Quantinuum has reported logical-qubit counts from 94 down to one for Helios, its trapped-ion computer with 98 physical qubits, in less than a year. At the machine’s launch in November 2025, the company described 94 logical qubits in one entangled state and 48 that it called “fully error-corrected.” It also described 50 error-detected logical qubits in a magnetism simulation. In October 2026, its researchers reported a single logical qubit whose error rate fell 12-fold each time they enlarged the code.
The team built the 94 from a code that can flag errors but cannot correct them. It measured about 95% fidelity for the qubits’ shared entangled state in the runs it kept, a quarter of the total, according to a February preprint. For the single qubit, the team compared three code sizes, the standard test of whether a code corrects more errors than it introduces.
From a logical-qubit count alone, a reader learns how many encoded qubits a team prepared, but not whether the code corrected errors, how long the qubits lasted, or whether they computed anything.
Companies now set their roadmap targets in logical qubits. In its Quantum Genesis Q Competition, the U.S. Department of Energy (DOE) plans to split $100 million among companies that demonstrate at least 100 logical qubits, with two further pools of $50 million each for companies that reach 150 and 200. For architectures “not naturally measurable in total logical qubits,” DOE will “identify equivalent technical metrics during negotiation” with each company. A reader outside those negotiations can recover the facts missing from a bare count by asking five questions of the paper behind it.
Physical, encoded, corrected
A physical qubit is a piece of hardware, such as a superconducting circuit, a trapped ion, a neutral atom held by a laser, or a spin in silicon. A logical qubit is one unit of quantum information spread across several physical qubits by an error-correcting code. Researchers repeatedly measure parity checks, called syndrome measurements, that point to likely errors without reading the stored information. A classical processor called a decoder turns the results into corrections.
Researchers describe a code with three numbers, written [[n,k,d]]. The first is the number of physical data qubits and the second the count of logical qubits they store. The third is the code distance, the smallest number of errors on the data qubits that can change the stored information undetected.
A distance-2 code can flag any single error but cannot identify the qubit that failed. A distance-3 code can correct one error. In general, a code of distance d can correct up to (d−1)/2 errors on its data qubits, rounded down. A fault in a gate or a measurement can spread to several qubits, so a machine tolerates that many faults only if its check circuits are built to contain them.
Larger codes cost more physical qubits per logical qubit. Engineers gain from them only when the hardware’s physical error rate is below a level called the code’s threshold, above which a larger code performs worse than a smaller one.
Detection and correction
Teams have reported several of the largest logical-qubit counts to date with distance-2 codes. In the iceberg code Quantinuum used for the 94, each block has two extra physical qubits and a distance of 2. In the February preprint, the authors relied on error detection with postselection, the practice of keeping only the runs in which no check fires.
In December 2023, a Harvard-led team working with QuEra reported circuits with up to 48 logical qubits on 128 physical qubits, encoded in [[8,3,2]] blocks with error detection. The authors found that the encoding “substantially improves algorithmic performance with error detection.”
On its website, QuEra now summarizes the paper as “48 logical qubits with over 250 physical qubits,” followed by the phrase “below-threshold error correction.” The team used more than 250 physical qubits only in other experiments in the paper, such as one that prepared 40 color codes on 280. The correction result also came from a separate experiment, in which logical two-qubit gates improved as the team scaled a surface code, a code laid out on a two-dimensional grid of qubits, from distance 3 to 7.
Infleqtion announced 30 entangled logical qubits on 80 atoms on September 24, 2026. In a technical post, Chief Technology Officer Pranav Gokhale wrote that the team operated them in the [[8,3,2]] code, which “can detect any error or correct for a lost atom.” Infleqtion left the code’s distance out of its press release. In neither document did the company say what share of runs the team discarded, a gap Quantum Observer noted in its report on the Sqale result.
Teams that postselect keep fewer runs as their circuits grow, since every added operation is another chance for a check to fire. In a September 2026 preprint, Matthias Troyer and Chetan Nayak of Microsoft and John Martinis of Qolab wrote, “Error detection and post-selection can also be powerful.” Their example was the production of higher-quality resource states, special inputs that a computer consumes to run certain operations. They added that “post-selection at the application level by itself does not scale to long computations.”
For its 48 “fully error-corrected” logical qubits, Quantinuum’s team used a distance-4 code, which can correct some errors and flag others. In a benchmark of error-correction cycles with that code, the team kept 62% of its runs after “postselecting out uncorrectable errors,” the authors wrote in the February preprint.
The Energy Department will not fund detection alone. In its request for applications, DOE wrote that proposals for machines that “are only capable of error mitigation or detection and not correction” are “not of interest.”
Scaling below threshold
Researchers test correction by enlarging a code and measuring whether the logical error rate per round of checks goes down. They report a suppression factor, Λ (lambda), the number by which the logical error rate is divided each time a team adds two to the code distance. A Λ above 1 means the hardware is below threshold for that code over the distances tested.
Google Quantum AI crossed that line narrowly in 2023. Its team reported a logical error of 2.914% per cycle, or round of checks, for a distance-5 surface code, against 3.028% averaged over distance-3 codes on the same chip. In December 2024, on its Willow chip with 105 physical qubits, the team reported a distance-7 memory on 101 physical qubits with an error of 0.143% per cycle and a Λ of 2.14.
That Willow logical qubit lasted 2.4 times as long as the chip’s best physical qubit, past the point researchers call break-even. The team also ran a real-time decoder at distance 5, with an average latency of 63 microseconds.
On neutral atoms, a Harvard-led team reported in Nature in November 2025 that a distance-5 surface code had 2.14 times lower error per round than a distance-3 code, the same factor Google reported for Willow. The team measured it in a four-round test, without postselection. On the same platform, with arrays of up to 448 atoms, it also ran up to 96 distance-4 logical qubits at once. On superconducting hardware, Google’s team measured a Λ of 1.56 for color codes, a different code family, going from distance 3 to 5.
Quantinuum’s researchers reported a much steeper fall in October. They ran triangular color codes of distance 3, 5, and 7, which use 13, 37, and 73 physical qubits, for 20 rounds. The logical error per round fell from 5.5 in 10,000 at distance 3 to 5 in a million at distance 7, a Λ of 12, as Quantum Observer reported in its article on the Helios color codes.
The team decoded all the data after the runs. The authors wrote that one of their decoders, Tesseract, “is generally not fast enough to be used in real time.” They described two neural-network decoders as “capable of real-time decoding,” with speeds they timed separately from the machine. In its press release, Quantinuum called the work a “world-record quantum error-correction result” and did not say that the decoding was done offline or that the paper had not been peer reviewed.
A Λ also depends on what the larger code is compared against. Researchers at the University of Southern California (USC), Quantum Elements, and Madrid’s Instituto de Física Teórica ran surface codes on IBM’s heavy-hex Heron chips. In their preprint, since published in Nature Communications, they warned that comparing codes run with and without dynamical decoupling, a pulse technique that protects idle qubits, yields “spurious subthreshold claims.” On their best chip, they found suppression of one error type at a time, not of arbitrary logical states, as Quantum Observer reported in its article on the heavy-hex experiments.
A University of Sydney-led team ran surface codes on IBM’s ibm_miami, a superconducting chip with 120 physical qubits in a square lattice. The team reported in July that its distance-5 code had a lower error than the best distance-3 code in one basis, 0.98% against 1.26% per round. The team reached that result only after excluding defective components, the method the paper set out to test, and discarding runs flagged for leakage, in which qubits drift out of the two states that store information. The authors wrote that the leakage filtering “does not provide a scalable approach to improving QEC,” their abbreviation for quantum error correction.
IBM researchers Bence Hetényi and James Wootton tested both detection and correction in one paper in 2024. On an IBM device with 133 physical qubits, they reported a logical Bell state, the simplest entangled two-qubit state, with 94% fidelity at distance 2 using postselection. At distance 3, they showed a Bell-inequality violation using error correction alone.
Atom Computing and collaborators reported in June a “lower absolute logical error rate for the larger distance code” over up to eight rounds. They also reported logical error rates after up to 90 rounds, with lost atoms replaced from a reservoir. In the abstract, they did not give a suppression factor per round, the Λ measure the other teams in this section reported.
Memory and computation
In most of the experiments so far, teams stored logical qubits without computing with them. To compute, a machine needs logical gates. Clifford gates, a restricted set that a classical computer can simulate efficiently when circuits start from standard states, are cheap in many codes. A universal machine also needs a non-Clifford gate, usually the T gate, which most leading designs perform by consuming a specially prepared resource called a magic state.
Quantinuum’s team measured a logical two-qubit Clifford error of 7 in 100,000 at distance 5. The authors wrote that distance-7 gate circuits “require more qubits than what is available on Helios-1.”
Google Quantum AI researchers reported in Science on October 15, 2026, that they had cut the error of an encoded T state about 40-fold on Willow with magic-state cultivation, reaching a fidelity of 0.9999, or an error of about 1 in 10,000. They kept 8% of attempts, the kind of postselection that Troyer, Nayak, and Martinis described as useful for producing resource states. In his 2025 estimate for factoring a 2048-bit RSA key, Craig Gidney assumed cultivated states with errors of 1 in 10 million, which he distilled further before use.
In silicon, researchers at the International Quantum Academy in Shenzhen ran a universal set of gates on two logical qubits in March, using a [[4,2,2]] code and applying its checks in post-processing. The team measured an average logical-gate fidelity of about 86%, below the more than 95% of the device’s physical gates. For its logical T gate, it measured 82.6%, as Quantum Observer reported in its article on the Shenzhen experiment.
Troyer, Nayak, and Martinis would reserve the name “scalable logical qubit” for one that meets four conditions. It stays intact for a whole computation under repeated rounds of correction. Its logical error rate falls predictably as more physical qubits are devoted to it. It supports universal fault-tolerant operations with real-time decoding. It can also be replicated to hundreds or thousands of logical qubits. None of the experiments described here met all four.
What a count costs
Algorithm designers state their requirements in logical qubits because they assume that each one survives the whole computation. In his 2025 estimate, Gidney listed 1,399 logical qubits in his cost table, described 1,409 in use at the peak of his factoring circuit, and counted 1,537 including idle storage patches. He put the machine at 897,864 physical qubits, reported as fewer than 1 million, running for about 5 days with a uniform gate error of 0.1% and a surface-code cycle of 1 microsecond.
Troyer, Nayak, and Martinis placed the low end of useful computation at about 100 logical qubits with error rates on the order of 1 in 10 billion. They put high-end applications, “such as large-scale chemistry and cryptanalysis,” above 1,000 logical qubits with error rates of 1 in a quadrillion or better. A distance-2 code, which only detects errors, cannot keep a logical qubit at those rates through a long computation.
The hardware cost of those error rates depends on Λ. From Willow’s 0.143% per cycle at distance 7, a machine would need a 14-million-fold reduction to reach 1 in 10 billion. At Google’s measured Λ of 2.14, that takes 22 steps of two in code distance, to about 51, or roughly 5,200 physical qubits per logical qubit in a surface code. At a Λ of 4, a code would reach the same target at distance 31 with about 1,900 physical qubits per logical qubit.
These figures are an extrapolation from a measured trend, with Λ assumed to stay the same at larger sizes. They also treat the authors’ target as an error per cycle, which the authors did not specify. Λ improves when physical error rates fall further below threshold. Adding qubits to a chip does not raise it by itself.
The case for counting encoded qubits
Harvard, QuEra, and Quantinuum researchers have argued, with data, that encoded qubits help before machines can fully correct errors. The Harvard-led team found in 2023 that its error-detected encoding outperformed physical qubits in cross-entropy benchmarking and in simulations of fast scrambling. In February, Quantinuum’s authors reported computations with 48 to 94 logical qubits that beat their unencoded versions, with what they called “reasonable postselection rates” that “can be suppressed by increasing the code distance via concatenation.”
On that view, a team that reports a large encoded count has shown real engineering, the control of many qubits in an entangled, checked state, with better-than-physical results on short circuits. Troyer, Nayak, and Martinis accepted part of that argument when they called detection and postselection “powerful.”
The engineering in the Harvard, QuEra, and Quantinuum experiments is real. Readers go wrong when they compare those counts without the code, the distance, and the share of runs kept.
On its Helios product page, Quantinuum lists “50 logical qubits” next to its gate fidelities.
Five tests for the next announcement
A reader can sort most logical-qubit announcements with five questions, each answerable from the paper or preprint behind them.
Code and distance
A reader should first ask which code the team used, at what distance. A distance of 2 means the code detects errors without correcting them, except erasures, errors at known positions such as a lost atom. A distance of 3 or more means it can correct some. The ratio of n to k in the code’s [[n,k,d]] parameters is the cost in physical data qubits per logical qubit, before measurement qubits are added.
Discarded runs
The second is whether the team discarded runs. If it did, the team should report its acceptance rate beside its fidelity, along with how that rate changes as circuits lengthen. Discarding failed attempts inside a protocol for preparing resource states, as Google’s team did in cultivation, is a different practice from filtering the output of a whole application.
Scaling against a stated baseline
The third is whether the logical error rate fell as the code grew. Teams that claim correction should report Λ per round across at least two code distances, against a stated baseline. A reader should check whether the smaller code is the best one or an average, how many rounds the team ran, and whether both codes ran under the same settings, as the USC team warned.
What was computed
The fourth is what the logical qubits did. Storing a logical qubit, applying Clifford gates to it, and running a universal gate set with a non-Clifford gate are three separate milestones. Infleqtion’s circuit included four logical CCZ gates, a non-Clifford operation, on 30 logical qubits under error detection. A non-Clifford gate under full correction, decoded in real time, is a further step.
Real time, hardware, or simulation
The fifth is whether the team decoded in real time on hardware, decoded afterward, or worked only in simulation. When a team decodes after the runs, as Quantinuum’s did for its color-code result, it has not yet shown that its decoder keeps pace inside the machine’s control loop, even if it has timed the decoder separately. In October, Google researchers reported that modular codes could reduce physical-qubit overhead “by tenfold or more” compared with the surface code. They based the estimate on simulations and have not run the codes on hardware.
What would change this reading
If builders and buyers adopted one definition of a logical qubit, a bare count would mean the same thing in every announcement.
Two efforts could produce such a definition. Independent evaluators at the Defense Advanced Research Projects Agency (DARPA) are testing companies’ designs in Stage C of its Quantum Benchmarking Initiative. Troyer, Nayak, and Martinis have put their definition forward in a preprint. DOE’s competition is less likely to, because DOE will apply metrics negotiated with each company at a final evaluation it plans for September 2028.
Companies have scheduled the next tests. QuEra plans its Libra system for 2028, with 256 logical qubits at a target logical error rate of 1 in a million. Infleqtion has said it is on track for 100 logical qubits in 2028, and IBM has said its Starling machine will run 100 million operations on 200 logical qubits by 2029. Quantinuum has said it will validate and tune Sol, due in the second half of 2027, toward 100 logical qubits at a target logical error rate of 1 in 100,000.
If the four companies report those machines with different codes, distances, and acceptance rules, their counts will not be comparable.
