Atom Computing and collaborators at Microsoft Quantum, Stanford, and Montana State University reported running an error-correcting code called the toric code for up to 90 cycles of error checks on the company’s neutral-atom processor, replacing atoms lost during the runs. The team submitted the results to arXiv on June 2, 2026, as a preprint, a paper not yet peer reviewed. Atom Computing announced them on June 3.
In error correction, one logical qubit, the unit a program computes with, is spread across many physical qubits so that errors can be caught by repeated checks, known as syndrome extraction, before they spoil the result. The logical error rate is how often error correction fails to protect the encoded information. In the toric code, qubits are linked as if on the surface of a doughnut, so those at opposite edges of the layout must interact.
On hardware, the team measured a lower logical error rate for its larger code in runs of up to eight rounds, but over longer runs with atom reloading the authors concluded only that logical error rates did not increase with code distance. Code distance is the smallest number of physical errors that can corrupt the encoded information without detection.
The codes and the hardware
The team trapped ytterbium-171 atoms in optical tweezers, tightly focused laser beams, and moved them between zones for storage, measurement, and two-qubit gates, the operations that act on pairs of qubits. The processor’s register zone is currently configured for 128 qubits, the authors wrote. Each of those qubits is a single atom, a physical qubit.
The authors tested two variants of the code that they call twisted toric codes and wrote their parameters as [[16, 1, (4, 3)]] and [[32, 1, (6, 4)]]. In that notation, the first figure is the number of physical data qubits and the second is the number of logical qubits. The pairs in parentheses are the code distances against the two basic kinds of qubit error, X-type and then Z-type.
Ancilla qubits are helpers that the team measured each cycle to detect errors in the data qubits. For the smaller code, the team used 16 physical data qubits and an equal number of physical ancilla qubits to encode one logical qubit. For the larger code, it used 32 of each, 64 physical qubits in all, for one logical qubit.
If the hardware is good enough, logical errors become rarer as the code distance grows. Physicists express that improvement as Λ, the ratio of the smaller code’s logical error rate to the larger code’s.
What the team measured
In runs of up to eight cycles without reloading, the team measured a Z-type logical error rate of 0.56% per cycle for the larger code and 0.74% for the smaller. At four cycles, it reported Λ of 1.9 for the Z-type logical observable, 1.20 for the X-type observable, and 1.30 averaged over both.
The authors wrote that the lower logical error rate in the larger code “is consistent with sub-threshold behavior in this regime,” but that “several aspects of the result suggest care in extrapolating these results.” Sub-threshold behavior means hardware error rates low enough for a larger code to reduce logical errors.
The team ran the smaller code for 90 cycles and the larger for 70. It measured the ancilla qubits in every cycle without stopping the run. It also replaced lost atoms and refilled a storage zone every 10th cycle with fresh atoms drawn from a cloud of cold atoms 30 centimeters below the array.
In those runs, the authors measured Z-type logical error rates of 0.63% per cycle for the smaller code and 0.64% for the larger. They measured X-type rates of 3.4% for the smaller code and 3.0% for the larger. They wrote that “over an arbitrary number of cycles, the logical error rates do not increase with larger code distance.”
In a separate experiment, the team ran repetition codes at distances 3 and 7 and added a 0.5-second idle period to every cycle. A repetition code is a simpler code with protection against only one of the two kinds of qubit error.
The team ran these codes for up to 95 cycles, up to about 1 minute in the authors’ account. By fitting the decay of the stored information, it estimated logical lifetimes of 225 seconds for distance 7 and 44 seconds for distance 3.
The authors reported baseline atom 1/e lifetimes of 10.5 seconds in the interaction, measurement, and storage zones and 15.6 seconds in the register.
The team measured all of these figures on hardware. When the authors simulated the circuits with a noise model, a computer model of the processor’s errors, they obtained lower logical error rates than they measured. They also measured an atom loss of 0.96% per two-qubit gate and named lower gate loss as one target for improvement.
Claims and next steps
In its announcement, Atom Computing called the work “the industry’s first full demonstration of quantum error correction using a toric code.” The company placed itself “among only two companies that have demonstrated many rounds of sustained quantum error correction” and described its result as “the first time this has been achieved using neutral atoms.” In the preprint itself, the authors wrote that “this is the first demonstration of continuous syndrome extraction in a code that requires non-local connectivity.”
Two Microsoft Quantum researchers, David Aasen and Juan M. Bello-Rivas, are among the roughly 100 authors.
The authors wrote that moving “from these demonstrations to useful, utility-scale quantum computing requires advancement on multiple fronts.” They listed larger systems running codes of greater distance, better two-qubit gates with less atom loss, and logical operations. Logical operations are the gates a fault-tolerant computer applies to encoded qubits.
Update, November 13, 2026: DARPA moved Atom Computing to the final stage of its Quantum Benchmarking Initiative on October 7. As of November 13, the preprint was still at version 1, with no journal reference.
