Quantum computers solving useful chemistry problems

How far are we from quantum computers that beat classical methods on a useful chemistry or materials problem?

Quantum computers have run small chemistry calculations on real hardware, but no source reviewed shows one beating the best classical methods on a chemistry or materials problem that matters in practice. Google reports a verifiable quantum advantage on a benchmark task, and D-Wave claims one on a spin-glass model. A 2025 classical tensor-network preprint reports state-of-the-art accuracy on the spin-glass models used in the D-Wave claim. A 2020 resource estimate for the FeMoco cofactor of nitrogenase needs about four million physical qubits and under four days, well above the 77-qubit circuits run in 2025.

AI illustration · Illustrative scene, not a photograph of the specific device or experiment.
WHERE WE AREScience demonstrated

Far away. The science works, but nobody has built a working system yet.

Quantum hardware has computed molecular energies for small molecules and iron-sulfur clusters, and a 2025 IBM-led study ran circuits of up to 77 qubits with classical supercomputer support. These are science demonstrations. The advantage claims reviewed are on benchmark or model systems and are disputed. No source reviewed shows a quantum computer beating classical methods on a chemistry problem of practical value, so the stage is science demonstrated rather than engineering prototype.

The tech tree

Everything recorded on Vrulum that this future needs, oldest foundations at the top and the goal at the bottom. Lines show what each step requires.

What it takes: Quantum computers solving useful chemistry problems Unlocked Being researched Locked
  1. 2018Topological qubitsLab demonstration Being researched.
  1. 1995Quantum error correctionLab demonstrationRequires: Topological qubits. Being researched.
  1. 2007Superconducting quantum computersResearch and prototypesRequires: Quantum error correction. Being researched.
  2. 2019Trapped-ion quantum computersPilot and early commercial Unlocked.
  3. 2020Silicon spin qubitsResearch and prototypes Being researched.
  4. 2023Neutral-atom quantum computersResearch and prototypesRequires: Quantum error correction. Being researched.
  5. 2024Photonic quantum computersResearch and prototypesRequires: Quantum error correction. Being researched.
  1. 2016Resource estimates for a nitrogenase reaction on a quantum computer publishedDone Unlocked.
  2. 2020Resource estimate for the FeMoco cofactor of about four million physical qubitsDone Unlocked.
  3. 2025Claimed quantum advantage on a spin-glass model tested by classical methodsIn progress Being researched.
  4. 2025Small molecules and iron-sulfur clusters computed on quantum hardware with classical supportDone Unlocked.
  5. 2025Verifiable quantum advantage on a benchmark task with physical observablesIn progress Being researched.
  6. Date not recordedQuantum advantage on a chemistry problem of practical sizeNot started Locked.
  7. Date not recordedChemistry circuits run on error-corrected logical qubitsNot started Locked.
  1. GoalQuantum computers solving useful chemistry problemsGoalRequires: Superconducting quantum computers, Trapped-ion quantum computers, Neutral-atom quantum computers, Photonic quantum computers, Silicon spin qubits, Resource estimates for a nitrogenase reaction on a quantum computer published, Small molecules and iron-sulfur clusters computed on quantum hardware with classical support, Resource estimate for the FeMoco cofactor of about four million physical qubits, Claimed quantum advantage on a spin-glass model tested by classical methods, Verifiable quantum advantage on a benchmark task with physical observables, Quantum advantage on a chemistry problem of practical size, Chemistry circuits run on error-corrected logical qubits. Locked.

The road so far

3 of 7 steps done, 2 in progress.

  1. Done · 11 May 2016Resource estimates for a nitrogenase reaction on a quantum computer published

    Reiher and colleagues proposed using a quantum computer to study the reaction mechanism of nitrogenase, the enzyme that fixes nitrogen. The abstract says detailed resource estimates, including error-correction overheads, show the necessary computations can be performed in reasonable time on small quantum computers. The abstract gives no figures. [1]

  2. Done · 20 Jun 2025Small molecules and iron-sulfur clusters computed on quantum hardware with classical support

    A 2025 Science Advances study by IBM researchers used a Heron superconducting processor and the Fugaku supercomputer. It simulated the dissociation of a nitrogen molecule and the ground-state properties of [2Fe-2S] and [4Fe-4S] clusters, with circuits of up to 77 qubits and 10,570 gates. The abstract says classical computing handles every part of the workflow except the inherently quantum component, and it gives no classical benchmark figures. [2]

  3. Done · 6 Nov 2020Resource estimate for the FeMoco cofactor of about four million physical qubits

    Lee and colleagues estimated that FeMoco could be simulated with about four million physical qubits and under four days of runtime. The estimate assumes surface-code error correction, 1 microsecond cycle times and physical gate error rates no worse than 0.1 percent. It is an estimate in a preprint and journal paper, not a run on hardware. [3]

  4. In progress · 2025Claimed quantum advantage on a spin-glass model tested by classical methods

    D-Wave's Science paper argues that its annealers can produce samples that closely match solutions of the Schrödinger equation for spin-glass quench dynamics, and that some practically important questions may remain out of reach for classical computation. A March 2025 preprint by Tindall and colleagues simulates Ising spin-glass models run on D-Wave's Advantage2 annealer, using two- and three-dimensional tensor networks. It reports state-of-the-art accuracy with modest resources, after extensive comparison with existing numerical methods. This is a disputed claim, not a settled result. [4][5]

  5. In progress · 22 Oct 2025Verifiable quantum advantage on a benchmark task with physical observables

    Google Quantum AI reports a verifiable quantum advantage for its Quantum Echoes algorithm, run on a 65-qubit experiment on its Willow chip. Google estimates the task would take about 13,000 times longer on a classical supercomputer. The result applies to a set of benchmarking circuits, not a practical application. A companion molecular NMR experiment with UC Berkeley is described as not yet beyond classical methods, and its preprint has not yet been peer reviewed. [6]

  6. Not startedQuantum advantage on a chemistry problem of practical size

    No source reviewed shows a quantum computer beating the best classical methods on a chemistry problem of practical value. Chan notes that a 54-orbital FeMoco model can be treated with standard quantum chemistry methods in a few hours on a laptop, though that model lacks the hard open-shell features of the real cofactor. He reports a 2026 classical study that reached chemical accuracy on a 76-orbital model, and he describes the theoretical support for exponential quantum advantage on this problem as much weaker than for random circuit sampling. [7][3]

  7. Not startedChemistry circuits run on error-corrected logical qubits

    The FeMoco estimate assumes a fault-tolerant machine with error correction. The 2025 IBM chemistry runs used physical qubits, and the cited abstract does not describe error correction. No source reviewed shows a chemistry calculation on logical qubits at useful scale. [3][2]

Why it matters

Chemistry and materials design, such as new catalysts, fertilisers and batteries, could benefit if quantum computers can model molecules that classical methods handle poorly. Claims of advantage shape where funding and effort go, so it matters that they are tested against the best classical methods, not weaker ones.

What stands in the way

  • A 2025 classical tensor-network preprint reports state-of-the-art accuracy on the spin-glass models used in the D-Wave claim, so that advantage is contested.
  • The FeMoco resource estimate reviewed needs about four million physical qubits and under four days, much more than the 77-qubit circuits run in 2025.
  • The 2025 IBM chemistry study offloads every part of the workflow except the quantum component to classical supercomputers.
  • Advantage demonstrations so far use benchmark or model systems, not a chemistry question with a practical answer.
  • Chemistry on error-corrected logical qubits at useful scale has not been shown in the sources reviewed.

Signals to watch

  • A chemistry result on quantum hardware where classical baselines are fixed in advance and the quantum result is more accurate.
  • Classical rebuttals of Google's Quantum Echoes result, or independent checks that confirm it.
  • Peer review of the Google and Berkeley NMR preprint, and whether its result moves beyond classical reach.
  • A calculation on error-corrected logical qubits that runs a chemistry circuit.
  • Revised FeMoco resource estimates that fall well below four million physical qubits, or a classical method that settles the cofactor model.

Sources

  1. preprint
    Elucidating Reaction Mechanisms on Quantum Computers
    Markus Reiher, Nathan Wiebe, Krysta M. Svore et al.. arXiv, 11 May 2016.
  2. peer reviewed paper
    Chemistry beyond the scale of exact diagonalization on a quantum-centric supercomputer
    Javier Robledo-Moreno, Mario Motta, Holger Haas et al.. Science Advances, 20 Jun 2025.
  3. preprint
    Even more efficient quantum computations of chemistry through tensor hypercontraction
    Joonho Lee, Dominic W. Berry, Craig Gidney et al.. arXiv (PRX Quantum 2, 030305, 2021), 6 Nov 2020.
  4. peer reviewed paper
    Beyond-classical computation in quantum simulation
    Andrew D. King et al.. Science 388, 199-204 (2025); preprint arXiv:2403.00910, 2025.
  5. preprint
    Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
    Joseph Tindall, Antonio Mello, Matthew Fishman et al.. arXiv, 7 Mar 2025.
  6. company announcement
    A verifiable quantum advantage
    Xiao Mi, Kostyantyn Kechedzhi. Google Research, 22 Oct 2025.
  7. other
    The FeMo-cofactor and classical and quantum computing
    Garnet Chan. Quantum Frontiers (blog), 12 Mar 2026.

Last reviewed 21 Oct 2026.