What was shown
The authors worked out, on paper, how many resources a chemistry simulation would need. Think of a stadium. One method keeps a list of every seat and marks whether it is taken. The other keeps a list of the people and notes where each one sits. With few people and many seats, the second list is far shorter. The paper uses the second method for electrons. It gives exact constant factors for the cost and improves them more than a thousandfold. This is a calculation, not a run on any machine.
“Our implementation of these algorithms allows us to report the first constant factors for the scaling of any first quantized chemistry algorithm (or any Dyson series based simulation), and also optimizes those constant factors more than a thousandfold.”
— Section I.2 (Overview of the Hamiltonian simulation frameworks deployed in this work), in: Fault-Tolerant Quantum Simulations of Chemistry in First Quantization1
- How it was done: a calculation on paper, not run on any machine
- Qubits: The system register needs about 2 × 10³ qubits, according to a resource estimate rather than a hardware run.
- Error correction: The estimate assumes machines that detect and correct their own errors, and it counts cost in a demanding type of operation.
- Compared against classical computing: no comparison stated in the paper
Who it affects
This concerns anyone who hopes to design molecules or materials by simulating their electrons, for example in drug or battery research. Today nothing changes for them: no machine can run this, and the paper offers a planning figure for the size of future machines, not a tool.
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 estimate assumes error-corrected machines that run very long sequences of demanding operations, and nothing was run on hardware. The target problem has 100 electrons and 10⁶ basis functions, and the register alone needs about 2 × 10³ qubits. The paper also compares only against other quantum methods, not against the best classical chemistry methods.
Against published roadmaps: the task needs 2,000 logical qubits. These announcements cover that:
- IonQ2 (a vendor describing its own planned product): 8,000 logical qubits for 2029.
- IBM3 (a vendor describing its own planned product): 2,000 logical qubits for 2033 or later.
The year in the verdict is the latest of these, and its source says “or later”. An announcement is not a delivered machine.
Who is working on it
The paper (May 2021) lists its authors' affiliations as: Google Quantum AI, Venice, CA 90291, United States; Institute for Quantum Information and Matter, Caltech, Pasadena, CA 91125, United States; Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia; Department of Computer Science, University of Toronto, ON M5S 2E4, Canada; and 1 further institution. That is who signed this work — it is not a ranking of who is ahead.
It strengthens the approach that tracks each electron's position on a grid of plane waves and runs on error-corrected machines, rather than the approach built on orbitals shaped like atomic clouds.
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 PRX Quantum 2, 040332 (2021). Georg Singer holds no shares in any company or institution named in this brief (as of October 2026).
Sources
- arxiv.org Fault-Tolerant Quantum Simulations of Chemistry in First Quantization
- ionq.com IonQ
- ibm.com IBM