Application
Quantum and quantum-inspired algorithms for complex mathematical problems
Interdisciplinary Thematic Platform on Quantum Technologies at CSIC
Group Description:
Within CSIC, the objectives of this project align with one of the fundamental pillars of the Interdisciplinary Thematic Platform on Quantum Technologies, to which the participating research groups belong. This platform coordinates CSIC researchers’ access to quantum computing resources and conducts research on quantum algorithms of both fundamental (scientific) and commercial interest (in collaboration with companies and third parties). CSIC contributes unique expertise in the design of quantum optimization and simulation algorithms, quantum artificial intelligence algorithms, and the operation of quantum computers.
Several groups from CSIC institutes are actively involved in quantum algorithm development. The QUINFOG group at the Institute of Fundamental Physics develops quantum optimization algorithms and quantum machine learning. Additionally, new numerical simulation methods based on tensor networks are being researched. The Institute of Theoretical Physics group, led by professors Germán Sierra and Alejandro Bermúdez, focuses on quantum algorithms applied to processes in condensed matter physics and high-energy physics. The group at the Center for Research in Nanomaterials and Nanotechnology, led by Daniel Barredo, experiments with the use of cold atoms to simulate quantum processes, including circuits and algorithms developed by the community. The Institute of Interdisciplinary Physics and Complex Systems researches new models of quantum computing and artificial intelligence for application to complex systems.
The mentioned QTEP thematic platform coordinates various courses in quantum computing, including the CSIC Master’s in Quantum Technologies, as well as dissemination and outreach activities aimed at businesses. Additionally, the platform promotes transfer activities and the creation of spin-offs.
Activity description:
- Development of quantum and quantum-inspired algorithms to solve optimization and machine learning problems of practical relevance.
- Development of error mitigation techniques and variational methods enabling the use of quantum computers under realistic conditions of noise and imperfections, such as in devices based on trapped ions.
- Development of quantum algorithms for the study and simulation of complex quantum systems in condensed matter and particle physics.
- Tensor networks for the simulation, optimization, and training of quantum algorithms.
Results
Bou-Comas, A.; Marimón, C. R.; Schneider, J. T.; Ramos Marimón, C.; Schneider, J. T.; Carignano, S.; Tagliacozzo, L.
Measuring temporal entanglement in experiments as a hallmark for integrability Working paper
2025.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@workingpaper{nokey,
title = {Measuring temporal entanglement in experiments as a hallmark for integrability},
author = {Bou-Comas, A. and Marimón, C.R. and Schneider, J.T. and Ramos Marimón, C. and Schneider, J.T. and Carignano, S. and Tagliacozzo, L. },
url = {https://arxiv.org/abs/2409.05517},
doi = {doi.org/10.48550/arXiv.2409.05517},
year = {2025},
date = {2025-09-09},
abstract = {We introduce a novel experimental approach to probe many-body quantum systems by developing a protocol to measure generalized temporal entropies. We demonstrate that the recently proposed generalized temporal entropies [Phys. Rev. Research 6, 033021] are equivalent to observing the out-of-equilibrium dynamics of a replicated system induced by a double quench protocol using local operators as probes. This equivalence, confirmed through state-of-the-art tensor network simulations for one-dimensional systems, validates the feasibility of measuring generalized temporal entropies experimentally. Our results reveal that the dynamics governed by the transverse field Ising model integrable Hamiltonian differ qualitatively from those driven by the same model with an additional parallel field, breaking integrability. They thus suggest that generalized temporal entropies can serve as a tool for identifying different dynamical classes. This work represents the first practical application of generalized temporal entropy characterization in one-dimensional many-body quantum systems and offers a new pathway for experimentally detecting integrability. We conclude by outlining the experimental requirements for implementing this protocol with state of the art quantum simulators.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {workingpaper}
}
We introduce a novel experimental approach to probe many-body quantum systems by developing a protocol to measure generalized temporal entropies. We demonstrate that the recently proposed generalized temporal entropies [Phys. Rev. Research 6, 033021] are equivalent to observing the out-of-equilibrium dynamics of a replicated system induced by a double quench protocol using local operators as probes. This equivalence, confirmed through state-of-the-art tensor network simulations for one-dimensional systems, validates the feasibility of measuring generalized temporal entropies experimentally. Our results reveal that the dynamics governed by the transverse field Ising model integrable Hamiltonian differ qualitatively from those driven by the same model with an additional parallel field, breaking integrability. They thus suggest that generalized temporal entropies can serve as a tool for identifying different dynamical classes. This work represents the first practical application of generalized temporal entropy characterization in one-dimensional many-body quantum systems and offers a new pathway for experimentally detecting integrability. We conclude by outlining the experimental requirements for implementing this protocol with state of the art quantum simulators.
Edmunds, C. L.; Rico, E.; Arrazola, I.; Brennen, G. K.; Meth, M.; Blatt, R.; Ringbauer, M.
Constructing the spin-1 Haldane phase on a qudit quantum processor Working paper
2025.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@workingpaper{nokey,
title = {Constructing the spin-1 Haldane phase on a qudit quantum processor},
author = {Edmunds, C. L. . and Rico, E. and Arrazola, I. and Brennen, G. K. and Meth, M. and Blatt, R. and Ringbauer, M.},
url = {https://arxiv.org/abs/2408.04702},
doi = {doi.org/10.48550/arXiv.2408.04702},
year = {2025},
date = {2025-08-08},
abstract = {Symmetry-protected topological phases have fundamentally changed our understanding of quantum matter. An archetypal example of such a quantum phase of matter is the Haldane phase, containing the spin-1 Heisenberg chain. The intrinsic quantum nature of such phases, however, often makes it challenging to study them using classical means. Here, we use trapped-ion qutrits to natively engineer spin-1 chains within the Haldane phase. Using a scalable, deterministic procedure to prepare the Affleck-Kennedy-Lieb-Tasaki (AKLT) state within the Haldane phase, we study the topological features of this system on a qudit quantum processor. Notably, we verify the long-range string order of the state, despite its short-range correlations, and observe spin fractionalization of the physical spin-1 particles into effective qubits at the chain edges, a defining feature of this system. The native realization of Haldane physics on a qudit quantum processor and the scalable preparation procedures open the door to the efficient exploration of a wide range of systems beyond spin-1/2},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {workingpaper}
}
Symmetry-protected topological phases have fundamentally changed our understanding of quantum matter. An archetypal example of such a quantum phase of matter is the Haldane phase, containing the spin-1 Heisenberg chain. The intrinsic quantum nature of such phases, however, often makes it challenging to study them using classical means. Here, we use trapped-ion qutrits to natively engineer spin-1 chains within the Haldane phase. Using a scalable, deterministic procedure to prepare the Affleck-Kennedy-Lieb-Tasaki (AKLT) state within the Haldane phase, we study the topological features of this system on a qudit quantum processor. Notably, we verify the long-range string order of the state, despite its short-range correlations, and observe spin fractionalization of the physical spin-1 particles into effective qubits at the chain edges, a defining feature of this system. The native realization of Haldane physics on a qudit quantum processor and the scalable preparation procedures open the door to the efficient exploration of a wide range of systems beyond spin-1/2
Bǎzǎvan, O.; Saner, S.; Tirrito, E.; Araneda, G.; Srinivas, R.; Bermudez, A.
Synthetic Z2 gauge theories based on parametric excitations of trapped ions Journal Article
In: Communications Physics, vol. 7, pp. 229, 2025.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@article{nokey,
title = {Synthetic Z2 gauge theories based on parametric excitations of trapped ions},
author = {Bǎzǎvan, O. and Saner, S. and Tirrito, E. and Araneda, G. and Srinivas, R. and Bermudez, A.},
url = {https://www.nature.com/articles/s42005-024-01691-w#citeas},
doi = {doi.org/10.1038/s42005-024-01691-w},
year = {2025},
date = {2025-07-12},
journal = {Communications Physics},
volume = {7},
pages = {229},
abstract = {Resource efficient schemes for the quantum simulation of lattice gauge theories can benefit from hybrid encodings of gauge and matter fields that use the native degrees of freedom, such as internal qubits and motional phonons in trapped-ion devices. We propose to use a parametric scheme to induce a tunneling of the phonons conditioned to the internal qubit state which, when implemented with a single trapped ion, corresponds to a minimal Z2 gauge theory. To evaluate the feasibility of this scheme, we perform numerical simulations of the state-dependent tunneling using realistic parameters, and identify the leading sources of error in future experiments. We discuss how to generalize this minimal case to more complex settings by increasing the number of ions, moving from a single link to a Z2 plaquette, and to an entire Z2 chain. We present analytical expressions for the gauge-invariant dynamics and the corresponding confinement, which are benchmarked using matrix product state simulations.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {article}
}
Resource efficient schemes for the quantum simulation of lattice gauge theories can benefit from hybrid encodings of gauge and matter fields that use the native degrees of freedom, such as internal qubits and motional phonons in trapped-ion devices. We propose to use a parametric scheme to induce a tunneling of the phonons conditioned to the internal qubit state which, when implemented with a single trapped ion, corresponds to a minimal Z2 gauge theory. To evaluate the feasibility of this scheme, we perform numerical simulations of the state-dependent tunneling using realistic parameters, and identify the leading sources of error in future experiments. We discuss how to generalize this minimal case to more complex settings by increasing the number of ions, moving from a single link to a Z2 plaquette, and to an entire Z2 chain. We present analytical expressions for the gauge-invariant dynamics and the corresponding confinement, which are benchmarked using matrix product state simulations.
Bou-Comas, A.; Płodzień, M.; Tagliacozzo, L.; García-Ripoll, J. J.
Quantics Tensor Train for solving Gross-Pitaevskii equation Working paper
2025.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@workingpaper{nokey,
title = {Quantics Tensor Train for solving Gross-Pitaevskii equation},
author = {Bou-Comas, A. and Płodzień, M. and Tagliacozzo, L. and García-Ripoll, J.J.},
url = {https://arxiv.org/abs/2507.03134},
doi = {doi.org/10.48550/arXiv.2507.03134},
year = {2025},
date = {2025-07-03},
abstract = {We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and runtime barriers that limit conventional finite-difference and spectral schemes. Two complementary algorithms are developed: an imaginary-time projector that drives the condensate toward its variational ground state and a rank-adapted fourth-order Runge-Kutta integrator for real-time dynamics. The framework captures a broad range of physical scenarios - including barrier-confined condensates, quasi-random potentials, long-range dipolar interactions, and multicomponent spinor dynamics - without leaving the compressed representation. Relative to standard discretizations, the QTT approach achieves an exponential reduction in computational resources while retaining quantitative accuracy, thereby extending the practicable regime of Gross-Pitaevskii simulations on classical hardware. These results position tensor networks as a practical bridge between high-performance classical computing and prospective quantum hardware for the numerical treatment of nonlinear Schrodinger-type partial differential equations.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {workingpaper}
}
We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and runtime barriers that limit conventional finite-difference and spectral schemes. Two complementary algorithms are developed: an imaginary-time projector that drives the condensate toward its variational ground state and a rank-adapted fourth-order Runge-Kutta integrator for real-time dynamics. The framework captures a broad range of physical scenarios - including barrier-confined condensates, quasi-random potentials, long-range dipolar interactions, and multicomponent spinor dynamics - without leaving the compressed representation. Relative to standard discretizations, the QTT approach achieves an exponential reduction in computational resources while retaining quantitative accuracy, thereby extending the practicable regime of Gross-Pitaevskii simulations on classical hardware. These results position tensor networks as a practical bridge between high-performance classical computing and prospective quantum hardware for the numerical treatment of nonlinear Schrodinger-type partial differential equations.
Ruiz, R.; Sopena, A.; López, E.; Sierra, G.; Pozsgay, B.
Bethe Ansatz, quantum circuits, and the F-basis Journal Article
In: SciPost Physics, vol. 18, pp. 187, 2025.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@article{nokey,
title = {Bethe Ansatz, quantum circuits, and the F-basis},
author = {Ruiz, R. and Sopena, A. and López, E. and Sierra, G. and Pozsgay, B. },
url = {https://scipost.org/SciPostPhys.18.6.187},
doi = {doi: 10.21468/SciPostPhys.18.6.187},
year = {2025},
date = {2025-06-12},
journal = {SciPost Physics},
volume = {18},
pages = {187},
abstract = {The Bethe Ansatz is a method for constructing exact eigenstates of quantum-integrable spin chains. Recently, deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the spin-1/2 XXZ model. These circuits represent a unitary formulation of the standard algebraic Bethe Ansatz, expressed using matrix-product states that act on both the spin chain and an auxiliary space. In this work, we systematize these previous results, and show that algebraic Bethe circuits can be derived by a change of basis in the auxiliary space. The new basis, identical to the "F-basis" known from the theory of quantum-integrable models, generates the linear superposition of plane waves that is characteristic of the coordinate Bethe Ansatz. We explain this connection, highlighting that certain properties of the F-basis (namely, the exchange symmetry of the spins) are crucial for the construction of algebraic Bethe circuits. We demonstrate our approach by presenting new quantum circuits for the inhomogeneous spin-1/2 XXZ model.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {article}
}
The Bethe Ansatz is a method for constructing exact eigenstates of quantum-integrable spin chains. Recently, deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the spin-1/2 XXZ model. These circuits represent a unitary formulation of the standard algebraic Bethe Ansatz, expressed using matrix-product states that act on both the spin chain and an auxiliary space. In this work, we systematize these previous results, and show that algebraic Bethe circuits can be derived by a change of basis in the auxiliary space. The new basis, identical to the "F-basis" known from the theory of quantum-integrable models, generates the linear superposition of plane waves that is characteristic of the coordinate Bethe Ansatz. We explain this connection, highlighting that certain properties of the F-basis (namely, the exchange symmetry of the spins) are crucial for the construction of algebraic Bethe circuits. We demonstrate our approach by presenting new quantum circuits for the inhomogeneous spin-1/2 XXZ model.
H.C., Zhang; Sierra, G.
Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective Journal Article
In: Journal of High Energy Physics (JHEP), 2025.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@article{nokey,
title = {Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective},
author = {Zhang H.C. and Sierra, G. },
url = {https://link.springer.com/article/10.1007/JHEP05(2025)157},
doi = {doi.org/10.1007/JHEP05(2025)157},
year = {2025},
date = {2025-05-20},
urldate = {2025-05-20},
journal = {Journal of High Energy Physics (JHEP)},
abstract = {The Kramers-Wannier self-duality of critical quantum chains is examined from the perspective of model wave functions. We demonstrate, using the transverse-field Ising chain and the 3-state Potts chain as examples, that the symmetry operator for the Kramers-Wannier self-duality follows in a simple and direct way from a ‘generalised’ translation symmetry of the model wave function in the anyonic fusion basis. This translation operation, in turn, comprises a sequence of F-moves in the underlying fusion category. The symmetry operator thus obtained naturally admits the form of a matrix product operator and obeys non-invertible fusion rules. The findings reveal an intriguing connection between the (non-invertible) translation symmetry on the lattice and topological aspects of the conformal field theory describing the scaling limit.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {article}
}
The Kramers-Wannier self-duality of critical quantum chains is examined from the perspective of model wave functions. We demonstrate, using the transverse-field Ising chain and the 3-state Potts chain as examples, that the symmetry operator for the Kramers-Wannier self-duality follows in a simple and direct way from a ‘generalised’ translation symmetry of the model wave function in the anyonic fusion basis. This translation operation, in turn, comprises a sequence of F-moves in the underlying fusion category. The symmetry operator thus obtained naturally admits the form of a matrix product operator and obeys non-invertible fusion rules. The findings reveal an intriguing connection between the (non-invertible) translation symmetry on the lattice and topological aspects of the conformal field theory describing the scaling limit.
Ruiz, R.; Sopena, A.; Pozsgay, B.; López, E.
Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation Working paper
2024.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@workingpaper{nokey,
title = {Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation},
author = {Ruiz, R. and Sopena, A. and Pozsgay, B. and López, E. },
url = {https://arxiv.org/abs/2411.15132},
doi = {doi.org/10.48550/arXiv.2411.15132},
year = {2024},
date = {2024-12-03},
abstract = {We consider the preparation of all the eigenstates of spin chains using quantum circuits. It is known that generic eigenstates of free-fermionic spin chains can be prepared with circuits whose depth grows only polynomially with the length of the chain and the number of particles. We show that the polynomial growth is also achievable for selected interacting models where the interaction between the particles is sufficiently simple. Our working example is the folded XXZ model, an integrable spin chain that exhibits Hilbert space fragmentation. We present the explicit quantum circuits that prepare arbitrary eigenstates of this model on an open chain efficiently. We perform error-mitigated noisy simulations with circuits of up to 13 qubits and different connectivities between qubits, achieving a relative error below 5%. As a byproduct, we extend a recent reformulation of the Bethe ansatz as a quantum circuit from closed to open boundary conditions.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {workingpaper}
}
We consider the preparation of all the eigenstates of spin chains using quantum circuits. It is known that generic eigenstates of free-fermionic spin chains can be prepared with circuits whose depth grows only polynomially with the length of the chain and the number of particles. We show that the polynomial growth is also achievable for selected interacting models where the interaction between the particles is sufficiently simple. Our working example is the folded XXZ model, an integrable spin chain that exhibits Hilbert space fragmentation. We present the explicit quantum circuits that prepare arbitrary eigenstates of this model on an open chain efficiently. We perform error-mitigated noisy simulations with circuits of up to 13 qubits and different connectivities between qubits, achieving a relative error below 5%. As a byproduct, we extend a recent reformulation of the Bethe ansatz as a quantum circuit from closed to open boundary conditions.
Sannia, A.; Tacchino, F.; I. Giorgi Tavernelli, G. L.; Zambrini, R.
Engineered dissipation to mitigate barren plateaus Journal Article
In: NPJ/Quantum Information, vol. 10, iss. 81, 2024.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@article{nokey,
title = {Engineered dissipation to mitigate barren plateaus},
author = { Sannia, A. and Tacchino, F. and Tavernelli, I. Giorgi, G.L. and Zambrini, R.},
url = {https://www.nature.com/articles/s41534-024-00875-0#citeas},
doi = {doi.org/10.1038/s41534-024-00875-0},
year = {2024},
date = {2024-09-04},
journal = {NPJ/Quantum Information},
volume = {10},
issue = {81},
abstract = {Variational quantum algorithms represent a powerful approach for solving optimization problems on noisy quantum computers, with a broad spectrum of potential applications ranging from chemistry to machine learning. However, their performances in practical implementations crucially depend on the effectiveness of quantum circuit training, which can be severely limited by phenomena such as barren plateaus. While, in general, dissipation is detrimental for quantum algorithms, and noise itself can actually induce barren plateaus, here we describe how the inclusion of properly engineered Markovian losses after each unitary quantum circuit layer allows for the trainability of quantum models. We identify the required form of the dissipation processes and establish that their optimization is efficient. We benchmark the generality of our proposal in both a synthetic and a practical quantum chemistry example, demonstrating its effectiveness and potential impact across different domains.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {article}
}
Variational quantum algorithms represent a powerful approach for solving optimization problems on noisy quantum computers, with a broad spectrum of potential applications ranging from chemistry to machine learning. However, their performances in practical implementations crucially depend on the effectiveness of quantum circuit training, which can be severely limited by phenomena such as barren plateaus. While, in general, dissipation is detrimental for quantum algorithms, and noise itself can actually induce barren plateaus, here we describe how the inclusion of properly engineered Markovian losses after each unitary quantum circuit layer allows for the trainability of quantum models. We identify the required form of the dissipation processes and establish that their optimization is efficient. We benchmark the generality of our proposal in both a synthetic and a practical quantum chemistry example, demonstrating its effectiveness and potential impact across different domains.
Labay-Mora, A.; Fiorelli, E.; Zambrini, R.; Giorgi, G. L.
Theoretical framework for quantum associative memories Working paper
2024.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@workingpaper{nokey,
title = {Theoretical framework for quantum associative memories},
author = {Labay-Mora, A. and Fiorelli, E. and Zambrini, R. and Giorgi, G.L. },
url = {https://arxiv.org/abs/2408.14272},
doi = {doi.org/10.48550/arXiv.2408.14272},
year = {2024},
date = {2024-08-26},
abstract = {Associative memory refers to the ability to relate a memory with an input and targets the restoration of corrupted patterns. It has been intensively studied in classical physical systems, as in neural networks where an attractor dynamics settles on stable solutions. Several extensions to the quantum domain have been recently reported, displaying different features. In this work, we develop a comprehensive framework for a quantum associative memory based on open quantum system dynamics, which allows us to compare existing models, identify the theoretical prerequisites for performing associative memory tasks, and extend it in different forms. The map that achieves an exponential increase in the number of stored patterns with respect to classical systems is derived. We establish the crucial role of symmetries and dissipation in the operation of quantum associative memory. Our theoretical analysis demonstrates the feasibility of addressing both quantum and classical patterns, orthogonal and non-orthogonal memories, stationary and metastable operating regimes, and measurement-based outputs. Finally, this opens up new avenues for practical applications in quantum computing and machine learning, such as quantum error correction or quantum memories.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {workingpaper}
}
Associative memory refers to the ability to relate a memory with an input and targets the restoration of corrupted patterns. It has been intensively studied in classical physical systems, as in neural networks where an attractor dynamics settles on stable solutions. Several extensions to the quantum domain have been recently reported, displaying different features. In this work, we develop a comprehensive framework for a quantum associative memory based on open quantum system dynamics, which allows us to compare existing models, identify the theoretical prerequisites for performing associative memory tasks, and extend it in different forms. The map that achieves an exponential increase in the number of stored patterns with respect to classical systems is derived. We establish the crucial role of symmetries and dissipation in the operation of quantum associative memory. Our theoretical analysis demonstrates the feasibility of addressing both quantum and classical patterns, orthogonal and non-orthogonal memories, stationary and metastable operating regimes, and measurement-based outputs. Finally, this opens up new avenues for practical applications in quantum computing and machine learning, such as quantum error correction or quantum memories.
Cabot, A.; Giorgi, G. L.; Zambrini, R.
Nonequilibrium transition between dissipative time crystals Journal Article
In: PRX Quantum, vol. 5, iss. 3, no. 30325, 2024.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@article{nokey,
title = {Nonequilibrium transition between dissipative time crystals},
author = {Cabot, A. and Giorgi, G.L. and Zambrini, R.},
url = {https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.5.030325},
doi = {doi.org/10.1103/PRXQuantum.5.030325},
year = {2024},
date = {2024-08-06},
journal = {PRX Quantum},
volume = {5},
number = {30325},
issue = {3},
abstract = {We show a dissipative phase transition in a driven nonlinear quantum oscillator in which a discrete time-translation symmetry is spontaneously broken in two different ways. The corresponding regimes display either discrete or incommensurate time-crystal order, which we analyze numerically and analytically beyond the classical limit, addressing observable dynamics, phenomenology in different (laboratory and rotating) frames, Liouvillian spectral features, and quantum fluctuations. Via an effective semiclassical description, we show that phase diffusion dominates in the incommensurate time crystal (or continuous time crystal in the rotating frame), which manifests as a band of eigenmodes with a lifetime growing linearly with the mean-field excitation number. Instead, in the discrete time-crystal phase, the leading fluctuation process corresponds to quantum activation with a single mode that has an exponentially growing lifetime. Interestingly, the transition between these two regimes manifests itself already in the quantum regime as a spectral singularity, namely, as an exceptional point mediating between phase diffusion and quantum activation. Finally, we discuss this transition between different time-crystal orders in the context of synchronization phenomena.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {article}
}
We show a dissipative phase transition in a driven nonlinear quantum oscillator in which a discrete time-translation symmetry is spontaneously broken in two different ways. The corresponding regimes display either discrete or incommensurate time-crystal order, which we analyze numerically and analytically beyond the classical limit, addressing observable dynamics, phenomenology in different (laboratory and rotating) frames, Liouvillian spectral features, and quantum fluctuations. Via an effective semiclassical description, we show that phase diffusion dominates in the incommensurate time crystal (or continuous time crystal in the rotating frame), which manifests as a band of eigenmodes with a lifetime growing linearly with the mean-field excitation number. Instead, in the discrete time-crystal phase, the leading fluctuation process corresponds to quantum activation with a single mode that has an exponentially growing lifetime. Interestingly, the transition between these two regimes manifests itself already in the quantum regime as a spectral singularity, namely, as an exceptional point mediating between phase diffusion and quantum activation. Finally, we discuss this transition between different time-crystal orders in the context of synchronization phenomena.
Nokkala, J.; Giorgi, G. L.; Zambrini, R.
Retrieving past quantum features with deep hybrid classical-quantum reservoir computing Journal Article
In: Machine Learning: Science and Technology, vol. 5, 2024.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@article{nokey,
title = {Retrieving past quantum features with deep hybrid classical-quantum reservoir computing},
author = {Nokkala, J. and Giorgi, G.L. and Zambrini, R. },
url = {https://iopscience.iop.org/article/10.1088/2632-2153/ad5f12},
doi = {10.1088/2632-2153/ad5f12},
year = {2024},
date = {2024-07-19},
journal = {Machine Learning: Science and Technology},
volume = {5},
abstract = {Machine learning techniques have achieved impressive results in recent years and the possibility of harnessing the power of quantum physics opens new promising avenues to speed up classical learning methods. Rather than viewing classical and quantum approaches as exclusive alternatives, their integration into hybrid designs has gathered increasing interest, as seen in variational quantum algorithms, quantum circuit learning, and kernel methods. Here we introduce deep hybrid classical-quantum reservoir computing for temporal processing of quantum states where information about, for instance, the entanglement or the purity of past input states can be extracted via a single-step measurement. We find that the hybrid setup cascading two reservoirs not only inherits the strengths of both of its constituents but is even more than just the sum of its parts, outperforming comparable non-hybrid alternatives. The quantum layer is within reach of state-of-the-art multimode quantum optical platforms while the classical layer can be implemented in silico.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {article}
}
Machine learning techniques have achieved impressive results in recent years and the possibility of harnessing the power of quantum physics opens new promising avenues to speed up classical learning methods. Rather than viewing classical and quantum approaches as exclusive alternatives, their integration into hybrid designs has gathered increasing interest, as seen in variational quantum algorithms, quantum circuit learning, and kernel methods. Here we introduce deep hybrid classical-quantum reservoir computing for temporal processing of quantum states where information about, for instance, the entanglement or the purity of past input states can be extracted via a single-step measurement. We find that the hybrid setup cascading two reservoirs not only inherits the strengths of both of its constituents but is even more than just the sum of its parts, outperforming comparable non-hybrid alternatives. The quantum layer is within reach of state-of-the-art multimode quantum optical platforms while the classical layer can be implemented in silico.
Domanti, E. C.; Zappalà, D.; Bermudez, A.; Amico, L.
Floquet-Rydberg quantum simulator for confinement in gauge theories Journal Article
In: Physical Review Research, vol. 6, 2024.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@article{nokey,
title = {Floquet-Rydberg quantum simulator for confinement in gauge theories},
author = {Domanti, E.C. and Zappalà, D. and Bermudez, A. and Amico, L. },
url = {https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.L022059},
doi = {doi.org/10.1103/PhysRevResearch.6.L022059},
year = {2024},
date = {2024-06-11},
journal = {Physical Review Research},
volume = {6},
abstract = {Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators of lattice gauge theories which, among other goals, aim at improving our understanding on the nonperturbative mechanisms underlying the confinement of quarks. In this work, considering periodically driven arrays of Rydberg atoms in a tweezer ladder geometry, we devise a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a LGT, in which hardcore bosons/spinless fermions are coupled to dynamical gauge fields. Resorting to an external magnetic field to tune the angular dependence of the Rydberg dipolar interactions, and by a suitable tuning of the driving parameters, we manage to suppress the main gauge-violating terms and show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques. Depending on the lattice size, we present a thorough numerical test of the validity of this scheme using either exact diagonalization or matrix-product-state algorithms for the periodically modulated real-time dynamics.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {article}
}
Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators of lattice gauge theories which, among other goals, aim at improving our understanding on the nonperturbative mechanisms underlying the confinement of quarks. In this work, considering periodically driven arrays of Rydberg atoms in a tweezer ladder geometry, we devise a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a LGT, in which hardcore bosons/spinless fermions are coupled to dynamical gauge fields. Resorting to an external magnetic field to tune the angular dependence of the Rydberg dipolar interactions, and by a suitable tuning of the driving parameters, we manage to suppress the main gauge-violating terms and show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques. Depending on the lattice size, we present a thorough numerical test of the validity of this scheme using either exact diagonalization or matrix-product-state algorithms for the periodically modulated real-time dynamics.
Ruiz, R.; Sopena, A.; Hunter Gordon, M.; Sierra, G.; López, E.
The Bethe Ansatz as a Quantum Circuit Journal Article
In: Quantum, vol. 8, pp. 1356 , 2024.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@article{nokey,
title = {The Bethe Ansatz as a Quantum Circuit},
author = {Ruiz, R. and Sopena, A. and Hunter Gordon, M. and Sierra, G. and López, E.},
url = {https://quantum-journal.org/papers/q-2024-05-23-1356/#},
doi = {doi.org/10.22331/q-2024-05-23-1356},
year = {2024},
date = {2024-05-23},
journal = {Quantum},
volume = {8},
pages = {1356 },
abstract = {The Bethe ansatz represents an analytical method enabling the exact solution of numerous models in condensed matter physics and statistical mechanics. When a global symmetry is present, the trial wavefunctions of the Bethe ansatz consist of plane wave superpositions. Previously, it has been shown that the Bethe ansatz can be recast as a deterministic quantum circuit. An analytical derivation of the quantum gates that form the circuit was lacking however. Here we present a comprehensive study of the transformation that brings the Bethe ansatz into a quantum circuit, which leads us to determine the analytical expression of the circuit gates. As a crucial step of the derivation, we present a simple set of diagrammatic rules that define a novel Matrix Product State network building Bethe wavefunctions. Remarkably, this provides a new perspective on the equivalence between the coordinate and algebraic versions of the Bethe ansatz.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {article}
}
The Bethe ansatz represents an analytical method enabling the exact solution of numerous models in condensed matter physics and statistical mechanics. When a global symmetry is present, the trial wavefunctions of the Bethe ansatz consist of plane wave superpositions. Previously, it has been shown that the Bethe ansatz can be recast as a deterministic quantum circuit. An analytical derivation of the quantum gates that form the circuit was lacking however. Here we present a comprehensive study of the transformation that brings the Bethe ansatz into a quantum circuit, which leads us to determine the analytical expression of the circuit gates. As a crucial step of the derivation, we present a simple set of diagrammatic rules that define a novel Matrix Product State network building Bethe wavefunctions. Remarkably, this provides a new perspective on the equivalence between the coordinate and algebraic versions of the Bethe ansatz.
Martínez-Peña, R.; Soriano, M. C.; Zambrini, R.
Quantum fidelity kernel with a trapped-ion simulation platform Journal Article
In: Physical Review A, vol. 109, iss. 4, 2024, ISSN: 2469-9926.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@article{nokey,
title = {Quantum fidelity kernel with a trapped-ion simulation platform},
author = {Martínez-Peña, R. and Soriano, M.C. and Zambrini, R.
},
url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.042612},
doi = {10.1103/PhysRevA.109.042612},
issn = {2469-9926},
year = {2024},
date = {2024-04-08},
urldate = {2024-04-08},
journal = {Physical Review A},
volume = {109},
issue = {4},
abstract = {Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels becomes an issue. To overcome these challenges, various strategies under the concept of inductive bias have been proposed. Bandwidth optimization is a promising approach that can be implemented using quantum simulation platforms. We propose trapped-ion simulation platforms as a means to compute quantum kernels, filling a gap in the previous literature and demonstrating their effectiveness for binary classification tasks. We compare the performance of the proposed method with an optimized classical kernel and evaluate the robustness of the quantum kernel against noise. The results show that ion trap platforms are well-suited for quantum kernel computation and can achieve high accuracy with only a few qubits.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {article}
}
Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels becomes an issue. To overcome these challenges, various strategies under the concept of inductive bias have been proposed. Bandwidth optimization is a promising approach that can be implemented using quantum simulation platforms. We propose trapped-ion simulation platforms as a means to compute quantum kernels, filling a gap in the previous literature and demonstrating their effectiveness for binary classification tasks. We compare the performance of the proposed method with an optimized classical kernel and evaluate the robustness of the quantum kernel against noise. The results show that ion trap platforms are well-suited for quantum kernel computation and can achieve high accuracy with only a few qubits.
Labay-Mora, A.; Zambrini, R.; Giorgi, G. L.
Quantum memories for squeezed and coherent superpositions in a driven-dissipative nonlinear oscillator Journal Article
In: Physical Review A, vol. 109, iss. 3, 2024, ISSN: 2469-9926.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@article{nokey,
title = {Quantum memories for squeezed and coherent superpositions in a driven-dissipative nonlinear oscillator},
author = {Labay-Mora, A. and Zambrini, R. and Giorgi, G.L.
},
url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.032407},
doi = {doi.org/10.1103/PhysRevA.109.032407},
issn = {2469-9926},
year = {2024},
date = {2024-03-08},
journal = {Physical Review A},
volume = {109},
issue = {3},
abstract = {Quantum oscillators with nonlinear driving and dissipative terms have gained significant attention due to their ability to stabilize cat states for universal quantum computation. Recently, superconducting circuits have been employed to realize such long-lived qubits stored in coherent states. We present a generalization of these oscillators, which are not limited to coherent states. The key ingredient lies in the presence of different nonlinearities in driving and dissipation, beyond the quadratic one. Through an extensive analysis of the asymptotic dynamical features for different nonlinearities, we identify the conditions for the storage and retrieval of quantum states, such as squeezed states, in both coherent and incoherent superpositions. We explore their applications in quantum computing, where squeezing prolongs the lifetime of memory storage for qubits encoded in the superposition of two symmetric squeezed states, and in quantum associative memory, which has so far been limited to the storage of classical patterns.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {article}
}
Quantum oscillators with nonlinear driving and dissipative terms have gained significant attention due to their ability to stabilize cat states for universal quantum computation. Recently, superconducting circuits have been employed to realize such long-lived qubits stored in coherent states. We present a generalization of these oscillators, which are not limited to coherent states. The key ingredient lies in the presence of different nonlinearities in driving and dissipation, beyond the quadratic one. Through an extensive analysis of the asymptotic dynamical features for different nonlinearities, we identify the conditions for the storage and retrieval of quantum states, such as squeezed states, in both coherent and incoherent superpositions. We explore their applications in quantum computing, where squeezing prolongs the lifetime of memory storage for qubits encoded in the superposition of two symmetric squeezed states, and in quantum associative memory, which has so far been limited to the storage of classical patterns.
García-Beni, J.; Giorgi, G. L.; Soriano, M. C.; Zambrini, R.
Squeezing as a resource for time series processing in quantum reservoir computing Journal Article
In: Optics Express, vol. 32, iss. 4, pp. 6733-6747, 2024.
Abstract | Links | BibTeX | Tags: CSIC-4.7
@article{nokey,
title = {Squeezing as a resource for time series processing in quantum reservoir computing},
author = {García-Beni, J. and Giorgi, G.L. and Soriano, M.C. and Zambrini, R.},
url = {https://opg.optica.org/oe/fulltext.cfm?uri=oe-32-4-6733&id=546462},
doi = {doi.org/10.1364/OE.507684},
year = {2024},
date = {2024-02-09},
journal = {Optics Express},
volume = {32},
issue = {4},
pages = { 6733-6747},
abstract = {Squeezing is known to be a quantum resource in many applications in metrology, cryptography, and computing, being related to entanglement in multimode settings. In this work, we address the effects of squeezing in neuromorphic machine learning for time-series processing. In particular, we consider a loop-based photonic architecture for reservoir computing and address the effect of squeezing in the reservoir, considering a Hamiltonian with both active and passive coupling terms. Interestingly, squeezing can be either detrimental or beneficial for quantum reservoir computing when moving from ideal to realistic models, accounting for experimental noise. We demonstrate that multimode squeezing enhances its accessible memory, which improves the performance in several benchmark temporal tasks. The origin of this improvement is traced back to the robustness of the reservoir to readout noise, which is increased with squeezing.},
keywords = {CSIC-4.7},
pubstate = {published},
tppubtype = {article}
}
Squeezing is known to be a quantum resource in many applications in metrology, cryptography, and computing, being related to entanglement in multimode settings. In this work, we address the effects of squeezing in neuromorphic machine learning for time-series processing. In particular, we consider a loop-based photonic architecture for reservoir computing and address the effect of squeezing in the reservoir, considering a Hamiltonian with both active and passive coupling terms. Interestingly, squeezing can be either detrimental or beneficial for quantum reservoir computing when moving from ideal to realistic models, accounting for experimental noise. We demonstrate that multimode squeezing enhances its accessible memory, which improves the performance in several benchmark temporal tasks. The origin of this improvement is traced back to the robustness of the reservoir to readout noise, which is increased with squeezing.
