2 bits of forward communication with shared randomness suffice to reproduce the statistics of any single-qubit measurement. We argue, however, that true channel simulation requires reproducing statistics of joint measurements—including entangled effects—on Alice’s state and an auxiliary system held by Bob. Such scenarios naturally arise in network communication, where some nodes know the state, while others do not. We prove that a perfect qubit channel cannot be simulated with any finite amount of classical communication, even using the most general multi-round, bidirectional protocols. We further show that this no-go result is rooted in the necessity of reproducing statistics associated with entangled effects. On the other hand, we show that noisy qubit channels, such as depolarizing channels, admit classical simulation, though the required communication diverges as noise decreases.
Abellanet-Vidal, J.; Müller-Rigat, G.; Rajchel-Mieldzioć, G.; Sanpera, A.
Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses Artículo de revista
En: 2025.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses},
author = {Abellanet-Vidal, J. and Müller-Rigat, G. and Rajchel-Mieldzioć, G. and Sanpera, A.},
url = {https://iopscience.iop.org/article/10.1088/1361-6633/ae0cfa},
doi = {10.1088/1361-6633/ae0cfa},
year = {2025},
date = {2025-10-24},
urldate = {2025-10-24},
abstract = {Quantum states that remain separable (i.e. not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely unknown. In this work, we employ linear maps and their inverses to derive new sufficient analytical conditions for absolute separability in arbitrary dimensions, providing extremal points of this set and improving its characterization. Additionally, we employ convex geometry optimization to refine the characterization of the set when multiple non-comparable criteria for absolute separability are available. We also address the closely related problem of characterizing the absolute PPT (positive partial transposition) set, which consists of quantum states that remain positive under partial transposition across all unitary transformations. Finally, we extend our results to multipartite states. We are proud to dedicate our work to Professor Ryszard Horodecki, whose pioneering contributions to the field of quantum entanglement continue to inspire us all. With deep gratitude and respect.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
Quantum states that remain separable (i.e. not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely unknown. In this work, we employ linear maps and their inverses to derive new sufficient analytical conditions for absolute separability in arbitrary dimensions, providing extremal points of this set and improving its characterization. Additionally, we employ convex geometry optimization to refine the characterization of the set when multiple non-comparable criteria for absolute separability are available. We also address the closely related problem of characterizing the absolute PPT (positive partial transposition) set, which consists of quantum states that remain positive under partial transposition across all unitary transformations. Finally, we extend our results to multipartite states. We are proud to dedicate our work to Professor Ryszard Horodecki, whose pioneering contributions to the field of quantum entanglement continue to inspire us all. With deep gratitude and respect.
Becker, S.; Galke, N.; Salzmann, R.; Van Luijk, L.
Convergence Rates for the Trotter Splitting for Unbounded Operators Artículo de revista
En: Foundations of Computational Mathematics , 2025.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Convergence Rates for the Trotter Splitting for Unbounded Operators},
author = {Becker, S. and Galke, N. and Salzmann, R. and Van Luijk, L.},
url = {https://link.springer.com/article/10.1007/s10208-025-09730-w},
doi = {doi.org/10.1007/s10208-025-09730-w},
year = {2025},
date = {2025-09-29},
urldate = {2024-07-04},
journal = {Foundations of Computational Mathematics },
abstract = {We study convergence rates of the Trotter splitting e^(A+L) = lim(n→∞) (e^(L/n) e^(A/n))^n in the strong operator topology. In the first part, we use complex interpolation theory to treat generators L and A of contraction semigroups on Banach spaces, with L relatively A-bounded. In the second part, we study unitary dynamics on Hilbert spaces and develop a new technique based on the concept of energy constraints. Our results provide a complete picture of the convergence rates for the Trotter splitting for all common types of Schrödinger and Dirac operators, including singular, confining and magnetic vector potentials, as well as molecular many-body Hamiltonians in dimension d = 3. Using the Brezis-Mironescu inequality, we derive convergence rates for the Schrödinger operator with V(x) = ±|x|^(-a) potential. In each case, our conditions are fully explicit.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
We study convergence rates of the Trotter splitting e^(A+L) = lim(n→∞) (e^(L/n) e^(A/n))^n in the strong operator topology. In the first part, we use complex interpolation theory to treat generators L and A of contraction semigroups on Banach spaces, with L relatively A-bounded. In the second part, we study unitary dynamics on Hilbert spaces and develop a new technique based on the concept of energy constraints. Our results provide a complete picture of the convergence rates for the Trotter splitting for all common types of Schrödinger and Dirac operators, including singular, confining and magnetic vector potentials, as well as molecular many-body Hamiltonians in dimension d = 3. Using the Brezis-Mironescu inequality, we derive convergence rates for the Schrödinger operator with V(x) = ±|x|^(-a) potential. In each case, our conditions are fully explicit.
Fontana, P.; Miranda Riaza, M.; Celi, A.
Efficient Finite-Resource Formulation of Non-Abelian Lattice Gauge Theories beyond One Dimension Artículo de revista
En: 2025.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Efficient Finite-Resource Formulation of Non-Abelian Lattice Gauge Theories beyond One Dimension},
author = {Fontana, P. and Miranda Riaza, M. and Celi, A.},
url = {https://journals.aps.org/prx/abstract/10.1103/k9p6-c649},
doi = {doi.org/10.1103/k9p6-c649},
year = {2025},
date = {2025-09-09},
urldate = {2025-09-09},
abstract = {Non-Abelian gauge theories provide the most accurate description of fundamental interactions, showing remarkable agreement with experimental data in cosmology and particle physics. Highly precise predictions can be made using standard techniques, both in the continuum and in the lattice frameworks. However, classical methods have limitations, particularly when attempting to extrapolate the continuum limit from the study of lattice gauge theories. Complementing classical computations or combining them with quantum computational methods, to improve the predictions toward the continuum limit with current quantum resources, is a formidable open challenge. In this paper, we propose a resource-efficient method to compute the running of the coupling in non-Abelian gauge theories beyond one spatial dimension. We first represent the Hamiltonian on periodic lattices in terms of loop variables and conjugate loop electric fields, exploiting the Gauss law to retain the gauge-independent ones. Then, we identify a local basis for small and large loops variationally to minimize the truncation error while computing the running of the coupling on small tori. Our method enables computations at arbitrary values of the bare coupling and lattice spacing with current quantum computers, simulators, and tensor-network calculations, in regimes otherwise inaccessible.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
Non-Abelian gauge theories provide the most accurate description of fundamental interactions, showing remarkable agreement with experimental data in cosmology and particle physics. Highly precise predictions can be made using standard techniques, both in the continuum and in the lattice frameworks. However, classical methods have limitations, particularly when attempting to extrapolate the continuum limit from the study of lattice gauge theories. Complementing classical computations or combining them with quantum computational methods, to improve the predictions toward the continuum limit with current quantum resources, is a formidable open challenge. In this paper, we propose a resource-efficient method to compute the running of the coupling in non-Abelian gauge theories beyond one spatial dimension. We first represent the Hamiltonian on periodic lattices in terms of loop variables and conjugate loop electric fields, exploiting the Gauss law to retain the gauge-independent ones. Then, we identify a local basis for small and large loops variationally to minimize the truncation error while computing the running of the coupling on small tori. Our method enables computations at arbitrary values of the bare coupling and lattice spacing with current quantum computers, simulators, and tensor-network calculations, in regimes otherwise inaccessible.
Rout, S.; Sakharwade, N.; Sankar Bhattacharya, S.; Ramanathan, R.; Horodecki, P.
Unbounded quantum advantage in communication with minimal input scaling Artículo de revista
En: Physical Review Research, 2025.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Unbounded quantum advantage in communication with minimal input scaling},
author = {Rout, S. and Sakharwade, N. and Sankar Bhattacharya, S. and Ramanathan, R. and Horodecki, P. },
url = {https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023104},
doi = {doi.org/10.1103/PhysRevResearch.7.023104},
year = {2025},
date = {2025-04-30},
journal = {Physical Review Research},
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) bit with respect to classical communication Θ(𝑛) bit. 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) relation reconstruction, we study the one-way zero-error communication complexity of a relation induced by a distributed clique labeling problem for orthogonality graphs. While we prove no quantum advantage in the first task, we show an 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(log2𝑚). Remarkably, the input size is Θ(log2𝑚) bit and the order of its scaling with respect to classical communication is 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.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
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) bit with respect to classical communication Θ(𝑛) bit. 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) relation reconstruction, we study the one-way zero-error communication complexity of a relation induced by a distributed clique labeling problem for orthogonality graphs. While we prove no quantum advantage in the first task, we show an 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(log2𝑚). Remarkably, the input size is Θ(log2𝑚) bit and the order of its scaling with respect to classical communication is 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.
Schindler, J.; Strasberg, P.; Galke, N.; Winter, A.; Jabbour, M.
Unification of observational entropy with maximum entropy principles Working paper
2025.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@workingpaper{nokey,
title = {Unification of observational entropy with maximum entropy principles},
author = {Schindler, J. and Strasberg, P. and Galke, N. and Winter, A. and Jabbour, M.
},
url = {https://arxiv.org/abs/2503.15612},
doi = {doi.org/10.48550/arXiv.2503.15612},
year = {2025},
date = {2025-03-19},
abstract = {We introduce a definition of coarse-grained entropy that unifies measurement-based (observational entropy) and max-entropy-based (Jaynes) approaches to coarse-graining, by identifying physical constraints with information theoretic priors. The definition is shown to include as special cases most other entropies of interest in physics. We then consider second laws, showing that the definition admits new entropy increase theorems and connections to thermodynamics. We survey mathematical properties of the definition, and show it resolves some pathologies of the traditional observational entropy in infinite dimensions. Finally, we study the dynamics of this entropy in a quantum random matrix model and a classical hard sphere gas. Together the results suggest that this generalized observational entropy can form the basis of a highly general approach to statistical mechanics.},
keywords = {UAB},
pubstate = {published},
tppubtype = {workingpaper}
}
We introduce a definition of coarse-grained entropy that unifies measurement-based (observational entropy) and max-entropy-based (Jaynes) approaches to coarse-graining, by identifying physical constraints with information theoretic priors. The definition is shown to include as special cases most other entropies of interest in physics. We then consider second laws, showing that the definition admits new entropy increase theorems and connections to thermodynamics. We survey mathematical properties of the definition, and show it resolves some pathologies of the traditional observational entropy in infinite dimensions. Finally, we study the dynamics of this entropy in a quantum random matrix model and a classical hard sphere gas. Together the results suggest that this generalized observational entropy can form the basis of a highly general approach to statistical mechanics.
Fanizza, M.; Galke, N.; Lumbreras, J.; Rouzé, C.; Winter, A.
Learning finitely-correlated states: stability of the spectral reconstruction Working paper
2025.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@workingpaper{nokey,
title = {Learning finitely-correlated states: stability of the spectral reconstruction},
author = {Fanizza, M. and Galke, N. and Lumbreras, J. and Rouzé, C. and Winter, A. },
url = {https://arxiv.org/abs/2312.07516},
doi = {doi.org/10.48550/arXiv.2312.07516},
year = {2025},
date = {2025-03-06},
abstract = {Matrix product operators allow efficient descriptions (or realizations) of states on a 1D lattice. We consider the task of learning a realization of minimal dimension from copies of an unknown state, such that the resulting operator is close to the density matrix in trace norm. For finitely correlated translation-invariant states on an infinite chain, a realization of minimal dimension can be exactly reconstructed via linear algebra operations from the marginals of a size depending on the representation dimension. We establish a bound on the trace norm error for an algorithm that estimates a candidate realization from estimates of these marginals and outputs a matrix product operator, estimating the state of a chain of arbitrary length . This bound allows us to establish an upper bound on the sample complexity of the learning task, with an explicit dependence on the site dimension, realization dimension and spectral properties of a certain map constructed from the state. A refined error bound can be proven for -finitely correlated states, which have an operational interpretation in terms of sequential quantum channels applied to the memory system. We can also obtain an analogous error bound for a class of matrix product density operators on a finite chain reconstructible by local marginals. In this case, a linear number of marginals must be estimated, obtaining a sample complexity of . The learning algorithm also works for states that are sufficiently close to a finitely correlated state, with the potential of providing competitive algorithms for other interesting families of states.},
keywords = {UAB},
pubstate = {published},
tppubtype = {workingpaper}
}
Matrix product operators allow efficient descriptions (or realizations) of states on a 1D lattice. We consider the task of learning a realization of minimal dimension from copies of an unknown state, such that the resulting operator is close to the density matrix in trace norm. For finitely correlated translation-invariant states on an infinite chain, a realization of minimal dimension can be exactly reconstructed via linear algebra operations from the marginals of a size depending on the representation dimension. We establish a bound on the trace norm error for an algorithm that estimates a candidate realization from estimates of these marginals and outputs a matrix product operator, estimating the state of a chain of arbitrary length . This bound allows us to establish an upper bound on the sample complexity of the learning task, with an explicit dependence on the site dimension, realization dimension and spectral properties of a certain map constructed from the state. A refined error bound can be proven for -finitely correlated states, which have an operational interpretation in terms of sequential quantum channels applied to the memory system. We can also obtain an analogous error bound for a class of matrix product density operators on a finite chain reconstructible by local marginals. In this case, a linear number of marginals must be estimated, obtaining a sample complexity of . The learning algorithm also works for states that are sufficiently close to a finitely correlated state, with the potential of providing competitive algorithms for other interesting families of states.
Llorens, S.; González, W.; Sentís, G.; Calsamiglia, J.; Muñoz-Tapia, R.; Bagan, Em.
Quantum Edge Detection Artículo de revista
En: Quantum, vol. 8, pp. 1289, 2025.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Quantum Edge Detection},
author = {Llorens, S. and González, W. and Sentís, G. and Calsamiglia, J. and Muñoz-Tapia, R. and Bagan, Em.},
url = {https://quantum-journal.org/papers/q-2025-04-03-1687/},
doi = {doi.org/10.22331/q-2025-04-03-1687},
year = {2025},
date = {2025-03-04},
journal = {Quantum},
volume = {8},
pages = {1289},
abstract = {We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing problems and put forward the usage of sequential strategies where the signal is analyzed in real time, allowing the experiment to be concluded as soon as the underlying hypothesis can be identified with a certified prescribed success probability. We analyze the performance of sequential tests by studying the stopping-time behavior, showing a considerable advantage over currently-used strategies based on a fixed predetermined measurement time.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing problems and put forward the usage of sequential strategies where the signal is analyzed in real time, allowing the experiment to be concluded as soon as the underlying hypothesis can be identified with a certified prescribed success probability. We analyze the performance of sequential tests by studying the stopping-time behavior, showing a considerable advantage over currently-used strategies based on a fixed predetermined measurement time.
Romero-Pallejà, J.; Ahiable, J.; Marconi, C.; Sanpera, A.
Multipartite entanglement in the diagonal symmetric subspace Artículo de revista
En: Journal of Mathematical Physics, vol. 66, pp. 22203, 2025.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Multipartite entanglement in the diagonal symmetric subspace},
author = {Romero-Pallejà, J. and Ahiable, J. and Marconi, C. and Sanpera, A. },
url = {https://pubs.aip.org/aip/jmp/article-abstract/66/2/022203/3335365/Multipartite-entanglement-in-the-diagonal?redirectedFrom=fulltext},
doi = {doi.org/10.1063/5.0240964},
year = {2025},
date = {2025-02-11},
journal = {Journal of Mathematical Physics},
volume = {66},
pages = {22203},
abstract = {We investigate the entanglement properties in the symmetric subspace of N-partite d-dimensional systems (qudits). As it happens already for bipartite diagonal symmetric states, also in the multipartite case the local dimension d plays a crucial role. Here, we demonstrate that there is no bound entanglement for d = 3, 4 and N = 3. Using different techniques, we present strong analytical evidence that no bound entanglement exist for any N if d ≤ 4. Interestingly, bound entanglement of diagonal symmetric states exist for any number of parties, N ≥ 2, and local dimensions d ≥ 5.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
We investigate the entanglement properties in the symmetric subspace of N-partite d-dimensional systems (qudits). As it happens already for bipartite diagonal symmetric states, also in the multipartite case the local dimension d plays a crucial role. Here, we demonstrate that there is no bound entanglement for d = 3, 4 and N = 3. Using different techniques, we present strong analytical evidence that no bound entanglement exist for any N if d ≤ 4. Interestingly, bound entanglement of diagonal symmetric states exist for any number of parties, N ≥ 2, and local dimensions d ≥ 5.
Rout, S.; Sankar Bhattacharya, S.; Horodecki, P.
Randomness-free detection of non-projective measurements: qubits & beyond Artículo de revista
En: 2024.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Randomness-free detection of non-projective measurements: qubits & beyond},
author = {Rout, S. and Sankar Bhattacharya, S. and Horodecki, P.},
url = {https://iopscience.iop.org/article/10.1088/1367-2630/adc0b4},
doi = {10.1088/1367-2630/adc0b4},
year = {2024},
date = {2024-11-29},
urldate = {2024-11-29},
abstract = {Non-projective measurements play a crucial role in various information-processing protocols. In this work, we propose an operational task to identify measurements that are neither projective nor classical post-processing of data obtained from projective measurements. Our setup involves space-like separated parties with access to a shared state with bounded local dimensions. Specifically, in the case of qubits, we focus on a bipartite scenario with different sets of target correlations. While some of these correlations can be obtained through non-projective measurements on a shared two-qubit state, it is impossible to generate these correlations using projective simulable measurements on bipartite qubit states, or equivalently, by using one bit of shared randomness and local post-processing. For certain target correlations, we show that detecting qubit non-projective measurements is robust under arbitrary depolarizing noise, except in the limiting case. We extend this task for qutrits and demonstrate that some correlations achievable via local non-projective measurements cannot be reproduced by both parties performing the same qutrit projective simulable measurements on their pre-shared state. We provide numerical evidence for the robustness of this scheme under arbitrary depolarizing noise. For a more generic consideration (bipartite and tripartite scenario), we provide numerical evidence for a projective-simulable bound on the reward function for our task. We also show a violation of this bound by using qutrit positive operator valued measures. From a foundational perspective, we extend the notion of non-projective measurements to general probabilistic theories (GPTs) and use a randomness-free test to demonstrate that a class of GPTs, called square-bits or box-world are unphysical.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
Non-projective measurements play a crucial role in various information-processing protocols. In this work, we propose an operational task to identify measurements that are neither projective nor classical post-processing of data obtained from projective measurements. Our setup involves space-like separated parties with access to a shared state with bounded local dimensions. Specifically, in the case of qubits, we focus on a bipartite scenario with different sets of target correlations. While some of these correlations can be obtained through non-projective measurements on a shared two-qubit state, it is impossible to generate these correlations using projective simulable measurements on bipartite qubit states, or equivalently, by using one bit of shared randomness and local post-processing. For certain target correlations, we show that detecting qubit non-projective measurements is robust under arbitrary depolarizing noise, except in the limiting case. We extend this task for qutrits and demonstrate that some correlations achievable via local non-projective measurements cannot be reproduced by both parties performing the same qutrit projective simulable measurements on their pre-shared state. We provide numerical evidence for the robustness of this scheme under arbitrary depolarizing noise. For a more generic consideration (bipartite and tripartite scenario), we provide numerical evidence for a projective-simulable bound on the reward function for our task. We also show a violation of this bound by using qutrit positive operator valued measures. From a foundational perspective, we extend the notion of non-projective measurements to general probabilistic theories (GPTs) and use a randomness-free test to demonstrate that a class of GPTs, called square-bits or box-world are unphysical.
Piccolini, M.; Karczewski, M.; Winter, A.; Lo Franco, R.
Robust generation of N-partite N-level singlet states by identical particle interferometry Artículo de revista
En: Quantum Science and Technology, vol. 10, iss. 1, no 15013 , 2024.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Robust generation of N-partite N-level singlet states by identical particle interferometry},
author = {Piccolini, M. and Karczewski, M. and Winter, A. and Lo Franco, R. },
url = {https://iopscience.iop.org/article/10.1088/2058-9565/ad8214},
doi = {10.1088/2058-9565/ad8214},
year = {2024},
date = {2024-10-15},
journal = {Quantum Science and Technology},
volume = {10},
number = {15013 },
issue = {1},
abstract = {We propose an interferometric scheme for generating the totally antisymmetric state of N identical bosons with N internal levels (generalized singlet). This state is a resource for various problems with dramatic quantum advantage. The procedure uses a sequence of Fourier multi-ports, combined with coincidence measurements filtering the results. Successful preparation of the generalized singlet is confirmed when the N particles of the input state stay separate (anti-bunch) on each multiport. The scheme is robust to local lossless noise and works even with a totally mixed input state.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
We propose an interferometric scheme for generating the totally antisymmetric state of N identical bosons with N internal levels (generalized singlet). This state is a resource for various problems with dramatic quantum advantage. The procedure uses a sequence of Fourier multi-ports, combined with coincidence measurements filtering the results. Successful preparation of the generalized singlet is confirmed when the N particles of the input state stay separate (anti-bunch) on each multiport. The scheme is robust to local lossless noise and works even with a totally mixed input state.
Skotiniotis, M.; Llorens, S.; Hotz, R.; J. Muñoz-Tapia Calsamiglia, R.
Identification of malfunctioning quantum devices Artículo de revista
En: Physical Review Research, vol. 6, 2024.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Identification of malfunctioning quantum devices},
author = {Skotiniotis, M. and Llorens, S. and Hotz, R. and Calsamiglia, J. Muñoz-Tapia, R. },
url = {https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.033329},
doi = {doi.org/10.1103/PhysRevResearch.6.033329},
year = {2024},
date = {2024-09-23},
urldate = {2025-09-23},
journal = {Physical Review Research},
volume = {6},
abstract = {We consider the problem of correctly identifying a malfunctioning quantum device that forms part of a network of 𝑁 such devices, which can be considered as the quantum analog of classical anomaly detection. In the case where the devices in question are sources assumed to prepare identical quantum pure states, with the faulty source producing a different anomalous pure state, we show that the optimal probability of successful identification requires a global quantum measurement. We also put forth several local measurement strategies—both adaptive and nonadaptive—that achieve the same optimal probability of success in the limit where the number of devices to be checked is large. In the case where the faulty device performs a known unitary operation, we show that the use of entangled probes provides an improvement that even allows perfect identification for values of the unitary parameter that surpass a certain threshold. Finally, if the faulty device implements a known qubit channel, we find that the optimal probability for detecting the position of rank-one and rank-two Pauli channels can be achieved by product state inputs and separable measurements for any size of network, whereas for rank-three and general amplitude damping channels, optimal identification requires entanglement with 𝑁 qubit ancillas.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
We consider the problem of correctly identifying a malfunctioning quantum device that forms part of a network of 𝑁 such devices, which can be considered as the quantum analog of classical anomaly detection. In the case where the devices in question are sources assumed to prepare identical quantum pure states, with the faulty source producing a different anomalous pure state, we show that the optimal probability of successful identification requires a global quantum measurement. We also put forth several local measurement strategies—both adaptive and nonadaptive—that achieve the same optimal probability of success in the limit where the number of devices to be checked is large. In the case where the faulty device performs a known unitary operation, we show that the use of entangled probes provides an improvement that even allows perfect identification for values of the unitary parameter that surpass a certain threshold. Finally, if the faulty device implements a known qubit channel, we find that the optimal probability for detecting the position of rank-one and rank-two Pauli channels can be achieved by product state inputs and separable measurements for any size of network, whereas for rank-three and general amplitude damping channels, optimal identification requires entanglement with 𝑁 qubit ancillas.
Llorens, S.; Sentís, G.; Muñoz-Tapia, R.
Quantum multi-anomaly detection Artículo de revista
En: Quantum, vol. 8, pp. 1452, 2024.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Quantum multi-anomaly detection},
author = {Llorens, S. and Sentís, G. and Muñoz-Tapia, R.},
url = {https://quantum-journal.org/papers/q-2024-08-28-1452/},
doi = {doi.org/10.22331/q-2024-08-28-1452},
year = {2024},
date = {2024-08-28},
urldate = {2024-08-28},
journal = {Quantum},
volume = {8},
pages = {1452},
abstract = {A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of
n preparations with k anomalies. We analyze the minimum-error protocol and the zero-error (unambiguous) protocol and obtain closed expressions for the success probability when both reference and anomalous states are known to the observer and anomalies can appear equally likely in any position of the preparation series. We find the solution using results from association schemes theory, thus establishing a connection between graph theory and quantum hypothesis testing. In particular, we use the Johnson association scheme which arises naturally from the Gram matrix of this problem. We also study the regime of large n and obtain the expression of the success probability that is non-vanishing. Finally, we address the case in which the observer is blind to the reference and the anomalous states. This scenario requires a universal protocol for which we prove that in the asymptotic limit, the success probability corresponds to the average of the known state scenario.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of
n preparations with k anomalies. We analyze the minimum-error protocol and the zero-error (unambiguous) protocol and obtain closed expressions for the success probability when both reference and anomalous states are known to the observer and anomalies can appear equally likely in any position of the preparation series. We find the solution using results from association schemes theory, thus establishing a connection between graph theory and quantum hypothesis testing. In particular, we use the Johnson association scheme which arises naturally from the Gram matrix of this problem. We also study the regime of large n and obtain the expression of the success probability that is non-vanishing. Finally, we address the case in which the observer is blind to the reference and the anomalous states. This scenario requires a universal protocol for which we prove that in the asymptotic limit, the success probability corresponds to the average of the known state scenario.
n preparations with k anomalies. We analyze the minimum-error protocol and the zero-error (unambiguous) protocol and obtain closed expressions for the success probability when both reference and anomalous states are known to the observer and anomalies can appear equally likely in any position of the preparation series. We find the solution using results from association schemes theory, thus establishing a connection between graph theory and quantum hypothesis testing. In particular, we use the Johnson association scheme which arises naturally from the Gram matrix of this problem. We also study the regime of large n and obtain the expression of the success probability that is non-vanishing. Finally, we address the case in which the observer is blind to the reference and the anomalous states. This scenario requires a universal protocol for which we prove that in the asymptotic limit, the success probability corresponds to the average of the known state scenario.
Learning Quantum Processes Without Input Control Artículo de revista
En: PRX Quantum, vol. 5, iss. 2, no 20367, 2024.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Learning Quantum Processes Without Input Control},
url = {https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.5.020367},
doi = {doi.org/10.1103/PRXQuantum.5.020367},
year = {2024},
date = {2024-06-27},
journal = {PRX Quantum},
volume = {5},
number = {20367},
issue = {2},
abstract = {We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process governed by classical parameters that are out of one’s control. This framework is applicable, for example, to the study of astronomical phenomena, disordered systems and biological processes not controlled by the observer. We provide an algorithm for learning with high probability in this setting with a finite amount of samples, even if the concept class is infinite. To do this, we review and adapt existing algorithms for shadow tomography and hypothesis selection, and combine their guarantees with the uniform convergence on the data of the loss functions of interest. As a byproduct, we obtain sufficient conditions for performing shadow tomography of classical-quantum states with a number of copies, which depends on the dimension of the quantum register, but not on the dimension of the classical one. We give concrete examples of processes that can be learned in this manner, based on quantum circuits or physically motivated classes, such as systems governed by Hamiltonians with random perturbations or data-dependent phase shifts.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process governed by classical parameters that are out of one’s control. This framework is applicable, for example, to the study of astronomical phenomena, disordered systems and biological processes not controlled by the observer. We provide an algorithm for learning with high probability in this setting with a finite amount of samples, even if the concept class is infinite. To do this, we review and adapt existing algorithms for shadow tomography and hypothesis selection, and combine their guarantees with the uniform convergence on the data of the loss functions of interest. As a byproduct, we obtain sufficient conditions for performing shadow tomography of classical-quantum states with a number of copies, which depends on the dimension of the quantum register, but not on the dimension of the classical one. We give concrete examples of processes that can be learned in this manner, based on quantum circuits or physically motivated classes, such as systems governed by Hamiltonians with random perturbations or data-dependent phase shifts.
Aniello, P.; L’Innocente, S.; Mancini, S.; Parisi, V.; Svampa, I.; Winter, A.
Invariant measures on p-adic Lie groups: the p-adic quaternion algebra and the Haar integral on the p-adic rotation groups Artículo de revista
En: Letters in Mathematical Physics, vol. 114, iss. 3, no 78, 2024.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Invariant measures on p-adic Lie groups: the p-adic quaternion algebra and the Haar integral on the p-adic rotation groups},
author = {Aniello, P. and L’Innocente, S. and Mancini, S. and Parisi, V. and Svampa, I. and Winter, A. },
url = {https://link.springer.com/article/10.1007/s11005-024-01826-8},
doi = {doi.org/10.1007/s11005-024-01826-8},
year = {2024},
date = {2024-06-06},
urldate = {2024-06-06},
journal = {Letters in Mathematical Physics},
volume = {114},
number = {78},
issue = {3},
abstract = {We provide a general expression of the Haar measure—that is, the essentially unique translation‑invariant measure—on a p‑adic Lie group. We then argue that this measure can be regarded as the measure naturally induced by the invariant volume form on the group, as it happens for a standard Lie group over the reals.
As an important application, we next consider the problem of determining the Haar measure on the p‑adic special orthogonal groups in dimension two, three, and four (for every prime number p). In particular, the Haar measure on SO(2, ℚₚ) is obtained by a direct application of our general formula. As for SO(3, ℚₚ) and SO(4, ℚₚ), instead, we show that Haar integrals on these two groups can conveniently be lifted to Haar integrals on certain p‑adic Lie groups from which the special orthogonal groups are obtained as quotients. This construction involves a suitable quaternion algebra over the field ℚₚ and is reminiscent of the quaternionic realization of the real rotation groups. Our results should pave the way to the development of harmonic analysis on the p‑adic special orthogonal groups, with potential applications in p‑adic quantum mechanics and in the recently proposed p‑adic quantum information theory.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
We provide a general expression of the Haar measure—that is, the essentially unique translation‑invariant measure—on a p‑adic Lie group. We then argue that this measure can be regarded as the measure naturally induced by the invariant volume form on the group, as it happens for a standard Lie group over the reals.
As an important application, we next consider the problem of determining the Haar measure on the p‑adic special orthogonal groups in dimension two, three, and four (for every prime number p). In particular, the Haar measure on SO(2, ℚₚ) is obtained by a direct application of our general formula. As for SO(3, ℚₚ) and SO(4, ℚₚ), instead, we show that Haar integrals on these two groups can conveniently be lifted to Haar integrals on certain p‑adic Lie groups from which the special orthogonal groups are obtained as quotients. This construction involves a suitable quaternion algebra over the field ℚₚ and is reminiscent of the quaternionic realization of the real rotation groups. Our results should pave the way to the development of harmonic analysis on the p‑adic special orthogonal groups, with potential applications in p‑adic quantum mechanics and in the recently proposed p‑adic quantum information theory.
As an important application, we next consider the problem of determining the Haar measure on the p‑adic special orthogonal groups in dimension two, three, and four (for every prime number p). In particular, the Haar measure on SO(2, ℚₚ) is obtained by a direct application of our general formula. As for SO(3, ℚₚ) and SO(4, ℚₚ), instead, we show that Haar integrals on these two groups can conveniently be lifted to Haar integrals on certain p‑adic Lie groups from which the special orthogonal groups are obtained as quotients. This construction involves a suitable quaternion algebra over the field ℚₚ and is reminiscent of the quaternionic realization of the real rotation groups. Our results should pave the way to the development of harmonic analysis on the p‑adic special orthogonal groups, with potential applications in p‑adic quantum mechanics and in the recently proposed p‑adic quantum information theory.
Xu, Z. P.; Schwonnek, R.; Winter, A.
Bounding the Joint Numerical Range of Pauli Strings by Graph Parameters Artículo de revista
En: PRX Quantum, vol. 5, iss. 2, no 20318, 2024.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Bounding the Joint Numerical Range of Pauli Strings by Graph Parameters},
author = {Xu, Z.P. and Schwonnek, R. and Winter, A.
},
url = {https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.5.020318},
doi = {doi.org/10.1103/PRXQuantum.5.020318},
year = {2024},
date = {2024-04-22},
urldate = {2024-04-22},
journal = {PRX Quantum},
volume = {5},
number = {20318},
issue = {2},
abstract = {The relations among a given set of observables on a quantum system are effectively captured by their so-called joint numerical range, which is the set of tuples of jointly attainable expectation values. Here we explore geometric properties of this construct for Pauli strings, whose pairwise commutation and anticommutation relations determine a graph 𝐺. We investigate the connection between the parameters of this graph and the structure of minimal ellipsoids encompassing the joint numerical range, and we develop this approach in different directions. As a consequence, we find counterexamples to a conjecture by de Gois et al. [Phys. Rev. A 107, 062211 (2023)], and answer an open question raised by Hastings and O’Donnell [STOC 2022: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, pp. 776–789], which implies a new graph parameter that we call “𝛽(𝐺).” Furthermore, we provide new insights into the perennial problem of estimating the ground-state energy of a many-body Hamiltonian. Our methods give lower bounds on the ground-state energy, which are typically hard to come by, and might therefore be useful in a variety of related fields.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
The relations among a given set of observables on a quantum system are effectively captured by their so-called joint numerical range, which is the set of tuples of jointly attainable expectation values. Here we explore geometric properties of this construct for Pauli strings, whose pairwise commutation and anticommutation relations determine a graph 𝐺. We investigate the connection between the parameters of this graph and the structure of minimal ellipsoids encompassing the joint numerical range, and we develop this approach in different directions. As a consequence, we find counterexamples to a conjecture by de Gois et al. [Phys. Rev. A 107, 062211 (2023)], and answer an open question raised by Hastings and O’Donnell [STOC 2022: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, pp. 776–789], which implies a new graph parameter that we call “𝛽(𝐺).” Furthermore, we provide new insights into the perennial problem of estimating the ground-state energy of a many-body Hamiltonian. Our methods give lower bounds on the ground-state energy, which are typically hard to come by, and might therefore be useful in a variety of related fields.
Skotiniotis, M.; Llorens, S.; Calsamiglia, J.; Muñoz-Tapia, R.
Topological obstructions to quantum computation with unitary oracles Artículo de revista
En: Physical Review Research, vol. 9, iss. 3, pp. 32625, 2024.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Topological obstructions to quantum computation with unitary oracles},
author = {Skotiniotis, M. and Llorens, S. and Calsamiglia, J. and Muñoz-Tapia, R. },
url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.032625},
doi = {doi.org/10.1103/PhysRevA.109.032625},
year = {2024},
date = {2024-03-28},
urldate = {2024-03-28},
journal = {Physical Review Research},
volume = {9},
issue = {3},
pages = {32625},
abstract = {Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speedup. The search for new quantum algorithms benefits from understanding their limitations: Some tasks are impossible in quantum circuits, although their classical versions are easy, for example, cloning. An example with a unitary oracle 𝑈 is the if clause, the task to implement controlled 𝑈 (up to the phase on 𝑈). In classical computation the conditional statement is easy and essential. In quantum circuits the if clause was shown impossible from one query to 𝑈. Is it possible from polynomially many queries? Here we unify algorithms with a unitary oracle and develop a topological method to prove their limitations: No number of queries to 𝑈 and 𝑈† lets quantum circuits implement the if clause, even if admitting approximations, postselection, and relaxed causality. We also show limitations of process tomography, oracle neutralization, and dim𝑈√𝑈, 𝑈𝑇, and 𝑈† algorithms. Our results strengthen an advantage of linear optics, challenge the experiments on relaxed causality, and motivate new algorithms with many-outcome measurements.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speedup. The search for new quantum algorithms benefits from understanding their limitations: Some tasks are impossible in quantum circuits, although their classical versions are easy, for example, cloning. An example with a unitary oracle 𝑈 is the if clause, the task to implement controlled 𝑈 (up to the phase on 𝑈). In classical computation the conditional statement is easy and essential. In quantum circuits the if clause was shown impossible from one query to 𝑈. Is it possible from polynomially many queries? Here we unify algorithms with a unitary oracle and develop a topological method to prove their limitations: No number of queries to 𝑈 and 𝑈† lets quantum circuits implement the if clause, even if admitting approximations, postselection, and relaxed causality. We also show limitations of process tomography, oracle neutralization, and dim𝑈√𝑈, 𝑈𝑇, and 𝑈† algorithms. Our results strengthen an advantage of linear optics, challenge the experiments on relaxed causality, and motivate new algorithms with many-outcome measurements.
Gasbarri, G.; Bilkis, M.; Roda-Salichs, E.; Calsamiglia, J.
Sequential hypothesis testing for continuously-monitored quantum systems Artículo de revista
En: Quantum, vol. 8, 2024.
Resumen | Enlaces | BibTeX | Etiquetas: UAB
@article{nokey,
title = {Sequential hypothesis testing for continuously-monitored quantum systems},
author = {Gasbarri, G. and Bilkis, M. and Roda-Salichs, E. and Calsamiglia, J. },
url = {https://quantum-journal.org/papers/q-2024-03-20-1289/#},
doi = {doi.org/10.22331/q-2024-03-20-1289},
year = {2024},
date = {2024-03-20},
urldate = {2024-03-20},
journal = {Quantum},
volume = {8},
abstract = {We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing problems and put forward the usage of sequential strategies where the signal is analyzed in real time, allowing the experiment to be concluded as soon as the underlying hypothesis can be identified with a certified prescribed success probability. We analyze the performance of sequential tests by studying the stopping-time behavior, showing a considerable advantage over currently-used strategies based on a fixed predetermined measurement time.},
keywords = {UAB},
pubstate = {published},
tppubtype = {article}
}
We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing problems and put forward the usage of sequential strategies where the signal is analyzed in real time, allowing the experiment to be concluded as soon as the underlying hypothesis can be identified with a certified prescribed success probability. We analyze the performance of sequential tests by studying the stopping-time behavior, showing a considerable advantage over currently-used strategies based on a fixed predetermined measurement time.
