Electronic structure on fault-tolerant computers (catalysts such as FeMoco)
Algorithms and benchmarks / Chemistry and materials
Computes energies of molecules and materials to chemical accuracy where classical methods struggle, such as the iron-molybdenum cofactor (FeMoco) of nitrogenase, which fixes nitrogen in nature. It combines Hamiltonian simulation with phase estimation.
- Era
- Fault-tolerant
- Problem class
- Chemistry and materials
- Speedup
- Expected exponential for strongly correlated systems where classical methods scale badly; no general proof.
How it works
The electronic Hamiltonian in a chosen basis of orbitals is encoded (for example with tensor hypercontraction to cut its cost), and phase estimation of the qubitized walk operator returns the ground-state energy.
Typical use cases
- Catalysts, batteries and drug molecules.
- Materials for carbon capture.
Documented use cases on related problems
From the use case directory; the sources of these cases may use other methods than this one.
- Simulating lithium-sulfur battery molecules on a quantum computer (Daimler and IBM)
- Quantum computing method for carbon dioxide capture materials (TotalEnergies and Quantinuum)
- Hybrid quantum chemistry software for drug research (KvasirAccelerator)
- Quantum algorithm for water placement in proteins (Pasqal and Qubit Pharmaceuticals)
Resource estimates
Figures exactly as stated by their authors, with their assumptions. They are estimates under those assumptions, not forecasts, and they tend to fall as methods improve.
| Quantity | Value as stated |
|---|---|
| Physical qubits | about four million |
| Runtime | under four days |
Assumptions: Tensor hypercontraction representation of the Hamiltonian, a 1 microsecond cycle time and a physical gate error rate of at most 0.1%.
Source: J. Lee et al. 2021, PRX Quantum 2, 030305 (2021); arXiv:2011.03494
Demonstrations
- 2020: Hartree-Fock calculations on a superconducting processor with up to a dozen qubits, 78 two-qubit and 114 one-qubit gates, for hydrogen chains and the isomerisation of diazene (a test of a building block, not of fault-tolerant chemistry). (F. Arute et al. 2020)
Hardware platforms that fit
- Superconducting qubits: The cited FeMoco estimate assumes a 1 microsecond cycle and at most 0.1% physical gate error, in line with surface-code superconducting architectures (Lee et al. 2021).
What you need to run it
- Classical simulation
- Classical chemistry methods remain the baseline; state-vector simulation of the quantum algorithm is limited to small molecules.
- Noisy hardware (NISQ)
- Not applicable for this family.
- Fault-tolerant machine
- For FeMoco under the cited assumptions, about four million physical qubits for under four days.
- 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
European tools in the software directory
Other open-source frameworks
- OpenFermion (Google Quantum AI (United States); non-European)
A listing is not an endorsement; check each tool for the features you need.
Limitations and open questions
- Estimates depend on the model of the molecule and the target accuracy; Reiher et al. (2017) gave detailed estimates for nitrogenase, and Lee et al. (2021) cut the cost with tensor hypercontraction.
- A good initial state is needed for phase estimation.
In the Quantum Algorithm Zoo
- Preparing Eigenstates and Thermal States (Quantum Algorithm Zoo, external site): Approximation and Simulation Algorithms; speedup as the Zoo states it: Superpolynomial
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
- M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, M. Troyer (2017). Elucidating Reaction Mechanisms on Quantum Computers. PNAS 114, 7555 (2017); arXiv:1605.03590. Read: abstract page, retrieved 2026-10-23.
- J. Lee, D. W. Berry, C. Gidney, W. J. Huggins, J. R. McClean, N. Wiebe, R. Babbush (2021). Even more efficient quantum computations of chemistry through tensor hypercontraction. PRX Quantum 2, 030305 (2021); arXiv:2011.03494. Read: abstract page, retrieved 2026-10-23.
- F. Arute et al. (2020). Hartree-Fock on a superconducting qubit quantum computer. Science 369, 1084 (2020); arXiv:2004.04174. Read: abstract page, retrieved 2026-10-23.