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    Surface code

    Also known as planar code, rotated surface code

    The surface code is a quantum error-correcting code that stores one logical qubit in a square grid of data and measure qubits, catching errors through repeated checks.[1] In 2024 Google showed a surface code whose error rate fell as the grid grew, the first below-threshold demonstration, making it the reference design for superconducting quantum computers.[2][3]

    Editor reviewedUpdated Quantum computingComputingPhysics
    Key facts

    What it is

    The surface code arranges qubits on a square lattice, alternating data qubits, which hold the encoded information, with measure qubits, which repeatedly check small groups of neighbours.[1] Each round of checks reveals where physical errors have occurred without reading out, and so destroying, the logical information.[1] Because it only needs connections between neighbouring qubits, it suits flat chips such as superconducting processors.[3]

    The code’s size is measured by its distance: a larger distance means more physical qubits and more errors that can be tolerated. Google’s distance-7 code used 101 physical qubits.[3]

    The below-threshold result

    In December 2024 Google reported that on its Willow chip, growing the surface code from a 3x3 to a 5x5 to a 7x7 grid halved the logical error rate each time.[2] The peer-reviewed paper, published in Nature in 2025, reported 0.143% error per cycle at distance 7 and a suppression factor of 2.14 for each distance step.[3] The logical memory lasted about 2.4 times longer than the best physical qubit on the chip.[4] Errors were decoded in real time, with 63 microseconds of latency against a 1.1-microsecond cycle.[5] “Below threshold” is the regime in which adding qubits reduces errors rather than increasing them; a Harvard-led neutral-atom team reported crossing it on a different platform in 2025.[6]

    Refinements in 2026

    In January 2026 Google reported “dynamic” surface code circuits that need fewer couplers and reduce correlated errors, including a hexagonal layout that improved logical errors by a factor of 2.15 as it grew.[7] Instead of repeating one fixed circuit, the dynamic versions alternate between circuit constructions. Google demonstrated three: hexagonal circuits that cut the number of couplers, walking circuits that limit errors such as leakage, and iSWAP circuits that allow a non-standard two-qubit gate.[8] On a hexagonal lattice each qubit links to three neighbours instead of four, which Google says would simplify the design and fabrication of large chips.[9]

    In July 2026 it reported a reinforcement-learning controller that improved the code’s logical stability 3.5-fold by retuning the chip during operation.[10] The agent learns from the code’s own error-detection data and adjusts thousands of control parameters without stopping the computation, which matters because useful algorithms may need to run for days.[11]

    Limits and alternatives

    The same Google study found that rare correlated errors, roughly once an hour, limited repetition codes up to distance 29, a floor that larger codes must deal with.[12] The surface code’s main cost is overhead: many physical qubits per logical qubit. IBM has chosen qLDPC codes, which it says cut that overhead by about 90 percent.[13] Machines with all-to-all connectivity, such as Quantinuum’s Helios, have used other codes, reporting 48 error-corrected logical qubits from 98 physical qubits.[14] Neutral-atom machines can physically move qubits, which Caltech says enables more efficient error correction than hard-wired chips; the Harvard-led 448-atom experiment ran circuits with dozens of error-correction layers.[15][16]

    Resource estimates for breaking encryption still lean on surface-code-style hardware assumptions: Google’s March 2026 elliptic-curve estimate assumed a superconducting system with fewer than 500,000 physical qubits.[17]

    Questions readers ask

    How many physical qubits does a surface code logical qubit use?

    Google's distance-7 surface code used 101 physical qubits to hold one logical qubit.[3]

    Does the surface code actually work?

    Yes, as a memory. Google's distance-7 logical qubit outlived the best physical qubit on the chip by about 2.4 times.[4]

    Why does IBM not use the surface code for its roadmap?

    IBM says qLDPC codes cut error-correction overhead by about 90 percent compared with other leading codes.[13]

    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]

      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

    4. [4]

      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

    5. [5]

      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

    6. [6]

      Harvard describes the error threshold its 448-atom system crossed as the point where adding qubits further reduces errors rather than increasing them, and the lead author called it the first conceptually scalable architecture. confirmedas of 2025-11-12

    7. [7]

      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

    8. [8]

      Google's dynamic surface code work, published in Nature Physics, demonstrated three circuit types - hexagonal circuits that reduce the number of couplers, walking circuits that limit errors such as leakage, and iSWAP circuits that allow non-standard two-qubit gates. confirmedas of 2026-01-13

    9. [9]

      On a hexagonal lattice each qubit would connect to three neighbours instead of four, which Google says would simplify the design and fabrication of large chips; it tested this on Willow by switching off unused couplers. confirmedas of 2026-01-13

    10. [10]

      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

    11. [11]

      Google's July 2026 Nature paper describes a reinforcement-learning agent that learns from error-detection data to steer thousands of control parameters during a computation, instead of halting the computation to recalibrate. confirmedas of 2026-07-22

    12. [12]

      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

    13. [13]

      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

    14. [14]

      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

    15. [15]

      The Caltech team showed atoms could be moved hundreds of micrometres while keeping their superposition, a capability useful for error correction in neutral-atom systems. confirmedas of 2025-09-24

    16. [16]

      The Harvard-led 448-atom system combined physical entanglement, logical entanglement, logical magic and entropy removal, using techniques such as quantum teleportation, in circuits with dozens of error-correction layers. confirmedas of 2025-11-12

    17. [17]

      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

    Revision history (2)
    1. Page created.
    2. Expanded the 2026 refinements (three dynamic circuit types, hexagonal three-coupler layout, drift control) and added the neutral-atom and qLDPC comparisons.

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

    Cite this page

    "Surface code." ContentLora, updated Oct 10, 2026. https://contentlora.com/wiki/surface-code

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