What was shown
The authors counted the steps a quantum computer needs to find the lowest-energy state of a Hubbard system: a standard model of electrons that hop and repel each other on a grid of sites, called a lattice. Picture a marble resting in the lowest dip of a landscape that is reshaped very slowly, so it never leaves that dip. The machine reshapes an easy problem into the hard one in the same way. T-depth counts the sequential, expensive steps the machine must run; the two ranges above measure that count.
The paper builds on qubitization, a method for carrying out the simulation on a quantum computer, together with the rewind procedure, which prepares the state step by step. It sets this against product-formula time evolution, a method that approximates the change by chopping it into small slices. This is a calculation on paper. Nothing ran on a machine.
“By extrapolating the general trend of our results, we can predict that a time evolution as long as 10⁶-10¹⁴ (in T-depth) is required to prepare the ground state of an intermediate-size Hubbard system with the adiabatic algorithm. We have also proposed an improved adiabatic optimization that decreases these times to the range 10⁴-10⁸. The overall gain can be as large as 10⁶ for intermediate-size lattices.”
— VIII Conclusion, in: Resource estimate for quantum many-body ground-state preparation on a quantum computer1
- How it was done: a calculation on paper, not run on any machine
- Qubits: A few hundred qubits; the paper does not say whether these are raw hardware bits or error-protected ones.
- Error correction: The estimate assumes future machines that detect and correct their own errors; none was built or run.
- Compared against classical computing: no comparison stated in the paper
Who it affects
Chemistry, drug and materials researchers who need the lowest-energy state of strongly interacting electrons cannot use this today: it is a planning estimate, not a tool. They would watch for error-corrected machines of a few hundred qubits and for a comparison with the best classical method.
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 covers the Hubbard model, a generic model of interacting electrons, not a specific industrial material. It extends a trend from lattices small enough for classical computers to solve, so the larger sizes are a projection, not a check. Classical methods supply the target energy and how close the next-higher state lies. No comparison with the best classical method is given.
Against published roadmaps: the task needs 100 million gates. These announcements cover that:
- IBM2 (a vendor describing its own planned product): 100 million gates for 2029.
- Quantinuum3 (a vendor describing its own planned product, in a securities filing): 10 billion gates for 2029.
- UK Department for Science, Innovation and Technology4 (a government setting a target for its own national programme): 1 trillion gates for 2035.
The year in the verdict is the latest of these. An announcement is not a delivered machine. 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 (June 2020) lists its authors' affiliations as: Département de Physique & Institut Quantique, Université de Sherbrooke, Québec, Canada J1K 2R1; Canadian Institute for Advanced Research, Toronto, Ontario, Canada M5G 1Z8; Quantum Architecture and Computation Group, Microsoft Research, Redmond, WA 98052, USA. That is who signed this work — it is not a ranking of who is ahead.
Approach supported: qubitization combined with the rewind procedure for preparing a lowest-energy state step by step on error-corrected machines, rather than product-formula time evolution.
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 Phys. Rev. A 103, 052408 (2021). Georg Singer holds no shares in any company or institution named in this brief (as of October 2026).