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:1306.1674 · Physical Review Letters

Superconducting Circuits for Quantum Simulation of Dynamical Gauge Fields

D. Marcos, Peter Rabl, E. Rico, P. Zoller

Published Sep 13, 2013• 142 citations
arXivHTMLPDF

Abstract

We describe a superconducting-circuit lattice design for the implementation and simulation of dynamical lattice gauge theories. We illustrate our proposal by analyzing a one-dimensional U(1) quantum-link model, where superconducting qubits play the role of matter fields on the lattice sites and the gauge fields are represented by two coupled microwave resonators on each link between neighboring sites. A detailed analysis of a minimal experimental protocol for probing the physics related to string breaking effects shows that, despite the presence of decoherence in these systems, distinctive phenomena from condensed-matter and high-energy physics can be visualized with state-of-the-art technology in small superconducting-circuit arrays.

DOI
10.1103/physrevlett.111.110504

Related papers

Two-dimensional lattice gauge theories with superconducting quantum circuits

D. Marcos, Philippe Widmer, E. Rico +4 more

A quantum simulator of [Formula: see text] lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

arXiv:1407.6066•Annals of Physics•Sep 19, 2014•122 citations

Visualizing dynamics of charges and strings in (2 + 1)D lattice gauge theories

Tyler A. Cochran, B. Jobst, Eliott N. Rosenberg +97 more

Lattice gauge theories (LGTs)1–4 can be used to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials5–7. Studying dynamical properties of emergent phases can be challenging, as it requires solving many-body problems that are generally beyond perturbative limits8–10. Here we investigate the dynamics of local excitations in a $${{\mathbb{Z}}}_{2}$$ LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit that prepares low-energy states that have a large overlap with the ground state; then we create charge excitations with local gates and simulate their quantum dynamics by means of a discretized time evolution. As the electric field coupling constant is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the electric field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT, from which we uncover two distinct regimes inside the confining phase: for weak confinement, the string fluctuates strongly in the transverse direction, whereas for strong confinement, transverse fluctuations are effectively frozen11,12. We also demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a new set of techniques for investigating emergent excitations and string dynamics. In a quantum simulation of a (2+1)D lattice gauge theory using a superconducting quantum processor, the dynamics of strings reveal the transition from deconfined to confined excitations as the effective electric field is increased.

arXiv:2409.17142•Nature•Jun 4, 2025•55 citations

Lattice gauge theory and dynamical quantum phase transitions using noisy intermediate-scale quantum devices

Simon Panyella Pedersen, Nikolaj Thomas Zinner

Lattice gauge theories are a fascinating and rich class of theories relating to the most fundamental models of particle physics, and as experimental control on the quantum level increases there is a growing interest in nonequilibrium effects such as dynamical quantum phase transitions. To demonstrate how these physical theories can be accessed in near-term quantum devices, we study the dynamics of a $(1+1)\mathrm{D}$ U(1) quantum link model following quenches of its mass term. We find that the system undergoes dynamical quantum phase transitions for all system sizes considered, even the smallest where the dynamics can be solved analytically. We devise a gauge-invariant string order parameter whose zeros correlates with the structure of the Loschmidt amplitude, making the order parameter useful for experimental study in near-term devices. The zeros of the Loschmidt amplitude as well as the zeros of our order parameter are revealed by vortices in their phases, which can be counted by a topologically invariant winding number. With noisy intermediate-scale quantum devices in mind, we propose a class of superconducting circuits for the general implementation of U(1) quantum link models. The principles of these circuits can be generalized to implement other, more complicated gauge symmetries. Furthermore, the circuit can be modularly scaled to any lattice configuration. Simulating the circuit dynamics with realistic circuit parameters, we find that it implements the target dynamics with a steady average fidelity of $99.5%$ or higher. Finally, we consider readout of the circuit using a method that yields information about all the degrees of freedom with resonators coupled dispersively to only a subset of them. This constitutes a direct and relatively straightforward protocol to access both Loschmidt amplitudes and the order parameter.

arXiv:2008.08980•Physical review. B./Physical review. B•Jun 1, 2021•16 citations

Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics

Zi-Yong Ge, Rui-Zhen Huang, Zi Yang Meng +1 more

Recently, quantum simulation of low-dimensional lattice gauge theories (LGTs) has attracted many interests, which may improve our understanding of strongly correlated quantum many-body systems. Here, we propose an implementation to approximate ℤ2 LGT on superconducting quantum circuits, where the effective theory is a mixture of a LGT and a gauge-broken term. By using matrix product state based methods, both the ground state properties and quench dynamics are systematically investigated. With an increase of the transverse (electric) field, the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase. In the ordered phase, an approximate Gauss law of the ℤ2 LGT emerges in the ground state. Moreover, to shed light on the experiments, we also study the quench dynamics, where there is a dynamical signature of the spontaneous translational symmetry breaking. The spreading of the single particle of matter degree is diffusive under the weak transverse field, while it is ballistic with small velocity for the strong field. Furthermore, due to the emergent Gauss law under the strong transverse field, the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping. Our results pave the way for simulating the LGT on superconducting circuits, including the quantum phase transition and quench dynamics.

arXiv:2009.13350•Chinese Physics B•Nov 10, 2021•7 citations

Towards Analog Quantum Simulations of Dynamical Gauge Theories

Christopher Warren

A system which can implement an analog quantum simulation of lattice gauge theories \nhas been proposed. In particular, the Schwinger model is formulated in terms of a lattice \nand superconducting qubit implementation is found which maps onto these dynamics. This \nthesis details the design of the superconducting circuit implementation of the model. The \nHamiltonian of the superconducting circuit is designed to exhibit the gauge invariant dynamics \nof a U(1) symmetry. The gauge invariant set of states corresponds to those that are \nin the subspace of states that are shared by the Hamiltonian and the symmetry. Gauge invariance \nis simulated by looking at the dynamics of those states which obey a lattice version \nof Gauss' law. \nThe device is simulated in an open quantum system and the measurable observables \nare extracted and mapped onto processes which can be observed in the lab. We nd that \nthe dynamics occur over realistic time scales that can be observed with current laboratory \nequipment. These dynamics occur over hundred nanosecond timescales well within the minimum \nresolution of our equipment as well as well within the decoherence times of current \nsuperconducting devices.

•Sep 20, 2017•0 citations

Probing Hadron Scattering in Lattice Gauge Theories on Qudit Quantum Computers

Rohan Joshi, Jan C. Louw, M. Meth +5 more

An overarching goal in the flourishing field of quantum simulation for high-energy physics is the first-principles study of the microscopic dynamics of scattering processes on a quantum computer. Currently, this is hampered by small system sizes and a restriction to two-level representations of the gauge fields in state-of-the-art quantum simulators. Here, we propose efficient experimentally feasible digital qudit quantum circuits for far-from-equilibrium quench dynamics of a $\mathrm{U}(1)$ quantum link lattice gauge theory, where the electric and gauge fields are represented as spin-$1$ operators. Using dedicated numerical simulations, we probe scattering processes in this model on these proposed circuits, focusing on meson-meson and meson-antimeson collisions. The latter are not possible with a two-level representation of the fields, highlighting the suitability of qudits in exploring scattering processes relevant to quantum electrodynamics. The probed scattering dynamics showcases rich physics, including meson flipping and a reflection-transmission transition in meson-antimeson collisions as a function of the gauge coupling strength. Our simulations, which include realistic noise models of dephasing and depolarization, show very good agreement with the exact noiseless dynamics, signaling the readiness of current qudit platforms to observe microscopic scattering dynamics with significantly shallower circuit depths than their qubit counterparts.

arXiv:2507.12614•Jul 16, 2025•0 citations
We describe a superconducting-circuit lattice design for the implementation and simulation of dynamical lattice gauge theories. We illustrate our proposal by analyzing a one-dimensional U(1) quantum-link model, where superconducting qubits play the role of matter fields on the lattice sites and the gauge fields are represented by two coupled microwave resonators on each link between neighboring sites. A detailed analysis of a minimal experimental protocol for probing the physics related to string breaking effects shows that, despite the presence of decoherence in these systems, distinctive phenomena from condensed-matter and high-energy physics can be visualized with state-of-the-art technology in small superconducting-circuit arrays.
A quantum simulator of [Formula: see text] lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.
Lattice gauge theories (LGTs)1–4 can be used to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials5–7. Studying dynamical properties of emergent phases can be challenging, as it requires solving many-body problems that are generally beyond perturbative limits8–10. Here we investigate the dynamics of local excitations in a Z2{{\mathbb{Z}}}_{2}Z2​ LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit that prepares low-energy states that have a large overlap with the ground state; then we create charge excitations with local gates and simulate their quantum dynamics by means of a discretized time evolution. As the electric field coupling constant is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the electric field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT, from which we uncover two distinct regimes inside the confining phase: for weak confinement, the string fluctuates strongly in the transverse direction, whereas for strong confinement, transverse fluctuations are effectively frozen11,12. We also demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a new set of techniques for investigating emergent excitations and string dynamics. In a quantum simulation of a (2+1)D lattice gauge theory using a superconducting quantum processor, the dynamics of strings reveal the transition from deconfined to confined excitations as the effective electric field is increased.
Lattice gauge theories are a fascinating and rich class of theories relating to the most fundamental models of particle physics, and as experimental control on the quantum level increases there is a growing interest in nonequilibrium effects such as dynamical quantum phase transitions. To demonstrate how these physical theories can be accessed in near-term quantum devices, we study the dynamics of a (1+1)D(1+1)\mathrm{D}(1+1)D U(1) quantum link model following quenches of its mass term. We find that the system undergoes dynamical quantum phase transitions for all system sizes considered, even the smallest where the dynamics can be solved analytically. We devise a gauge-invariant string order parameter whose zeros correlates with the structure of the Loschmidt amplitude, making the order parameter useful for experimental study in near-term devices. The zeros of the Loschmidt amplitude as well as the zeros of our order parameter are revealed by vortices in their phases, which can be counted by a topologically invariant winding number. With noisy intermediate-scale quantum devices in mind, we propose a class of superconducting circuits for the general implementation of U(1) quantum link models. The principles of these circuits can be generalized to implement other, more complicated gauge symmetries. Furthermore, the circuit can be modularly scaled to any lattice configuration. Simulating the circuit dynamics with realistic circuit parameters, we find that it implements the target dynamics with a steady average fidelity of 99.599.5%99.5 or higher. Finally, we consider readout of the circuit using a method that yields information about all the degrees of freedom with resonators coupled dispersively to only a subset of them. This constitutes a direct and relatively straightforward protocol to access both Loschmidt amplitudes and the order parameter.
Recently, quantum simulation of low-dimensional lattice gauge theories (LGTs) has attracted many interests, which may improve our understanding of strongly correlated quantum many-body systems. Here, we propose an implementation to approximate ℤ2 LGT on superconducting quantum circuits, where the effective theory is a mixture of a LGT and a gauge-broken term. By using matrix product state based methods, both the ground state properties and quench dynamics are systematically investigated. With an increase of the transverse (electric) field, the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase. In the ordered phase, an approximate Gauss law of the ℤ2 LGT emerges in the ground state. Moreover, to shed light on the experiments, we also study the quench dynamics, where there is a dynamical signature of the spontaneous translational symmetry breaking. The spreading of the single particle of matter degree is diffusive under the weak transverse field, while it is ballistic with small velocity for the strong field. Furthermore, due to the emergent Gauss law under the strong transverse field, the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping. Our results pave the way for simulating the LGT on superconducting circuits, including the quantum phase transition and quench dynamics.
A system which can implement an analog quantum simulation of lattice gauge theories \nhas been proposed. In particular, the Schwinger model is formulated in terms of a lattice \nand superconducting qubit implementation is found which maps onto these dynamics. This \nthesis details the design of the superconducting circuit implementation of the model. The \nHamiltonian of the superconducting circuit is designed to exhibit the gauge invariant dynamics \nof a U(1) symmetry. The gauge invariant set of states corresponds to those that are \nin the subspace of states that are shared by the Hamiltonian and the symmetry. Gauge invariance \nis simulated by looking at the dynamics of those states which obey a lattice version \nof Gauss' law. \nThe device is simulated in an open quantum system and the measurable observables \nare extracted and mapped onto processes which can be observed in the lab. We nd that \nthe dynamics occur over realistic time scales that can be observed with current laboratory \nequipment. These dynamics occur over hundred nanosecond timescales well within the minimum \nresolution of our equipment as well as well within the decoherence times of current \nsuperconducting devices.
An overarching goal in the flourishing field of quantum simulation for high-energy physics is the first-principles study of the microscopic dynamics of scattering processes on a quantum computer. Currently, this is hampered by small system sizes and a restriction to two-level representations of the gauge fields in state-of-the-art quantum simulators. Here, we propose efficient experimentally feasible digital qudit quantum circuits for far-from-equilibrium quench dynamics of a U(1)\mathrm{U}(1)U(1) quantum link lattice gauge theory, where the electric and gauge fields are represented as spin-111 operators. Using dedicated numerical simulations, we probe scattering processes in this model on these proposed circuits, focusing on meson-meson and meson-antimeson collisions. The latter are not possible with a two-level representation of the fields, highlighting the suitability of qudits in exploring scattering processes relevant to quantum electrodynamics. The probed scattering dynamics showcases rich physics, including meson flipping and a reflection-transmission transition in meson-antimeson collisions as a function of the gauge coupling strength. Our simulations, which include realistic noise models of dephasing and depolarization, show very good agreement with the exact noiseless dynamics, signaling the readiness of current qudit platforms to observe microscopic scattering dynamics with significantly shallower circuit depths than their qubit counterparts.