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    Quantum error correction: from noisy to logical qubits

    Quantum error correction spreads one logical qubit across many physical qubits and repeatedly checks for errors without destroying the stored information.[1] Since Google's 2024 below-threshold result, every major hardware team has shown logical qubits that beat their physical parts, and by 2026 counts reached dozens of logical qubits, though not yet full fault tolerance.[2][3][4]

    Editor reviewedUpdated Quantum computingComputingPhysics

    Why error correction is needed

    Qubits make mistakes. The best two-qubit operations today succeed about 99.9 to 99.99% of the time.[5][6] That sounds good, but useful programs such as breaking encryption would need hundreds of millions of operations, so errors must be corrected while the program runs.[7] Error correction groups many physical qubits into one “logical” qubit that is much more reliable.[8]

    Resource estimates for cryptographically relevant algorithms run to tens of millions of Toffoli gates on more than a thousand logical qubits, requiring logical error rates many orders of magnitude below physical gate errors.[7] Quantum error correction encodes logical states redundantly and extracts error syndromes by measuring ancilla (“measure”) qubits, leaving the logical information untouched.[1]

    The threshold idea

    Adding qubits adds more places for errors to happen. Error correction only helps if each physical qubit is good enough; past that point, called the threshold, bigger codes give fewer logical errors. In December 2024 Google showed this on its Willow chip: each time it grew its code from a 3x3 to a 5x5 to a 7x7 grid, the logical error rate halved.[2]

    Below threshold, logical error per cycle falls exponentially with code distance d. Google’s 101-qubit distance-7 surface-code reached 0.143% error per cycle with a suppression factor Λ of 2.14 per distance step, and the logical memory outlived the chip’s best physical qubit by about 2.4 times.[9][8] Decoding ran in real time at 63 microseconds latency against a 1.1-microsecond cycle.[10] Rare correlated errors, roughly once an hour, set a floor that larger codes must overcome.[11]

    Codes beyond the surface code

    The surface code needs many physical qubits per logical qubit but only nearest-neighbour connections.[1][9] IBM is betting on quantum low-density parity check (qLDPC) codes, which it says cut overhead by about 90 percent, as the basis for its 200-logical-qubit Starling machine planned for 2029.[12][13] Trapped-ion and neutral-atom machines can connect any qubit to any other, which lets them use more compact codes.[5][14] Quantinuum used iceberg and concatenated codes to report 48 error-corrected logical qubits from 98 physical qubits in March 2026.[3] Infleqtion reported 30 entangled logical qubits from 80 physical neutral atoms in September 2026.[15]

    From logical qubits to fault tolerance

    A logical memory is not a computer. Fault-tolerant computing also needs logical gates, including a special “magic” ingredient for universal computation, plus ways to remove accumulated errors. In November 2025 Harvard, MIT and QuEra reported a 448-atom architecture that combined these elements and stayed below threshold.[16] IBM’s Loon processor is designed to show all the hardware components for fault tolerance, and IBM reported decoding 10 times faster than earlier leading approaches.[17][18]

    Google has continued refining the surface code itself, reporting in 2026 dynamic circuits that need fewer couplers and a reinforcement-learning controller that improved logical stability 3.5-fold.[19][20]

    What is still missing

    None of these systems is yet a large fault-tolerant computer. Quantinuum’s March 2026 results were described as partially fault-tolerant, and the Harvard team’s lead author said many technical challenges remain on the way to millions of qubits.[4][21] DARPA’s Quantum Benchmarking Initiative is now testing hardware from six teams to see whether any can reach utility scale by 2033.[22][23]

    Questions readers ask

    What does "below threshold" mean?

    It means physical errors are rare enough that making the error-correcting code bigger reduces the logical error rate. Google showed this on Willow in 2024, halving errors at each step from a 3x3 to a 7x7 grid.[2]

    How many physical qubits does one logical qubit need?

    It depends on the code. Google's distance-7 surface code used 101 physical qubits for one logical qubit, while IBM says its qLDPC codes cut overhead by about 90 percent.[9][12]

    What is the difference between error detection and error correction?

    Detection flags that an error happened so the run can be discarded; correction fixes it. Quantinuum reported 94 error-detected but 48 error-corrected logical qubits on the same 98-qubit machine.[3]

    Is error correction solved?

    No. Experiments so far are described as partially fault-tolerant, and Google found rare correlated errors that limit performance.[4][11]

    Sources

    Each numbered claim is a statement we checked against the sources listed with it. Status shows how well established it is.

    1. [1]

      In the surface code, data qubits and measure qubits are interleaved on a square lattice; repeated measurements flag physical errors without disturbing the stored logical information. confirmedas of 2026-01-13

    2. [2]

      Google reported that as it scaled Willow's encoded qubit grids from 3x3 to 5x5 to 7x7, the logical error rate halved at each step, which it called the first below-threshold error correction. confirmedas of 2024-12-09

    3. [3]

      In March 2026 Quantinuum researchers reported computations with up to 94 error-detected and 48 error-corrected logical qubits on Helios, using iceberg and concatenated codes, with logical gate errors around one in ten thousand - better than the physical gates. confirmedas of 2026-03-10

    4. [4]

      The March 2026 Quantinuum results were described as partially rather than fully fault-tolerant computation. confirmedas of 2026-03-10

    5. [5]

      Quantinuum reports Helios two-qubit gate fidelity of 99.921% and single-qubit gate fidelity of 99.9975%, with all 98 qubits fully connected. confirmedas of 2026-10-10

    6. [6]

      In October 2025 IonQ reported 99.99% two-qubit gate fidelity using its Electronic Qubit Control technology, which drives qubits with precision electronics instead of lasers. confirmedas of 2025-10-21

    7. [7]

      In March 2026 Google researchers, in work framed around safeguarding cryptocurrency, estimated that 256-bit elliptic-curve cryptography could be broken with fewer than 1,200 logical qubits and 90 million Toffoli gates, or fewer than 500,000 physical superconducting qubits running for a few minutes, under standard hardware assumptions. confirmedas of 2026-03-31

    8. [8]

      In the same experiment the distance-7 logical memory outlived the best physical qubit on the chip by a factor of about 2.4. confirmedas of 2025-02-01

    9. [9]

      Google's below-threshold experiment, published in Nature in 2025, ran a 101-qubit distance-7 surface code with 0.143% logical error per cycle, with errors suppressed by a factor of 2.14 each time the code distance grew by two. confirmedas of 2025-02-01

    10. [10]

      The experiment decoded errors in real time, with an average decoder latency of 63 microseconds at distance 5 and an error-correction cycle time of 1.1 microseconds. confirmedas of 2025-02-01

    11. [11]

      Repetition-code tests up to distance 29 found performance limited by rare correlated error events occurring about once an hour. confirmedas of 2025-02-01

    12. [12]

      IBM's fault-tolerance plan uses quantum low-density parity check (qLDPC) codes, which it says cut error-correction overhead by about 90 percent compared with other leading codes. confirmedas of 2025-06-10

    13. [13]

      In June 2025 IBM said it would build IBM Quantum Starling, a fault-tolerant quantum computer with 200 logical qubits able to run 100 million quantum operations, in Poughkeepsie, New York, by 2029. confirmedas of 2025-06-10

    14. [14]

      QuEra says its neutral-atom systems use naturally identical qubits that operate at room temperature with flexible all-to-all connectivity. confirmedas of 2025-11-06

    15. [15]

      On 24 September 2026 Infleqtion reported entangling 30 logical qubits encoded in 80 physical neutral-atom qubits on its Sqale system, in a circuit of about 1,000 physical operations, and said it targets 100 logical qubits by 2028. reportedas of 2026-09-24

    16. [16]

      In November 2025 Harvard, MIT and QuEra researchers reported in Nature an architecture using up to 448 rubidium-atom qubits that combined the essential elements of scalable error-corrected computation and suppressed errors below the threshold. confirmedas of 2025-11-12

    17. [17]

      IBM described its experimental Loon processor as demonstrating all the key hardware components needed for fault-tolerant quantum computing. confirmedas of 2025-11-12

    18. [18]

      IBM said it achieved error decoding 10 times faster than previous leading approaches, a year ahead of schedule. confirmedas of 2025-11-12

    19. [19]

      In January 2026 Google reported dynamic surface code circuits that need fewer couplers and reduce correlated errors compared with static circuits, including a hexagonal variant that improved logical error rates by a factor of 2.15 as the code grew. confirmedas of 2026-01-13

    20. [20]

      In July 2026 Google reported that reinforcement-learning control, adjusting parameters during computation, improved the logical stability of its error-correcting code 3.5-fold on Willow. confirmedas of 2026-07-22

    21. [21]

      The Harvard study's lead author said many technical challenges remain before a very large-scale computer with millions of qubits. confirmedas of 2025-11-12

    22. [22]

      On 7 October 2026 DARPA advanced Atom Computing, Diraq, IBM and IonQ to QBI Stage C, joining Microsoft and PsiQuantum, which entered from the US2QC pilot. confirmedas of 2026-10-07

    23. [23]

      DARPA's Quantum Benchmarking Initiative aims to determine whether any quantum computing approach can reach utility-scale operation - computational value exceeding cost - by 2033. confirmedas of 2026-10-07

    Revision history (1)
    1. Page created.

    Created Oct 10, 2026. Last reviewed by an editor on Oct 10, 2026. Next scheduled review: Jan 10, 2027.

    Cite this page

    "Quantum error correction: from noisy to logical qubits." ContentLora, updated Oct 10, 2026. https://contentlora.com/explain/quantum-error-correction

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