What was shown
The authors worked out a recipe for a quantum computer to calculate stopping power: how quickly a fast particle loses energy as it pushes through dense matter. The case studied is an alpha particle slowing down in a hydrogen target. Picture a bowling ball rolling through a crowd that is constantly jostling. The recipe tracks every electron and the projectile one by one. Nothing ran on any machine; this is a calculation on paper. It sizes a case with 219 quantum particles, the size of the simulated system. A smaller benchmark case with 29 particles needs 10¹³ basic steps, the count the quotation gives as Toffoli gates.
“We estimated that fully converged (in system size and basis-set size, with respect to TDDFT) calculations for an alpha particle projectile stopping in a hydrogen target would require 10¹⁷ Toffoli gates using QSP as the time-evolution routine. If 8th -order product formulas are used to build the electron-projectile propagator then we estimate that approximately 10¹⁵ Toffoli gates would be required.”
— Section IV Discussion, in: Quantum computation of stopping power for inertial fusion target design1
- How it was done: a calculation on paper, not run on any machine
- Qubits: The estimate needs 10³ logical qubits, meaning error-protected units of computing; nothing was run on real qubits.
- Error correction: It assumes a fault-tolerant quantum computer, a machine that catches and corrects its own errors while it computes.
- Compared against classical computing: No timing comparison exists; the target goes beyond TDDFT, today's approximate classical method for treating the electrons.
Who it affects
This concerns teams that simulate how fast particles lose energy in dense, hot matter to design targets for inertial fusion, an approach to fusion energy. For them nothing changes today. The paper shows only what a more exact calculation would demand from hardware.
Chemicals and materials: McKinsey & Company estimates $450B to $800B by 2035 — value at stake for the industry, not vendor revenue (Quantum Technology Monitor, April 2026, p. 22).
This figure is an estimate, not a measurement: McKinsey & Company is a consultancy with its own quantum advisory business. It covers a whole use case, not the result of this paper.
What is still missing
The calculation needs a fault-tolerant quantum computer with about 10³ logical qubits that can run 10¹⁵ to 10¹⁷ basic steps. No such machine exists. The paper has not fully worked out the extra cost of handling the temperature of the electrons. It also gives no runtime comparison with existing classical TDDFT calculations, today's approximate classical way of treating the electrons.
Against published roadmaps: the task needs 10¹⁷ gates and 1,000 logical qubits. No announcement we have on file reaches that many gates. The furthest any of them goes:
- UK Department for Science, Innovation and Technology2 (a government setting a target for its own national programme): 1 trillion gates for 2035.
An announcement is not a delivered machine, and this one would still fall short of what the task needs. Roadmaps count gates of every kind, so a machine of that size is necessary for this task but may not be sufficient.
Who is working on it
The paper (August 2023) lists its authors' affiliations as: Google Quantum AI, Venice, CA, USA; School of Mathematical and Physical Sciences, Macquarie University, Sydney, NSW, AUS; Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, NM, USA; Quantum Simulation Technologies Inc., Boston, MA, USA; and 1 further institution. That is who signed this work — it is not a ranking of who is ahead.
The paper supports simulating quantum motion by tracking each electron and the projectile individually on a grid of waves, on error-corrected hardware. Of two alternative ways of calculating the time evolution, it finds the product-formula method cheaper than the one called QSP.
How this brief was made
This brief was written by software, not by a person: a language model read the full text of the paper, and code then checked every quotation, number and name in this brief against that text before it was published. The rules are set out under Method. Responsible for the rules and for this page: Georg Singer. The paper is peer-reviewed, published in Proceedings of the National Academy of Sciences Volume 121, Issue 23, 2024. Georg Singer holds no shares in any company or institution named in this brief (as of October 2026).