Analogue quantum simulation of spin and Hubbard models

Algorithms and benchmarks / Simulation of physical systems

A controllable quantum system, such as atoms in optical tweezers or lattices or a chain of ions, is engineered to behave like a model of magnetism or of electrons in a solid, and is measured directly.

Era: Analogue or special-purpose
Problem class: Simulation of physical systems
Area: Quantum simulation
Speedup: For many-body dynamics and some phases, simulations reach regimes classical methods cannot verify; Sim KPIs of the Quantum Flagship track this.

How it works

Interactions between atoms or ions are tuned to match the model Hamiltonian; the system is prepared, evolved and imaged atom by atom. No gate decomposition is needed.

Typical use cases

Phase transitions and dynamics of quantum magnets.
The Fermi-Hubbard model of high-temperature superconductors.
Materials and quantum transport.

Documented use cases on related problems

From the use case directory; the sources of these cases may use other methods than this one.

Programmable quantum simulators explored with industrial end users (PASQuanS)

KPI Sim 5: most advanced EU quantum simulator

Resource estimates

No resource estimate with stated assumptions was verified for this family in this release.

Demonstrations

2021: 2D antiferromagnetic transverse-field Ising model with up to 196 Rydberg atoms. (P. Scholl et al. 2021)
2017: Long-range antiferromagnet in the Fermi-Hubbard model on about 80 lattice sites at T/t = 0.25(2). (A. Mazurenko et al. 2017)
2017: Dynamical phase transition with up to 53 trapped-ion qubits. (J. Zhang et al. 2017)
2025: The KPI booklet gives 100 qubits or simulated particles for the most advanced non-gate-based simulator in the EU27 in 2022 to 2024 (KPI Sim 5). (Quantum Flagship Strategic Advisory Board 2025)

Hardware platforms that fit

Neutral atoms: Programmable arrays of up to 196 Rydberg atoms simulated 2D antiferromagnets (Scholl et al. 2021); 51 atoms probed many-body dynamics (Bernien et al. 2017).
Trapped ions: Up to 53 trapped-ion spins showed a dynamical phase transition in the transverse-field Ising model (Zhang et al. 2017).
Analogue quantum simulators: Ultracold fermions in an optical lattice of about 80 sites realised a long-range antiferromagnet in the Hubbard model (Mazurenko et al. 2017).

What you need to run it

Classical simulation: Small systems by exact diagonalisation; tensor networks for one-dimensional or weakly entangled cases.
Noisy hardware (NISQ): Not applicable for this family.
Fault-tolerant machine: Not applicable for this family.
Annealer or analogue simulator: A neutral-atom or ion simulator with the needed geometry and interactions; access through hosting HPC centres (see where to run it).

Calculate the memory of a simulation

Where to run it in Europe

Neutral atoms

JADE (Germany; Inaugurated, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. No access route named in the catalogue. Deployment milestones JADE
Ruby (France; Inaugurated, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones Ruby
SOL (Italy; Planned, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. No access route named in the catalogue. Deployment milestones SOL
LRZ Quantum Integration Centre (QIC) (Germany; In operation, per the source): Superconducting systems from IQM (54 qubits, up to 150 in future), a 20-qubit AQT ion-trap system, and a neutral-atom system being developed by planqc (MAQCS project). Access: LRZ quantum computing consulting.
France Hybrid HPC Quantum Initiative (HQI) platform (France; In operation, per the source): Hybrid HPC–quantum platform coupled to the Joliot-Curie supercomputer: Ruby (analogue neutral-atom system controlling 100 rubidium atoms), Lucy (12-photon photonic QPU) and Qaptiva QPU emulation. Access: GENCI eDARI resource allocation requests. Deployment milestones France Hybrid HPC Quantum Initiative (HQI) platform

Trapped ions

Piast-Q (Poland; Inaugurated, per the EuroHPC JU): Trapped ions; digital quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones Piast-Q
LRZ Quantum Integration Centre (QIC) (Germany; In operation, per the source): Superconducting systems from IQM (54 qubits, up to 150 in future), a 20-qubit AQT ion-trap system, and a neutral-atom system being developed by planqc (MAQCS project). Access: LRZ quantum computing consulting.

Analogue quantum simulators

JADE (Germany; Inaugurated, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. No access route named in the catalogue. Deployment milestones JADE
Ruby (France; Inaugurated, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones Ruby
SOL (Italy; Planned, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. No access route named in the catalogue. Deployment milestones SOL

The full infrastructure catalogue · The infrastructure deployment tracker

Software

European tools in the software directory

Pulser

Other open-source frameworks

Bloqade (QuEra Computing (United States); non-European)

A listing is not an endorsement; check each tool for the features you need.

Limitations and open questions

Each machine simulates a limited family of models; calibration errors are hard to bound without classical checks.
Altman et al. (2021) count over 300 quantum simulators worldwide, most of them research instruments rather than services.

In the Quantum Algorithm Zoo

Simulating Quantum Hamiltonian Dynamics (Quantum Algorithm Zoo, external site): Approximation and Simulation Algorithms; speedup as the Zoo states it: Superpolynomial

Closest Zoo entry; the Zoo describes digital simulation algorithms, not analogue simulators.

Index: the Quantum Algorithm Zoo by Stephen P. Jordan, last updated 2026-09-10, checked 2026-10-23. The portal links to it and copies no description from it. Browse the full Quantum Algorithm Zoo (external site)

Named in European procurements

Used in: EuroHPC procurement EuroQCS-Italy (now SOL) (Required in the benchmark suite (scored under the award criteria))

As the tender documents state; how a benchmark is weighted against others is described in each procurement.

Sources

E. Altman et al. (2021). Quantum Simulators: Architectures and Opportunities. PRX Quantum 2, 017003 (2021); arXiv:1912.06938. Read: abstract page, retrieved 2026-10-23.
P. Scholl et al. (A. Browaeys group) (2021). Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms. Nature 595, 233 (2021); arXiv:2012.12268. Read: abstract page, retrieved 2026-10-23.
H. Bernien et al. (2017). Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579 (2017); arXiv:1707.04344. Read: abstract page, retrieved 2026-10-23.
J. Zhang et al. (2017). Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator. Nature (2017), DOI 10.1038/nature24654; arXiv:1708.01044. Read: abstract page, retrieved 2026-10-23.
A. Mazurenko et al. (2017). Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms. Nature 545, 462 (2017); arXiv:1612.08436. Read: abstract page, retrieved 2026-10-23.
Quantum Flagship Strategic Advisory Board (2025). Quantum Flagship Strategic Advisory Board: KPI booklet (March 2025). Booklet read for the KPI observatory. Read: booklet (see the KPI observatory), retrieved 2026-10-23.