What was shown
The authors worked out, on paper, how a future quantum computer would simulate the chemistry of materials. Nothing was run on a machine, real or simulated. Think of a recipe that lists every step and every ingredient before anyone enters the kitchen. This paper writes a new recipe for the same dish. It tracks all the particles together, rather than orbital by orbital, and it works with any choice of mathematical building blocks. The authors then counted what the recipe would demand. Against the earlier method by Babbush and colleagues, the count of the costliest operations falls by four orders of magnitude. Qubits that are protected against errors, called logical qubits, also drop: 293 for 128 orbitals, against 492 in second quantization, the older way of setting up the problem.
“Comparison between the four algorithms show that our method substantially outperforms the previous DPW algorithm by Babbush et al. [42], requiring only a fraction of logical qubits and reducing the Toffoli count by four orders of magnitude.”
— Section II.4.4 Resource Estimates for Materials (Table 3), in: Quantum Simulations of Chemistry in First Quantization with any Basis Set1
- How it was done: a calculation on paper, not run on any machine
- Qubits: The estimate counts error-protected qubits: 293 for 128 orbitals, against 492 with the older setup.
- Error correction: It assumes a future machine with built-in error protection, a physical error rate of 0.1% and a cycle time of 10⁻⁶ seconds.
- Compared against classical computing: no comparison stated in the paper
Who it affects
This concerns anyone who hopes to use quantum computers to simulate materials, for example when searching for new compounds. Today, nothing changes for them. The paper is an estimate of what a future machine would need, and no such machine exists at this scale. What it does change is the price tag of a future project: the earlier method looked far more expensive to run. Planners can treat materials simulation as a smaller hardware ask on paper, but not as a service they can buy.
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 result is a resource estimate, not a run. It assumes error-corrected machines that must still be built, with 293 protected qubits for 128 orbitals, each protected qubit made of many physical ones. The assumed error rate of 0.1% and cycle time of 10⁻⁶ seconds are typical figures for superconducting qubits, not a demonstrated system. The paper compares only against other quantum algorithms. It does not test the method against the best classical methods on the same materials, so whether a quantum computer would pay off here is still open.
This paper lowers the number of operations, compared with the approach it improves on: four orders of magnitude. The quotation below says what is reduced. It is a calculation on paper, not a machine that runs it.
“Comparison between the four algorithms show that our method substantially outperforms the previous DPW algorithm by Babbush et al. [42], requiring only a fraction of logical qubits and reducing the Toffoli count by four orders of magnitude.”
Who is working on it
The paper (August 2024) lists its authors' affiliations as: Riverlane Ltd; Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford; Astex Pharmaceuticals. That is who signed this work — it is not a ranking of who is ahead.
It strengthens a way of setting up the problem in which the particles are tracked directly, with the needed data loaded by ordinary computers beforehand, over the older second-quantization setup for periodic materials. It stays comparable to first-quantization plane-wave algorithms that need no such data.
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 npj Quantum Inf 11, 55 (2025). Georg Singer holds no shares in any company or institution named in this brief (as of October 2026).