What was shown
A quantum computer's hardest basic step needs special prepared inputs, which a dedicated factory inside the machine must produce. The earlier factory made a simpler input, and the machine needed four of them for each such step. This paper designs a factory that makes one input that does the same job. Think of a kitchen that bakes one finished loaf where another must bake four rolls to build the same sandwich. The new factory takes up a floor area of 12d by 6d and delivers one input every 5.5d cycles, where d sets how much error protection the machine carries. This is a calculation on paper. Nothing was built or run on any machine.
“Because it takes four |T⟩ states to perform a Toffoli gate, but only one |CCZ⟩ state to do the same, algorithms dominated by applying Toffolis, such as Shor’s algorithm and the chemistry algorithm in [1], run five times as fast when using our |CCZ⟩ factory instead of the |T⟩ factory from [15].”
— Section 6 (Conclusions), in: Efficient magic state factories with a catalyzed |CCZ> to 2|T> transformation1
- How it was done: a calculation on paper, not run on any machine
- Qubits: The paper states no count of physical qubits; it gives the factory's size only in units of d, the level of error protection.
- Error correction: The design assumes a machine that corrects its own errors continuously, with each basic physical operation failing about once in a thousand tries (10⁻³).
- Compared against classical computing: no comparison stated in the paper
Who it affects
This concerns anyone who expects to use a future error-corrected quantum computer for code-breaking, as in Shor's algorithm, or for chemistry calculations too large for ordinary computers. For those jobs the design would cut run time. Today nothing changes for a buyer or planner. No machine exists that could run the factory, so the gain is an estimate that vendors can build toward, not a product feature.
Quantum computing vendors and their customers: McKinsey & Company estimates $43B to $71B by 2035 — quantum computing market size (vendor side) (Quantum Technology Monitor, April 2026, p. 8).
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
No machine exists that can run these factories. The estimates assume that each basic physical operation fails about once in a thousand tries (10⁻³), and that the machine corrects errors continuously. The authors' chemistry example falls from about 10 hours to about 2 hours only if its circuits can be reworked to keep up with the faster supply of inputs. That reworking must also avoid a bottleneck in moving data around the machine. The paper does not show that this works.
This paper lowers the run time, compared with the approach it improves on: from ~10 hours to ~2 hours. The quotation below says what is reduced. It is a calculation on paper, not a machine that runs it.
“Assuming that such a reworking is possible for [1], the runtimes at classically intractable sizes would be reduced from ~10 hours (see table VII of [1]) to ~2 hours.”
Who is working on it
The paper (December 2018) lists its authors' affiliations as: Google Inc., Santa Barbara, California 93117, USA. That is who signed this work — it is not a ranking of who is ahead.
The result strengthens quantum computers that correct errors by stitching patches of qubits together, known as lattice surgery on the surface code. It lowers the space and time cost of making the special inputs that the hardest basic steps need.
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 Quantum 3, 135 (2019). Georg Singer holds no shares in any company or institution named in this brief (as of October 2026).