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| <title id="title">Surface-code decoding: from noisy stabilizer measurements to a logical-flip decision</title> |
| <desc id="description">A real Sycamore distance-three validation shot is displayed on its hardware geometry and as an eight-check, ten-time-slice detection-event matrix. The decoder output is symbolic; no numerical prediction is claimed. Better decoding supports reliable logical memory.</desc> |
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| <text x="60" y="62" font-size="33" fill="#182534" font-weight="600" text-anchor="start">Recover a logical bit from noisy quantum measurements</text> |
| <text x="60" y="101" font-size="21" fill="#566675" font-weight="400" text-anchor="start">Repeated stabilizer checks reveal error patterns; a decoder infers whether the stored logical observable flipped.</text> |
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| <text x="60" y="182" font-size="24" fill="#182534" font-weight="600" text-anchor="start">A Quantum memory</text> |
| <text x="60" y="216" font-size="18" fill="#566675" font-weight="400" text-anchor="start">Sycamore · distance 3 · Z basis</text> |
| <text x="490" y="182" font-size="24" fill="#182534" font-weight="600" text-anchor="start">B Detection-event input</text> |
| <text x="490" y="216" font-size="18" fill="#566675" font-weight="400" text-anchor="start">One real shot, measured over 9 rounds</text> |
| <text x="1050" y="182" font-size="24" fill="#182534" font-weight="600" text-anchor="start">C Logical decoding</text> |
| <text x="1050" y="216" font-size="18" fill="#566675" font-weight="400" text-anchor="start">Model input: events + known geometry</text> |
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| <text x="102" y="558" font-size="17" fill="#566675" font-weight="400" text-anchor="start">9 data qubits</text> |
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| <text x="266" y="558" font-size="17" fill="#566675" font-weight="400" text-anchor="start">8 checks</text> |
| <text x="60" y="598" font-size="17" fill="#566675" font-weight="400" text-anchor="start">Checks probe parity without revealing</text> |
| <text x="60" y="623" font-size="17" fill="#566675" font-weight="400" text-anchor="start">the stored quantum information.</text> |
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| <text x="558" y="293" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(1,4)</text> |
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| <text x="558" y="325" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(2,5)</text> |
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| <text x="558" y="357" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(2,7)</text> |
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| <text x="558" y="389" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(3,4)</text> |
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| <text x="558" y="421" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(3,6)</text> |
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| <text x="558" y="453" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(4,3)</text> |
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| <text x="558" y="485" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(4,5)</text> |
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| <text x="558" y="517" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(5,6)</text> |
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| <text x="590" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">1</text> |
| <text x="624" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">2</text> |
| <text x="658" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">3</text> |
| <text x="692" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">4</text> |
| <text x="726" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">5</text> |
| <text x="760" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">6</text> |
| <text x="794" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">7</text> |
| <text x="828" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">8</text> |
| <text x="862" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">9</text> |
| <text x="896" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">final</text> |
| <text x="742" y="583" font-size="17" fill="#566675" font-weight="400" text-anchor="middle">Measurement round / final readout</text> |
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| <text x="518" y="618" font-size="16" fill="#566675" font-weight="400" text-anchor="start">event</text> |
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| <text x="618" y="618" font-size="16" fill="#566675" font-weight="400" text-anchor="start">no event</text> |
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| <text x="757" y="618" font-size="16" fill="#566675" font-weight="400" text-anchor="start">not defined</text> |
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| <text x="1295" y="296" font-size="23" fill="#276382" font-weight="600" text-anchor="middle">Decoder</text> |
| <text x="1295" y="324" font-size="17" fill="#566675" font-weight="400" text-anchor="middle">e.g., an AlphaQubit recurrent Transformer</text> |
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| <text x="1295" y="406" font-size="20" fill="#276382" font-weight="400" text-anchor="middle">p = P(logical flip | events, geometry)</text> |
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| <text x="1295" y="462" font-size="22" fill="#182534" font-weight="600" text-anchor="middle">Decision: flip if p ≥ 0.5</text> |
| <text x="1295" y="489" font-size="17" fill="#566675" font-weight="400" text-anchor="middle">Apply to the logical readout / Pauli frame</text> |
| <text x="1050" y="548" font-size="19" fill="#182534" font-weight="400" text-anchor="start">Validation target for this shot: flip = 0</text> |
| <text x="1050" y="578" font-size="16" fill="#566675" font-weight="400" text-anchor="start">Target shown for explanation; never a model input.</text> |
| <text x="1050" y="615" font-size="16" fill="#566675" font-weight="400" text-anchor="start">Output above is symbolic, not a measured prediction.</text> |
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| <text x="60" y="696" font-size="22" fill="#182534" font-weight="600" text-anchor="start">Scientific value</text> |
| <text x="60" y="733" font-size="20" fill="#182534" font-weight="400" text-anchor="start">Better decoding reduces logical readout errors, a bottleneck for reliable quantum memory and fault-tolerant computation.</text> |
| <text x="60" y="768" font-size="18" fill="#566675" font-weight="400" text-anchor="start">Benchmark scope: real hard-readout Sycamore data, distances 3 and 5; score held-out logical-flip decisions.</text> |
| <text x="60" y="818" font-size="15" fill="#566675" font-weight="400" text-anchor="start">Example: d3 / Z / center (3,5) / 9 rounds / source shot 39760 (validation). Source: Google Quantum AI, Zenodo 6804040, CC BY 4.0.</text> |
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