Application
AI and quantum machine learning techniques for quantum process identification
Quantum Information and Quantum Optics
Group Description:
The Quantum Information and Quantum Optics groups in the Physics department of the UAB have been working for years on topics related to the use of AI and machine learning for the optimization of quantum resources and to address some of the open questions in high-energy physics and condensed matter physics. On the group’s website, you can find more than 400 scientific publications in the field of quantum information, several of which focus on using AI and machine learning to understand quantum systems better. This includes methods for certifying and verifying quantum states. This experience is crucial for discerning whether what is generated on a quantum computer is indeed the state we want to study and not one that has been generated in error.
Activity description:
The goal of this task is to study the frontier between quantum algorithms and artificial intelligence and their application to the improvement of specifically quantum tasks. In particular, the following aspects will be addressed:
- Classification of quantum states from experimental data.
- Discrimination of quantum maps or processes using AI techniques.
- Certification and verification of quantum resources through quantum learning.
- Development of algorithms useful for high-energy physics and their evaluation on various quantum and classical platforms.
Results
Baghali Khanian, Z.; Winter, A.
A Rate-Distortion Perspective on Quantum State Redistribution Journal Article
In: IEEE Transactions on Information Theory, 2025.
Abstract | Links | BibTeX | Tags: 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 = {2025},
date = {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.
Skotiniotis, M.; Llorens, S.; Hotz, R.; J. Muñoz-Tapia Calsamiglia, R.
Identification of malfunctioning quantum devices Journal Article
In: Physical Review Research, vol. 6, 2025.
Abstract | Links | BibTeX | Tags: 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 = {2025},
date = {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.
Colomer, P.; Deppe, C.; Boche, H.; Winter, A.
Quantum Hypothesis Testing Lemma for Deterministic Identification over Quantum Channels Working paper
2025.
Abstract | Links | BibTeX | Tags: UAB
@workingpaper{nokey,
title = {Quantum Hypothesis Testing Lemma for Deterministic Identification over Quantum Channels},
author = {Colomer, P. and Deppe, C. and Boche, H. and Winter, A. },
url = {https://arxiv.org/abs/2504.20991},
doi = {doi.org/10.48550/arXiv.2504.20991},
year = {2025},
date = {2025-07-24},
abstract = {In our previous work, we presented the emph{Hypothesis Testing Lemma}, a key tool that establishes sufficient conditions for the existence of good deterministic identification (DI) codes for memoryless channels with finite output, but arbitrary input alphabets. In this work, we provide a full quantum analogue of this lemma, which shows that the existence of a DI code in the quantum setting follows from a suitable packing in a modified space of output quantum states. Specifically, we demonstrate that such a code can be constructed using product states derived from this packing. This result enables us to tighten the capacity lower bound for DI over quantum channels beyond the simultaneous decoding approach. In particular, we can now express these bounds solely in terms of the Minkowski dimension of a certain state space, giving us new insights to better understand the nature of the protocol, and the separation between simultaneous and non-simultaneous codes. We extend the discussion with a particular channel example for which we can construct an optimum code.},
keywords = {UAB},
pubstate = {published},
tppubtype = {workingpaper}
}
In our previous work, we presented the emph{Hypothesis Testing Lemma}, a key tool that establishes sufficient conditions for the existence of good deterministic identification (DI) codes for memoryless channels with finite output, but arbitrary input alphabets. In this work, we provide a full quantum analogue of this lemma, which shows that the existence of a DI code in the quantum setting follows from a suitable packing in a modified space of output quantum states. Specifically, we demonstrate that such a code can be constructed using product states derived from this packing. This result enables us to tighten the capacity lower bound for DI over quantum channels beyond the simultaneous decoding approach. In particular, we can now express these bounds solely in terms of the Minkowski dimension of a certain state space, giving us new insights to better understand the nature of the protocol, and the separation between simultaneous and non-simultaneous codes. We extend the discussion with a particular channel example for which we can construct an optimum code.
Gopalkrishna Naik, S.; Zartab, M.; Gisin, N.; Banik, M.
No-Go Theorem for Generic Simulation of Qubit Channels with Finite Classical Resources Working paper
2025.
Abstract | Links | BibTeX | Tags: UAB
@workingpaper{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://arxiv.org/abs/2501.15807},
doi = {doi.org/10.48550/arXiv.2501.15807},
year = {2025},
date = {2025-07-16},
urldate = {2025-07-16},
abstract = {The mathematical framework of quantum theory, though fundamentally distinct from classical physics, raises the question of whether quantum processes can be efficiently simulated using classical resources. For instance, a sender (Alice) possessing the classical description of a qubit state can simulate the action of a qubit channel through finite classical communication with a receiver (Bob), enabling Bob to reproduce measurement statistics for any observable on the state. In this work, we contend that a more general simulation requires reproducing statistics of joint measurements, potentially involving entangled effects, on Alice's system and an additional system held by Bob, even when Bob's system state is unknown or entangled with a larger system. Within this broad framework, we prove that no finite amount of classical messaging, regardless of how many rounds are used or how large each message can be, can reproduce a perfect qubit channel, highlighting an inescapable barrier in quantum channel simulation with classical resources. We also establish that entangled effects crucially underlies this no-go result. However, for noisy qubit channels, such as those with depolarizing noise, we demonstrate that general simulation is achievable with finite communication. Notably, the required communication increases as the noise decreases, revealing an intricate relationship between the noise in the channel and the resources necessary for its classical simulation.},
keywords = {UAB},
pubstate = {published},
tppubtype = {workingpaper}
}
The mathematical framework of quantum theory, though fundamentally distinct from classical physics, raises the question of whether quantum processes can be efficiently simulated using classical resources. For instance, a sender (Alice) possessing the classical description of a qubit state can simulate the action of a qubit channel through finite classical communication with a receiver (Bob), enabling Bob to reproduce measurement statistics for any observable on the state. In this work, we contend that a more general simulation requires reproducing statistics of joint measurements, potentially involving entangled effects, on Alice's system and an additional system held by Bob, even when Bob's system state is unknown or entangled with a larger system. Within this broad framework, we prove that no finite amount of classical messaging, regardless of how many rounds are used or how large each message can be, can reproduce a perfect qubit channel, highlighting an inescapable barrier in quantum channel simulation with classical resources. We also establish that entangled effects crucially underlies this no-go result. However, for noisy qubit channels, such as those with depolarizing noise, we demonstrate that general simulation is achievable with finite communication. Notably, the required communication increases as the noise decreases, revealing an intricate relationship between the noise in the channel and the resources necessary for its classical simulation.
Rout, S.; Sakharwade, N.; Sankar Bhattacharya, S.; Ramanathan, R.; Horodecki, P.
Unbounded quantum advantage in communication with minimal input scaling Journal Article
In: Physical Review Research, 2025.
Abstract | Links | BibTeX | Tags: 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.
Xu, Z. P.; Schwonnek, R.; Winter, A.
Bounding the Joint Numerical Range of Pauli Strings by Graph Parameters Journal Article
In: PRX Quantum, vol. 5, iss. 2, no. 20318, 2025.
Abstract | Links | BibTeX | Tags: 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 = {2025},
date = {2025-04-22},
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.
Fanizza, M.; Rouzé, C.; Stilck França, D.
Efficient Hamiltonian, structure and trace distance learning of Gaussian states Working paper
2025.
Abstract | Links | BibTeX | Tags: 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 = {2025},
date = {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.
Schindler, J.; Strasberg, P.; Galke, N.; Winter, A.; Jabbour, M.
Unification of observational entropy with maximum entropy principles Working paper
2025.
Abstract | Links | BibTeX | Tags: 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.
Abstract | Links | BibTeX | Tags: 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 Journal Article
In: Quantum, vol. 8, pp. 1289, 2025.
Abstract | Links | BibTeX | Tags: 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 Journal Article
In: Journal of Mathematical Physics, vol. 66, pp. 22203, 2025.
Abstract | Links | BibTeX | Tags: 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 Working paper
2024.
Abstract | Links | BibTeX | Tags: UAB
@workingpaper{nokey,
title = {Randomness-free Detection of Non-projective Measurements: Qubits & beyond},
author = {Rout, S. and Sankar Bhattacharya, S. and Horodecki, P.},
url = {https://doi.org/10.48550/arXiv.2412.00213},
doi = {doi.org/10.48550/arXiv.2412.00213},
year = {2024},
date = {2024-11-29},
urldate = {2024-11-29},
abstract = {Non-projective measurements are resourceful in several information-processing protocols. In this work, we propose an operational task involving space-like separated parties to detect measurements that are neither projective nor a classical post-processing of data obtained from a projective measurement. In the case of qubits, we consider a bipartite scenario and different sets of target correlations. While some correlations in each of these sets can be obtained by performing non-projective measurements on some shared two-qubit state it is impossible to simulate correlation in any of them using projective simulable measurements on bipartite qubit states or equivalently one bit of shared randomness. While considering certain sets of target correlations we show that the detection of qubit non-projective measurement is robust under arbitrary depolarising noise (except in the limiting case). For qutrits, while considering a similar task we show that some correlations obtained from local non-projective measurements are impossible to be obtained while performing the same qutrit projective simulable measurements by both parties. We provide numerical evidence of its robustness under arbitrary depolarising 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 POVMs. 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 = {workingpaper}
}
Non-projective measurements are resourceful in several information-processing protocols. In this work, we propose an operational task involving space-like separated parties to detect measurements that are neither projective nor a classical post-processing of data obtained from a projective measurement. In the case of qubits, we consider a bipartite scenario and different sets of target correlations. While some correlations in each of these sets can be obtained by performing non-projective measurements on some shared two-qubit state it is impossible to simulate correlation in any of them using projective simulable measurements on bipartite qubit states or equivalently one bit of shared randomness. While considering certain sets of target correlations we show that the detection of qubit non-projective measurement is robust under arbitrary depolarising noise (except in the limiting case). For qutrits, while considering a similar task we show that some correlations obtained from local non-projective measurements are impossible to be obtained while performing the same qutrit projective simulable measurements by both parties. We provide numerical evidence of its robustness under arbitrary depolarising 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 POVMs. 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.
Rout, S.; N. Bhattacharya Sakharwade, S. S.; Ramanathan, R.; Horodecki, P.
Unbounded Quantum Advantage in Communication with Minimal Input Scaling Working paper
Preprint, 2024.
Abstract | Links | BibTeX | Tags: UAB
@workingpaper{nokey,
title = {Unbounded Quantum Advantage in Communication with Minimal Input Scaling},
author = {Rout,S. and Sakharwade, N. Bhattacharya, S.S. and Ramanathan, R. and Horodecki, P.},
url = {https://arxiv.org/pdf/2305.10372},
doi = {doi.org/10.48550/arXiv.2305.10372},
year = {2024},
date = {2024-11-29},
urldate = {2024-11-29},
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 = {workingpaper}
}
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.
Abellanet-Vidal, J.; Müller-Rigat, G.; Rajchel-Mieldzioć, G.; Sanpera, A.
Improving absolute separability bounds for arbitrary dimensions Working paper
2024.
Abstract | Links | BibTeX | Tags: UAB
@workingpaper{nokey,
title = {Improving absolute separability bounds for arbitrary dimensions},
author = {Abellanet-Vidal, J. and Müller-Rigat, G. and Rajchel-Mieldzioć, G. and Sanpera, A.},
url = {https://arxiv.org/abs/2410.22415},
doi = {doi.org/10.48550/arXiv.2410.22415},
year = {2024},
date = {2024-10-29},
urldate = {2024-10-29},
abstract = {Sufficient analytical conditions for separability in composite quantum systems are very scarce and only known for low-dimensional cases. Here, we use linear maps and their inverses to derive powerful analytical conditions, providing tight bounds and extremal points of the set of absolutely separable states, i.e., states that remain separable under any global unitary transformation. Our analytical results apply to generic quantum states in arbitrary dimensions, and depend only on a single or very few eigenvalues of the considered state. Furthermore, we use convex geometry tools to improve the general characterization of the AS set given several non-comparable criteria. Finally, we present various conditions related to the twin problem of characterizing absolute PPT, that is, the set of quantum states that are positive under partial transposition and remain so under all unitary transformations.},
keywords = {UAB},
pubstate = {published},
tppubtype = {workingpaper}
}
Sufficient analytical conditions for separability in composite quantum systems are very scarce and only known for low-dimensional cases. Here, we use linear maps and their inverses to derive powerful analytical conditions, providing tight bounds and extremal points of the set of absolutely separable states, i.e., states that remain separable under any global unitary transformation. Our analytical results apply to generic quantum states in arbitrary dimensions, and depend only on a single or very few eigenvalues of the considered state. Furthermore, we use convex geometry tools to improve the general characterization of the AS set given several non-comparable criteria. Finally, we present various conditions related to the twin problem of characterizing absolute PPT, that is, the set of quantum states that are positive under partial transposition and remain so under all unitary transformations.
Piccolini, M.; Karczewski, M.; Winter, A.; Lo Franco, R.
Robust generation of N-partite N-level singlet states by identical particle interferometry Journal Article
In: Quantum Science and Technology, vol. 10, iss. 1, no. 15013 , 2024.
Abstract | Links | BibTeX | Tags: 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.
Fontana, P.; Miranda Riaza, M.; Celi, A.
An efficient finite-resource formulation of non-Abelian lattice gauge theories beyond one dimension Working paper
2024.
Abstract | Links | BibTeX | Tags: UAB
@workingpaper{nokey,
title = {An 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://arxiv.org/abs/2409.04441},
doi = {doi.org/10.48550/arXiv.2409.04441},
year = {2024},
date = {2024-09-06},
abstract = {Non-Abelian gauge theories provide an accurate description of fundamental interactions, as both perturbation theory and quantum Monte Carlo computations in lattice gauge theory, it when applicable, show remarkable agreement with experimental data from particle colliders and cosmological observations. Complementing these computations, or combining them with quantum-inspired Hamiltonian lattice computations on quantum machines to improve continuum limit predictions with current quantum resources, is a formidable open challenge. Here, 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 = {workingpaper}
}
Non-Abelian gauge theories provide an accurate description of fundamental interactions, as both perturbation theory and quantum Monte Carlo computations in lattice gauge theory, it when applicable, show remarkable agreement with experimental data from particle colliders and cosmological observations. Complementing these computations, or combining them with quantum-inspired Hamiltonian lattice computations on quantum machines to improve continuum limit predictions with current quantum resources, is a formidable open challenge. Here, 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.
Llorens, S.; Sentís, G.; Muñoz-Tapia, R.
Quantum multi-anomaly detection Journal Article
In: Quantum, vol. 8, pp. 1452, 2024.
Abstract | Links | BibTeX | Tags: 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.
Becker, S.; Galke, N.; Salzmann, R.; Van Luijk, L.
Convergence rates for the Trotter-Kato splitting Working paper
2024.
Abstract | Links | BibTeX | Tags: UAB
@workingpaper{nokey,
title = {Convergence rates for the Trotter-Kato splitting},
author = {Becker, S. and Galke, N. and Salzmann, R. and Van Luijk, L.},
url = {https://arxiv.org/abs/2407.04045},
doi = {doi.org/10.48550/arXiv.2407.04045},
year = {2024},
date = {2024-07-04},
urldate = {2024-07-04},
abstract = {We study convergence rates of the Trotter–Kato splitting exp(A + L) = limₙ→∞ (exp(L/n) · exp(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 potential V(x) = ±|x|^(–a). In each case, our conditions are fully explicit.
},
keywords = {UAB},
pubstate = {published},
tppubtype = {workingpaper}
}
We study convergence rates of the Trotter–Kato splitting exp(A + L) = limₙ→∞ (exp(L/n) · exp(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 potential V(x) = ±|x|^(–a). In each case, our conditions are fully explicit.
Learning Quantum Processes Without Input Control Journal Article
In: PRX Quantum, vol. 5, iss. 2, no. 20367, 2024.
Abstract | Links | BibTeX | Tags: 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 Journal Article
In: Letters in Mathematical Physics, vol. 114, iss. 3, no. 78, 2024.
Abstract | Links | BibTeX | Tags: 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.
Skotiniotis, M.; Llorens, S.; Calsamiglia, J.; Muñoz-Tapia, R.
Topological obstructions to quantum computation with unitary oracles Journal Article
In: Physical Review Research, vol. 9, iss. 3, pp. 32625, 2024.
Abstract | Links | BibTeX | Tags: 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 Journal Article
In: Quantum, vol. 8, 2024.
Abstract | Links | BibTeX | Tags: 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.
