What was shown
The authors worked out, on paper, what it would take to simulate FeMoCo, a molecule of chemical interest, on a future quantum computer. Nothing was run on a machine. Their method, called tensor hypercontraction, compresses the description of the molecule so the computer needs less working memory and fewer of a costly basic operation named Toffoli. The paper reports that this method needs fewer of both than the other competitive methods it compares. Think of a building site: the Toffoli operations are the slow crane lifts, and the qubits are the workers on site. Fewer lifts and fewer workers make a smaller project. In the authors' layout, the computation would span four million physical qubits and take 3 days to perform its Toffolis.
“With this layout the FeMoCo computation would span four million physical qubits.”
— Section IV.3.4 Routing and distilling, in: Even more efficient quantum computations of chemistry through tensor hypercontraction1
- How it was done: a calculation on paper, not run on any machine
- Qubits: Four million physical qubits, meaning the individual hardware qubits, before error correction groups them into protected units.
- Error correction: The design assumes error correction that bundles many fragile hardware qubits into protected units, with each hardware gate failing at a rate of 0.1%.
- Compared against classical computing: no comparison stated in the paper
Who it affects
For people in chemistry, drug or materials work, nothing changes today. The paper concerns the simulation of molecules such as FeMoCo, a task where quantum computers are meant to help chemists. It gives planners a concrete size for that task: a machine of four million physical qubits. Until such a machine exists, there is nothing to buy or switch to. The work remains a sizing exercise on paper.
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 presupposes an error-corrected machine with four million physical qubits, a physical gate error rate of 0.1% and a cycle time of 1 microsecond. It also assumes a sufficiently good starting state for the molecule and works with a simplified model of FeMoCo, an active space model. The paper itself says that the cost of preparing that starting state still needs to be analyzed. It states no comparison against classical computing.
Against published roadmaps: the task needs 4 million physical qubits. No announcement we have on file reaches that many physical qubits. The furthest any of them goes:
An announcement is not a delivered machine, and this one would still fall short of what the task needs.
Who is working on it
The paper (November 2020) lists its authors' affiliations as: Department of Chemistry, Columbia University, New York, NY, USA; Department of Physics and Astronomy, Macquarie University, Sydney, NSW, Australia; Google Quantum AI, Venice, CA, USA; Department of Physics, University of Washington, Seattle, WA, USA; and 1 further institution. That is who signed this work — it is not a ranking of who is ahead.
The result strengthens fault-tolerant quantum chemistry built on qubitization with tensor hypercontraction, compiled to the surface code, a scheme that arranges qubits on a grid so errors can be detected and corrected. Its logical qubit and Toffoli counts are lower than those of competing methods.
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, 030305 (2021). Georg Singer holds no shares in any company or institution named in this brief (as of October 2026).