Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1207.2664 · Physical Review Letters

Digital Quantum Simulation of the Holstein Model in Trapped Ions

Antonio Mezzacapo, Jorge Casanova, Lucas Lamata, E. Solano

Published Nov 13, 2012• 76 citations
arXivHTMLPDF

Abstract

We propose the implementation of the Holstein model by means of digital methods in a linear chain of trapped ions. We show how the simulation fidelity scales with the generation of phononic excitations. We propose a decomposition and a stepwise trapped-ion implementation of the Holstein Hamiltonian. Via numerical simulations, we study how the protocol is affected by realistic gates. Finally, we show how measurements of the size of the simulated polaron can be performed.

DOI
10.1103/physrevlett.109.200501

Related papers

Quantum Simulation of Small-Polaron Formation with Trapped Ions

Vladimir M. Stojanović, Tao Shi, Christoph Bruder +1 more

We propose an analog quantum simulation of small-polaron physics using a one-dimensional system of trapped ions acted upon by off-resonant standing waves. This system, envisioned as an array of microtraps, in the single-excitation case allows the realization of the antiadiabatic regime of the Holstein model. We show that the strong excitation-phonon coupling regime, characterized by the formation of small polarons, can be reached using realistic values of the relevant system parameters. Finally, we propose measurements of the quasiparticle residue and the average number of phonons in the ground state, experimental probes validating the polaronic character of the phonon-dressed excitation.

arXiv:1206.7010•Physical Review Letters•Dec 17, 2012•46 citations

Digital-Analog Quantum Simulation of Spin Systems in Trapped Ions

Iñigo Arrazola Maiztegui

We propose a method to simulate spin models in trapped ions, using digital-analog techniques. With a suitable multiqubit gate decomposition in terms of analog blocks and digital steps, we show that the dynamics of the spin-1/2 Heisenberg chain can be implemented in a linear ion array. This digital-analog proposal involves substantially less number of gates than a fully digital approach, making it a good candidate for experimental implementations. Our work may be adapted to different quantum platforms.

•Oct 2, 2015•0 citations

Digital-Analog Quantum Simulation of Spin Models in Trapped Ions

Íñigo Arrazola, Julen Simon Pedernales, Lucas Lamata +1 more

We propose a method to simulate spin models in trapped ions using a digital-analog approach, consisting in a suitable gate decomposition in terms of analog blocks and digital steps. In this way, we show that the quantum dynamics of an enhanced variety of spin models could be implemented with substantially less number of gates than a fully digital approach. Typically, analog blocks are built of multipartite dynamics providing the complexity of the simulated model, while the digital steps are local operations bringing versatility to it. Finally, we describe a possible experimental implementation in trapped-ion technologies.

arXiv:1602.06248•Scientific Reports•Jul 29, 2016•72 citations

Fundamentals of Trapped Ions and Quantum Simulation of Chemical Dynamics

Guido Pagano, Adamczyk, Wojciech, Visal So

Trapped atomic ions are among the most advanced platforms for quantum simulation, computation, and metrology, offering long coherence times and precise, individual control over both internal and motional degrees of freedom. In this review, we present a pedagogical introduction to trapped-ion systems, covering the physics of ion trapping, qubit encodings, and laser-ion interactions. We explain how spin-dependent forces generated by light fields enable both analog and digital quantum simulations of spin and spin-boson models, as well as high-fidelity quantum logic gates. We then highlight an emerging frontier in the simulation of chemical dynamics, summarizing recent experiments that demonstrate the capability of trapped ions to simulate vibronic models and excitation-transfer processes. Finally, we outline future directions in quantum simulation and discuss open challenges in scaling up trapped-ion architectures.

arXiv:2505.20412•May 26, 2025•0 citations

Spin-Holstein Models in Trapped-Ion Systems

Johannes Knörzer, Tao Shi, Eugene Demler +1 more

In this work, we highlight how trapped-ion quantum systems can be used to study generalized Holstein models, and benchmark expensive numerical calculations. We study a particular spin-Holstein model that can be implemented with arrays of ions confined by individual microtraps, and that is closely related to the Holstein model of condensed matter physics, used to describe electron-phonon interactions. In contrast to earlier proposals, we focus on simulating many-electron systems and inspect the competition between charge-density wave order, fermion pairing, and phase separation. In our numerical study, we employ a combination of complementary approaches, based on non-Gaussian variational ansatz states and matrix product states, respectively. We demonstrate that this hybrid approach outperforms standard density-matrix renormalization group calculations.

arXiv:2108.13730•Physical Review Letters•Mar 25, 2022•15 citations

Quantum simulation of extended polaron models using compound atom-ion systems

Krzysztof Jachymski, Antonio Negretti

We consider the prospects for quantum simulation of condensed matter models exhibiting strong electron-phonon coupling using a hybrid platform of trapped laser-cooled ions interacting with an ultracold atomic gas. This system naturally posesses a phonon structure, in contrast to the standard optical lattice scenarios usually employed with ultracold atoms in which the lattice is generated by laser light and thus it remains static. We derive the effective Hamiltonian describing the general system and discuss the arising energy scales, relating the results to commonly employed extended Hubbard-Holstein models. Although for a typical experimentally realistic system the coupling to phonons turns out to be small, we provide the means to enhance its role and reach interesting regimes with competing orders. Extended Lang-Firsov transformation reveals the emergence of phonon-induced long-range interactions between the atoms, which can give rise to both localized and extended bipolaron states with low effective mass, indicating the possibility of fermion pairing.

arXiv:2005.08635•Physical Review Research•Aug 28, 2020•15 citations
We propose the implementation of the Holstein model by means of digital methods in a linear chain of trapped ions. We show how the simulation fidelity scales with the generation of phononic excitations. We propose a decomposition and a stepwise trapped-ion implementation of the Holstein Hamiltonian. Via numerical simulations, we study how the protocol is affected by realistic gates. Finally, we show how measurements of the size of the simulated polaron can be performed.
We propose an analog quantum simulation of small-polaron physics using a one-dimensional system of trapped ions acted upon by off-resonant standing waves. This system, envisioned as an array of microtraps, in the single-excitation case allows the realization of the antiadiabatic regime of the Holstein model. We show that the strong excitation-phonon coupling regime, characterized by the formation of small polarons, can be reached using realistic values of the relevant system parameters. Finally, we propose measurements of the quasiparticle residue and the average number of phonons in the ground state, experimental probes validating the polaronic character of the phonon-dressed excitation.
We propose a method to simulate spin models in trapped ions, using digital-analog techniques. With a suitable multiqubit gate decomposition in terms of analog blocks and digital steps, we show that the dynamics of the spin-1/2 Heisenberg chain can be implemented in a linear ion array. This digital-analog proposal involves substantially less number of gates than a fully digital approach, making it a good candidate for experimental implementations. Our work may be adapted to different quantum platforms.
We propose a method to simulate spin models in trapped ions using a digital-analog approach, consisting in a suitable gate decomposition in terms of analog blocks and digital steps. In this way, we show that the quantum dynamics of an enhanced variety of spin models could be implemented with substantially less number of gates than a fully digital approach. Typically, analog blocks are built of multipartite dynamics providing the complexity of the simulated model, while the digital steps are local operations bringing versatility to it. Finally, we describe a possible experimental implementation in trapped-ion technologies.
Trapped atomic ions are among the most advanced platforms for quantum simulation, computation, and metrology, offering long coherence times and precise, individual control over both internal and motional degrees of freedom. In this review, we present a pedagogical introduction to trapped-ion systems, covering the physics of ion trapping, qubit encodings, and laser-ion interactions. We explain how spin-dependent forces generated by light fields enable both analog and digital quantum simulations of spin and spin-boson models, as well as high-fidelity quantum logic gates. We then highlight an emerging frontier in the simulation of chemical dynamics, summarizing recent experiments that demonstrate the capability of trapped ions to simulate vibronic models and excitation-transfer processes. Finally, we outline future directions in quantum simulation and discuss open challenges in scaling up trapped-ion architectures.
In this work, we highlight how trapped-ion quantum systems can be used to study generalized Holstein models, and benchmark expensive numerical calculations. We study a particular spin-Holstein model that can be implemented with arrays of ions confined by individual microtraps, and that is closely related to the Holstein model of condensed matter physics, used to describe electron-phonon interactions. In contrast to earlier proposals, we focus on simulating many-electron systems and inspect the competition between charge-density wave order, fermion pairing, and phase separation. In our numerical study, we employ a combination of complementary approaches, based on non-Gaussian variational ansatz states and matrix product states, respectively. We demonstrate that this hybrid approach outperforms standard density-matrix renormalization group calculations.
We consider the prospects for quantum simulation of condensed matter models exhibiting strong electron-phonon coupling using a hybrid platform of trapped laser-cooled ions interacting with an ultracold atomic gas. This system naturally posesses a phonon structure, in contrast to the standard optical lattice scenarios usually employed with ultracold atoms in which the lattice is generated by laser light and thus it remains static. We derive the effective Hamiltonian describing the general system and discuss the arising energy scales, relating the results to commonly employed extended Hubbard-Holstein models. Although for a typical experimentally realistic system the coupling to phonons turns out to be small, we provide the means to enhance its role and reach interesting regimes with competing orders. Extended Lang-Firsov transformation reveals the emergence of phonon-induced long-range interactions between the atoms, which can give rise to both localized and extended bipolaron states with low effective mass, indicating the possibility of fermion pairing.