What was shown
Quantum computers make errors in every operation. Error correction can cancel them, but only if each basic operation goes wrong less often than a proven limit. Think of a building code for a bridge: the design holds only if every beam stays under a stated flaw level, so an inspector has to measure each beam rather than assume. The team ran that inspection on three basic single-qubit operations on one trapped ion, using gate set tomography, a method that reconstructs everything an operation does, including errors nobody anticipated. This ran on a real physical device, not in a simulation. All three operations came out below the limit of 6.7×10⁻⁴, the highest limit currently proven to hold against general, unpredictable noise.
“Fig. 2b shows the diamond norm error of our gates over time, culminating […] in diamond norm error rates (with 95% confidence intervals) of (1.58±0.15)×10⁻⁴, (1.39±0.22)×10⁻⁴, and (1.62±0.27)×10⁻⁴ for GI, GX, and GY respectively. All three gates surpass the threshold with 95% confidence.”
— Section II.3 Demonstrating suitability for fault tolerance, in: Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography1
- How it was done: run on a physical quantum processor
- Qubits: One physical qubit: a single trapped ion held in a chip-style surface trap.
- Error correction: No error correction was run; the paper only checked gates against the limit that such correction would require.
- Compared against classical computing: no comparison stated in the paper
Who it affects
This concerns makers of quantum hardware and anyone who plans around error-corrected machines. It is a measurement of one component, not a product or a use case. For a company that wants to run quantum software, nothing changes today: no application is shown and no comparison with classical computers is stated. What the paper offers is a better yardstick. It shows how the quality of basic operations can be certified against a proven limit instead of being estimated, which is the kind of evidence that error-correction plans depend on.
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
Only one kind of operation on one qubit was certified: single-qubit gates, the simplest building blocks. Error correction would also need high-fidelity two-qubit gates, which link qubits together, and repeatable measurements, all certified below the limit of 6.7×10⁻⁴. It would also need many more qubits. None of these was shown here. The paper states plainly that this is not a demonstration of fault-tolerant error correction. It says its characterization method carries over to two-qubit gates and measurements, but that step has not been taken in this work.
Who is working on it
The paper (May 2016) lists its authors' affiliations as: Center for Computing Research, Sandia National Laboratories, Albuquerque, NM 87185, USA; Sandia National Laboratories, Albuquerque, NM 87185, USA. That is who signed this work — it is not a ranking of who is ahead.
It strengthens trapped-ion qubits as a hardware route toward error correction. It also supports gate set tomography over randomized benchmarking as the way to check gates against limits of this kind, because it measures error in the same metric in which the limits are stated.
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 Nat. Commun. 8, 2017. Georg Singer holds no shares in any company or institution named in this brief (as of October 2026).