IonQ researchers reported in a preprint submitted to arXiv on June 4, 2026, that they reached breakeven with error-correcting codes of the quantum low-density parity-check (qLDPC) type on a trapped-ion quantum computer. The 11 authors, all at IonQ, ran the codes on one chain of 40 barium-133 ions, each a physical qubit, without moving the ions or reconfiguring the hardware between codes.
A logical qubit is one unit of quantum information spread across several physical qubits so that errors can be detected and corrected. The authors described breakeven performance as logical qubits reaching lifetimes “comparable to or slightly exceeding” those of their trapped-ion qubits. In the best case, the team measured a logical-qubit lifetime of 3.95 ± 0.68 seconds with a code it labels GB4 [[26,2,5]], against a derived 3.3 ± 0.9 seconds for the physical qubits.
IonQ’s team measured logical qubits on 40 ions that lasted slightly longer than the physical qubits in two codes, by margins smaller than the reported uncertainties. The preprint has not been peer reviewed.
The codes
The authors wrote that qLDPC codes “feature higher encoding rates than planar alternatives such as the surface code” but often require hardware such as long-range couplers, links between distant qubits. A code’s encoding rate is its number of logical qubits per physical data qubit.
Codes are written [[n,k,d]], where n is the number of physical data qubits and k the number of logical qubits. The code distance, d, is a measure of how many errors a code can withstand.
The authors wrote that they demonstrated nine codes from three families, though they listed eight in Section III of the paper. Three are bivariate bicycle qLDPC codes labeled BB5, with parameters [[18,4,3]], [[24,4,4]], and [[30,4,5]]. Two more qLDPC codes, labeled GB4, are [[16,2,4]] and [[26,2,5]].
The two topological codes are both toric, a standard [[18,2,3]] code and a rotated [[16,2,4]] variant. Toric codes are defined on a grid that wraps around at its edges. The eighth is a [[16,4,4]] concatenated code, built from two layers of the [[4,2,2]] code.
Depending on the code, the team used 10 to 16 of the remaining ions as ancillas, physical helper qubits measured repeatedly to reveal errors without disturbing the logical information.
Comparison with a superconducting experiment
The authors compared their BB5 [[18,4,3]] code with what they called “a similar code” on superconducting qubits, one with the same numbers of logical and physical data qubits. Ke Wang and colleagues ran that code, [[18,4,4]], on a processor with 32 physical qubits and long-range couplers, as they reported in Nature Physics in January 2026.
IonQ’s team wrote that it achieved “a logical error rate 4× better for Z errors and 9× better for X errors.” A logical error rate is how often errors get past a code’s correction. An X error is a flip between 0 and 1, while a Z error is a flip of the qubit’s phase.
In the preprint’s Table 1, the IonQ code’s logical error rates per logical qubit per syndrome cycle were 2.01% and 1.08%, against 8.67% and 9.15% for the superconducting code. A syndrome cycle is one round of error-detecting checks.
What was measured, derived, and simulated
The team measured the error rates and lifetimes on the 40-ion chain in memory experiments, preparing logical states and running one to six cycles of error checks before measuring the qubits. It repeated every experiment 2,000 times, for 48,000 shots, or single runs, per code. The authors defined a qubit’s lifetime as the time for its survival probability to fall to 1/e, or about 37%, averaged over all single-qubit state preparations.
The authors derived the physical qubits’ 3.3-second lifetime from a measured coherence time, T2*, of 1.1 ± 0.3 seconds. T2* is a measure of how long a qubit keeps a well-defined phase. They took the lifetime as three times T2*, treating the qubits’ energy-relaxation time as too long to measure.
The team discarded any shot in which it detected leakage, an error in which an ion leaves the two energy levels that encode the qubit. For the largest code, BB5 [[30,4,5]], it rejected 17.8% of shots after one cycle and 74.8% after six, according to the preprint’s appendix. When the authors simulated resetting leaked qubits instead of discarding the run, they found worst-case relative increases in the logical error rate of 11% for the BB5 codes and 20% for the GB4 codes, or decreases of 10% and 17% in logical-qubit survival time.
The OMG architecture
To measure and reset some qubits partway through a computation while others keep their quantum states, the team used what it called “a novel implementation” of the optical-metastable-ground (OMG) architecture. Before each measurement, the team shelved the whole chain into protected, slow-decaying metastable states. It then measured the ancillas and used them to cool the chain’s motion before resetting them.
The authors wrote that they used the scheme to run the experiments without ion transport or dedicated coolant ions, requirements that “typically consume a large fraction of the runtime or ion count of trapped-ion quantum computers.” They wrote that, to their knowledge, the work is the first demonstration of the full OMG architecture in a fully functional trapped-ion quantum computer, after earlier demonstrations of its components in two ions.
Next steps
For larger systems, the authors named more laser-gate zones and electronic qubit control as ways to run more operations at once. They also wrote that dynamical decoupling, a noise-canceling pulse technique they did not use, “can significantly improve” the physical qubits’ T2* and the lifetimes of logical qubits.
Update, November 13, 2026: In a revised preprint posted September 14, the authors put the physical qubits’ lifetime at 3.84 ± 0.48 seconds and the best logical qubit’s at 3.95 ± 0.68 seconds. In the abstract, they still call some logical lifetimes “comparable to or slightly exceeding” that of their trapped-ion qubits.
