Sample-based quantum diagonalisation with supercomputers

Algorithms and benchmarks / Chemistry and materials

A quantum-centric supercomputing workflow: a quantum processor samples electronic configurations and a supercomputer diagonalises the Hamiltonian in the space they span, giving upper bounds for the ground-state energy.

Era: Noisy intermediate-scale (NISQ)
Problem class: Chemistry and materials
Area: Quantum simulation
Speedup: Not established; the method targets problems beyond exact classical diagonalisation.

How it works

Circuits prepare states close to the ground state; their measured bit strings select configurations; noisy samples are cleaned with classical processing, and a large classical diagonalisation runs on the selected space.

Typical use cases

Molecules and iron-sulfur clusters relevant to catalysis.

Resource estimates

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

Demonstrations

2025: Circuits of up to 77 qubits and 10,570 gates with the Fugaku supercomputer for the dissociation of N2 and the [2Fe-2S] and [4Fe-4S] clusters. (J. Robledo-Moreno et al. 2025)

Hardware platforms that fit

Superconducting qubits: Run with circuits of up to 77 qubits on a Heron superconducting processor together with the Fugaku supercomputer (Robledo-Moreno et al. 2025).

What you need to run it

Classical simulation: The diagonalisation step itself needs a supercomputer; the quantum part is too large for state-vector simulation at the published sizes.
Noisy hardware (NISQ): Around 50 to 100 qubits with thousands of gates, plus a tightly coupled HPC system: the model of hybrid HPC-quantum centres such as those of EuroHPC.
Fault-tolerant machine: Not applicable for this family.
Annealer or analogue simulator: Not applicable for this family.

Calculate the memory of a simulation

Where to run it in Europe

Superconducting qubits

VLQ (Czechia; Inaugurated, per the EuroHPC JU): Superconducting; digital quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones VLQ
Euro-Q-Exa (Germany; Inaugurated, per the EuroHPC JU): Superconducting; digital quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones Euro-Q-Exa
EuroQCS-Spain (Spain; Inaugurated, per the EuroHPC JU): Superconducting annealing; analogue quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones EuroQCS-Spain
Quantum Inspire (Netherlands; In operation, per the source): Online platform with superconducting transmon QPUs, a neutral-atom emulator and simulators; a Spin-2+ electron spin QPU is listed as archived. Access: Quantum Inspire registration.
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.
Finnish Quantum-Computing Infrastructure (FiQCI) (Finland; In operation, per the source): Hybrid HPC and quantum computing platform: VTT Q50 (53 qubits) and Aalto Q20 (20 qubits), superconducting systems made by IQM, used through the LUMI supercomputer environment. Access: FiQCI calls for academic projects.
Quantum Spain quantum computer at BSC-CNS (Spain; In operation, per the source): Superconducting; digital quantum computer with a 35-qubit processor, integrated into the MareNostrum 5 supercomputer. Access: Spanish Supercomputing Network (RES) quantum access. Deployment milestones Quantum Spain quantum computer at BSC-CNS

The full infrastructure catalogue · The infrastructure deployment tracker

Software

Other open-source frameworks

Qiskit (IBM (United States); non-European)

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

Limitations and open questions

The energies are variational upper bounds; their accuracy compared with the best classical methods has to be checked case by case.

In the Quantum Algorithm Zoo

No matching Zoo entry was found on 23 October 2026; the Zoo lists algorithms with a proven or conjectured speedup, not this family.

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

None of the procurement documents read for this release names it.

Sources

J. Robledo-Moreno et al. (2025). Chemistry Beyond the Scale of Exact Diagonalization on a Quantum-Centric Supercomputer. Science Advances 11, eadu9991 (2025); arXiv:2405.05068. Read: abstract page, retrieved 2026-10-23.