What was shown
The authors worked out on paper how much computing a future, error-corrected quantum machine would need to find the energy of a simple model of electrons in a material. The method splits the job into many small steps, and each step adds a little error. Think of building a bridge. If you cannot say how large the error is, you add a thick safety margin and pay for extra steel. A tighter estimate lets you shrink the margin. The paper supplies such estimates, and the count of the costliest operations falls, most clearly when few of the available slots for electrons are filled. No machine ran this. It is a calculation, not an experiment.
“Comparing the gate counts obtained using our novel Trotter error bounds to those obtained using the existing fermionic commutator bound, we observe a reduction in T count by a factor of between 2.3-12.7×. This improvement is more pronounced at lower filling fractions, demonstrating the anticipated benefit of using the fermionic seminorm.”
— Section VI.2 Phase estimation resource estimates, in: Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian1
- How it was done: a calculation on paper, not run on any machine
- Qubits: The estimate counts error-protected qubits; the two step-by-step methods use 16 additional qubits.
- Error correction: The calculation assumes a quantum computer that corrects its own errors, which does not exist yet.
- Compared against classical computing: no comparison stated in the paper
Who it affects
This concerns anyone who hopes quantum computers will one day simulate materials and chemistry. The task here is a textbook model of electrons, not a specific molecule or product. For a company in this field, nothing changes today. The result only suggests that one route to such simulations will need less computing than earlier estimates said.
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 estimates assume a quantum computer that corrects its own errors and starts from a perfectly prepared state. Neither exists. The target is a model system, not an industrial molecule or material. A rival method, qubitization, still needs fewer of the costliest operations, by a factor of 2-11, though it uses 5-7 times more helper qubits. So the paper lowers a cost estimate, but it does not make the method the cheapest.
This paper lowers the number of operations the task needs, compared with the approach it improves on: 2.3-12.7×. It is a calculation on paper: it says the task got cheaper, not when a machine will be able to run it, and no roadmap has been checked for the new figure.
“Comparing the gate counts obtained using our novel Trotter error bounds to those obtained using the existing fermionic commutator bound, we observe a reduction in T count by a factor of between 2.3-12.7×.”
Who is working on it
The paper (July 2021) lists its authors' affiliations as: AWS Center for Quantum Computing; Institute for Quantum Information and Matter, Caltech; Google Research. That is who signed this work — it is not a ranking of who is ahead.
It strengthens the step-by-step (Trotter) route to this calculation when few electron slots are filled, compared with earlier error estimates. Qubitization still needs fewer of the costliest operations for the systems considered.
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 a preprint that has not been peer-reviewed. Georg Singer holds no shares in any company or institution named in this brief (as of October 2026).