Corning/ai4sci-surface-code-decoding

1<svg xmlns="http://www.w3.org/2000/svg" width="1600" height="860" viewBox="0 0 1600 860" role="img" aria-labelledby="title description">2<title id="title">Surface-code decoding: from noisy stabilizer measurements to a logical-flip decision</title>3<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>4<defs><marker id="arrow" markerWidth="8" markerHeight="8" refX="7" refY="4" orient="auto"><path d="M0,0 L8,4 L0,8" fill="#566675"/></marker></defs>5<g font-family="DejaVu Sans, sans-serif">6<rect x="0" y="0" width="1600" height="860" fill="#ffffff" stroke="none"/>7<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>8<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>9<line x1="60" y1="129" x2="1540" y2="129" stroke="#d9e0e5" stroke-width="1.5"/>10<text x="60" y="182" font-size="24" fill="#182534" font-weight="600" text-anchor="start">A   Quantum memory</text>11<text x="60" y="216" font-size="18" fill="#566675" font-weight="400" text-anchor="start">Sycamore · distance 3 · Z basis</text>12<text x="490" y="182" font-size="24" fill="#182534" font-weight="600" text-anchor="start">B   Detection-event input</text>13<text x="490" y="216" font-size="18" fill="#566675" font-weight="400" text-anchor="start">One real shot, measured over 9 rounds</text>14<text x="1050" y="182" font-size="24" fill="#182534" font-weight="600" text-anchor="start">C   Logical decoding</text>15<text x="1050" y="216" font-size="18" fill="#566675" font-weight="400" text-anchor="start">Model input: events + known geometry</text>16<line x1="110.0" y1="394.0" x2="110.0" y2="342.0" stroke="#d9e0e5" stroke-width="2"/>17<line x1="110.0" y1="394.0" x2="162.0" y2="394.0" stroke="#d9e0e5" stroke-width="2"/>18<line x1="162.0" y1="342.0" x2="110.0" y2="342.0" stroke="#d9e0e5" stroke-width="2"/>19<line x1="162.0" y1="342.0" x2="162.0" y2="394.0" stroke="#d9e0e5" stroke-width="2"/>20<line x1="162.0" y1="342.0" x2="214.0" y2="342.0" stroke="#d9e0e5" stroke-width="2"/>21<line x1="162.0" y1="446.0" x2="162.0" y2="394.0" stroke="#d9e0e5" stroke-width="2"/>22<line x1="162.0" y1="446.0" x2="162.0" y2="498.0" stroke="#d9e0e5" stroke-width="2"/>23<line x1="162.0" y1="446.0" x2="214.0" y2="446.0" stroke="#d9e0e5" stroke-width="2"/>24<line x1="214.0" y1="290.0" x2="214.0" y2="342.0" stroke="#d9e0e5" stroke-width="2"/>25<line x1="214.0" y1="290.0" x2="266.0" y2="290.0" stroke="#d9e0e5" stroke-width="2"/>26<line x1="214.0" y1="394.0" x2="162.0" y2="394.0" stroke="#d9e0e5" stroke-width="2"/>27<line x1="214.0" y1="394.0" x2="214.0" y2="342.0" stroke="#d9e0e5" stroke-width="2"/>28<line x1="214.0" y1="394.0" x2="214.0" y2="446.0" stroke="#d9e0e5" stroke-width="2"/>29<line x1="214.0" y1="394.0" x2="266.0" y2="394.0" stroke="#d9e0e5" stroke-width="2"/>30<line x1="214.0" y1="498.0" x2="162.0" y2="498.0" stroke="#d9e0e5" stroke-width="2"/>31<line x1="214.0" y1="498.0" x2="214.0" y2="446.0" stroke="#d9e0e5" stroke-width="2"/>32<line x1="266.0" y1="342.0" x2="214.0" y2="342.0" stroke="#d9e0e5" stroke-width="2"/>33<line x1="266.0" y1="342.0" x2="266.0" y2="290.0" stroke="#d9e0e5" stroke-width="2"/>34<line x1="266.0" y1="342.0" x2="266.0" y2="394.0" stroke="#d9e0e5" stroke-width="2"/>35<line x1="266.0" y1="446.0" x2="214.0" y2="446.0" stroke="#d9e0e5" stroke-width="2"/>36<line x1="266.0" y1="446.0" x2="266.0" y2="394.0" stroke="#d9e0e5" stroke-width="2"/>37<line x1="266.0" y1="446.0" x2="318.0" y2="446.0" stroke="#d9e0e5" stroke-width="2"/>38<line x1="318.0" y1="394.0" x2="266.0" y2="394.0" stroke="#d9e0e5" stroke-width="2"/>39<line x1="318.0" y1="394.0" x2="318.0" y2="446.0" stroke="#d9e0e5" stroke-width="2"/>40<circle cx="110.0" cy="394.0" r="11" fill="white" stroke="#276382" stroke-width="2.5"/>41<circle cx="162.0" cy="342.0" r="11" fill="white" stroke="#276382" stroke-width="2.5"/>42<circle cx="162.0" cy="446.0" r="11" fill="white" stroke="#276382" stroke-width="2.5"/>43<circle cx="214.0" cy="290.0" r="11" fill="white" stroke="#276382" stroke-width="2.5"/>44<circle cx="214.0" cy="394.0" r="11" fill="white" stroke="#276382" stroke-width="2.5"/>45<circle cx="214.0" cy="498.0" r="11" fill="white" stroke="#276382" stroke-width="2.5"/>46<circle cx="266.0" cy="342.0" r="11" fill="white" stroke="#276382" stroke-width="2.5"/>47<circle cx="266.0" cy="446.0" r="11" fill="white" stroke="#276382" stroke-width="2.5"/>48<circle cx="318.0" cy="394.0" r="11" fill="white" stroke="#276382" stroke-width="2.5"/>49<rect x="102.0" y="334.0" width="16" height="16" fill="#8797a4" stroke="none"/>50<rect x="154.0" y="386.0" width="16" height="16" fill="#8797a4" stroke="none"/>51<rect x="154.0" y="490.0" width="16" height="16" fill="#8797a4" stroke="none"/>52<rect x="206.0" y="334.0" width="16" height="16" fill="#8797a4" stroke="none"/>53<rect x="206.0" y="438.0" width="16" height="16" fill="#8797a4" stroke="none"/>54<rect x="258.0" y="282.0" width="16" height="16" fill="#8797a4" stroke="none"/>55<rect x="258.0" y="386.0" width="16" height="16" fill="#8797a4" stroke="none"/>56<rect x="310.0" y="438.0" width="16" height="16" fill="#8797a4" stroke="none"/>57<circle cx="84" cy="552" r="7" fill="white" stroke="#276382" stroke-width="2"/>58<text x="102" y="558" font-size="17" fill="#566675" font-weight="400" text-anchor="start">9 data qubits</text>59<rect x="241" y="545" width="14" height="14" fill="#8797a4" stroke="none"/>60<text x="266" y="558" font-size="17" fill="#566675" font-weight="400" text-anchor="start">8 checks</text>61<text x="60" y="598" font-size="17" fill="#566675" font-weight="400" text-anchor="start">Checks probe parity without revealing</text>62<text x="60" y="623" font-size="17" fill="#566675" font-weight="400" text-anchor="start">the stored quantum information.</text>63<line x1="404" y1="384" x2="453" y2="384" stroke="#566675" stroke-width="2" marker-end="url(#arrow)"/>64<text x="558" y="293" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(1,4)</text>65<rect x="574" y="273" width="32" height="30" fill="#e6e9ec" stroke="#d9e0e5"/>66<rect x="608" y="273" width="32" height="30" fill="white" stroke="#d9e0e5"/>67<rect x="642" y="273" width="32" height="30" fill="white" stroke="#d9e0e5"/>68<rect x="676" y="273" width="32" height="30" fill="white" stroke="#d9e0e5"/>69<rect x="710" y="273" width="32" height="30" fill="white" stroke="#d9e0e5"/>70<rect x="744" y="273" width="32" height="30" fill="white" stroke="#d9e0e5"/>71<rect x="778" y="273" width="32" height="30" fill="white" stroke="#d9e0e5"/>72<rect x="812" y="273" width="32" height="30" fill="white" stroke="#d9e0e5"/>73<rect x="846" y="273" width="32" height="30" fill="white" stroke="#d9e0e5"/>74<rect x="880" y="273" width="32" height="30" fill="#e6e9ec" stroke="#d9e0e5"/>75<text x="558" y="325" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(2,5)</text>76<rect x="574" y="305" width="32" height="30" fill="#276382" stroke="#d9e0e5"/>77<rect x="608" y="305" width="32" height="30" fill="#276382" stroke="#d9e0e5"/>78<rect x="642" y="305" width="32" height="30" fill="white" stroke="#d9e0e5"/>79<rect x="676" y="305" width="32" height="30" fill="white" stroke="#d9e0e5"/>80<rect x="710" y="305" width="32" height="30" fill="white" stroke="#d9e0e5"/>81<rect x="744" y="305" width="32" height="30" fill="white" stroke="#d9e0e5"/>82<rect x="778" y="305" width="32" height="30" fill="white" stroke="#d9e0e5"/>83<rect x="812" y="305" width="32" height="30" fill="white" stroke="#d9e0e5"/>84<rect x="846" y="305" width="32" height="30" fill="white" stroke="#d9e0e5"/>85<rect x="880" y="305" width="32" height="30" fill="white" stroke="#d9e0e5"/>86<text x="558" y="357" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(2,7)</text>87<rect x="574" y="337" width="32" height="30" fill="white" stroke="#d9e0e5"/>88<rect x="608" y="337" width="32" height="30" fill="white" stroke="#d9e0e5"/>89<rect x="642" y="337" width="32" height="30" fill="white" stroke="#d9e0e5"/>90<rect x="676" y="337" width="32" height="30" fill="white" stroke="#d9e0e5"/>91<rect x="710" y="337" width="32" height="30" fill="white" stroke="#d9e0e5"/>92<rect x="744" y="337" width="32" height="30" fill="white" stroke="#d9e0e5"/>93<rect x="778" y="337" width="32" height="30" fill="white" stroke="#d9e0e5"/>94<rect x="812" y="337" width="32" height="30" fill="white" stroke="#d9e0e5"/>95<rect x="846" y="337" width="32" height="30" fill="white" stroke="#d9e0e5"/>96<rect x="880" y="337" width="32" height="30" fill="white" stroke="#d9e0e5"/>97<text x="558" y="389" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(3,4)</text>98<rect x="574" y="369" width="32" height="30" fill="#e6e9ec" stroke="#d9e0e5"/>99<rect x="608" y="369" width="32" height="30" fill="#276382" stroke="#d9e0e5"/>100<rect x="642" y="369" width="32" height="30" fill="white" stroke="#d9e0e5"/>101<rect x="676" y="369" width="32" height="30" fill="white" stroke="#d9e0e5"/>102<rect x="710" y="369" width="32" height="30" fill="white" stroke="#d9e0e5"/>103<rect x="744" y="369" width="32" height="30" fill="white" stroke="#d9e0e5"/>104<rect x="778" y="369" width="32" height="30" fill="white" stroke="#d9e0e5"/>105<rect x="812" y="369" width="32" height="30" fill="white" stroke="#d9e0e5"/>106<rect x="846" y="369" width="32" height="30" fill="white" stroke="#d9e0e5"/>107<rect x="880" y="369" width="32" height="30" fill="#e6e9ec" stroke="#d9e0e5"/>108<text x="558" y="421" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(3,6)</text>109<rect x="574" y="401" width="32" height="30" fill="#e6e9ec" stroke="#d9e0e5"/>110<rect x="608" y="401" width="32" height="30" fill="white" stroke="#d9e0e5"/>111<rect x="642" y="401" width="32" height="30" fill="white" stroke="#d9e0e5"/>112<rect x="676" y="401" width="32" height="30" fill="#276382" stroke="#d9e0e5"/>113<rect x="710" y="401" width="32" height="30" fill="white" stroke="#d9e0e5"/>114<rect x="744" y="401" width="32" height="30" fill="white" stroke="#d9e0e5"/>115<rect x="778" y="401" width="32" height="30" fill="#276382" stroke="#d9e0e5"/>116<rect x="812" y="401" width="32" height="30" fill="#276382" stroke="#d9e0e5"/>117<rect x="846" y="401" width="32" height="30" fill="white" stroke="#d9e0e5"/>118<rect x="880" y="401" width="32" height="30" fill="#e6e9ec" stroke="#d9e0e5"/>119<text x="558" y="453" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(4,3)</text>120<rect x="574" y="433" width="32" height="30" fill="white" stroke="#d9e0e5"/>121<rect x="608" y="433" width="32" height="30" fill="white" stroke="#d9e0e5"/>122<rect x="642" y="433" width="32" height="30" fill="white" stroke="#d9e0e5"/>123<rect x="676" y="433" width="32" height="30" fill="white" stroke="#d9e0e5"/>124<rect x="710" y="433" width="32" height="30" fill="white" stroke="#d9e0e5"/>125<rect x="744" y="433" width="32" height="30" fill="white" stroke="#d9e0e5"/>126<rect x="778" y="433" width="32" height="30" fill="white" stroke="#d9e0e5"/>127<rect x="812" y="433" width="32" height="30" fill="white" stroke="#d9e0e5"/>128<rect x="846" y="433" width="32" height="30" fill="white" stroke="#d9e0e5"/>129<rect x="880" y="433" width="32" height="30" fill="white" stroke="#d9e0e5"/>130<text x="558" y="485" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(4,5)</text>131<rect x="574" y="465" width="32" height="30" fill="white" stroke="#d9e0e5"/>132<rect x="608" y="465" width="32" height="30" fill="white" stroke="#d9e0e5"/>133<rect x="642" y="465" width="32" height="30" fill="white" stroke="#d9e0e5"/>134<rect x="676" y="465" width="32" height="30" fill="white" stroke="#d9e0e5"/>135<rect x="710" y="465" width="32" height="30" fill="white" stroke="#d9e0e5"/>136<rect x="744" y="465" width="32" height="30" fill="white" stroke="#d9e0e5"/>137<rect x="778" y="465" width="32" height="30" fill="white" stroke="#d9e0e5"/>138<rect x="812" y="465" width="32" height="30" fill="#276382" stroke="#d9e0e5"/>139<rect x="846" y="465" width="32" height="30" fill="white" stroke="#d9e0e5"/>140<rect x="880" y="465" width="32" height="30" fill="white" stroke="#d9e0e5"/>141<text x="558" y="517" font-size="16" fill="#566675" font-weight="400" text-anchor="end">(5,6)</text>142<rect x="574" y="497" width="32" height="30" fill="#e6e9ec" stroke="#d9e0e5"/>143<rect x="608" y="497" width="32" height="30" fill="white" stroke="#d9e0e5"/>144<rect x="642" y="497" width="32" height="30" fill="white" stroke="#d9e0e5"/>145<rect x="676" y="497" width="32" height="30" fill="white" stroke="#d9e0e5"/>146<rect x="710" y="497" width="32" height="30" fill="white" stroke="#d9e0e5"/>147<rect x="744" y="497" width="32" height="30" fill="white" stroke="#d9e0e5"/>148<rect x="778" y="497" width="32" height="30" fill="#276382" stroke="#d9e0e5"/>149<rect x="812" y="497" width="32" height="30" fill="white" stroke="#d9e0e5"/>150<rect x="846" y="497" width="32" height="30" fill="white" stroke="#d9e0e5"/>151<rect x="880" y="497" width="32" height="30" fill="#e6e9ec" stroke="#d9e0e5"/>152<text x="590" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">1</text>153<text x="624" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">2</text>154<text x="658" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">3</text>155<text x="692" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">4</text>156<text x="726" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">5</text>157<text x="760" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">6</text>158<text x="794" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">7</text>159<text x="828" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">8</text>160<text x="862" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">9</text>161<text x="896" y="556" font-size="15" fill="#566675" font-weight="400" text-anchor="middle">final</text>162<text x="742" y="583" font-size="17" fill="#566675" font-weight="400" text-anchor="middle">Measurement round / final readout</text>163<rect x="496" y="605" width="15" height="15" fill="#276382" stroke="none"/>164<text x="518" y="618" font-size="16" fill="#566675" font-weight="400" text-anchor="start">event</text>165<rect x="596" y="605" width="15" height="15" fill="white" stroke="#d9e0e5"/>166<text x="618" y="618" font-size="16" fill="#566675" font-weight="400" text-anchor="start">no event</text>167<rect x="735" y="605" width="15" height="15" fill="#e6e9ec" stroke="#d9e0e5"/>168<text x="757" y="618" font-size="16" fill="#566675" font-weight="400" text-anchor="start">not defined</text>169<line x1="959" y1="384" x2="1018" y2="384" stroke="#566675" stroke-width="2" marker-end="url(#arrow)"/>170<rect x="1050" y="264" width="490" height="80" fill="#eef4f7" stroke="#d9e0e5"/>171<text x="1295" y="296" font-size="23" fill="#276382" font-weight="600" text-anchor="middle">Decoder</text>172<text x="1295" y="324" font-size="17" fill="#566675" font-weight="400" text-anchor="middle">e.g., an AlphaQubit recurrent Transformer</text>173<line x1="1295" y1="350" x2="1295" y2="372" stroke="#566675" stroke-width="1.8" marker-end="url(#arrow)"/>174<text x="1295" y="406" font-size="20" fill="#276382" font-weight="400" text-anchor="middle">p = P(logical flip | events, geometry)</text>175<rect x="1050" y="430" width="490" height="73" fill="#f8fafb" stroke="#d9e0e5"/>176<text x="1295" y="462" font-size="22" fill="#182534" font-weight="600" text-anchor="middle">Decision: flip if p ≥ 0.5</text>177<text x="1295" y="489" font-size="17" fill="#566675" font-weight="400" text-anchor="middle">Apply to the logical readout / Pauli frame</text>178<text x="1050" y="548" font-size="19" fill="#182534" font-weight="400" text-anchor="start">Validation target for this shot: flip = 0</text>179<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>180<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>181<line x1="60" y1="655" x2="1540" y2="655" stroke="#d9e0e5" stroke-width="1.5"/>182<text x="60" y="696" font-size="22" fill="#182534" font-weight="600" text-anchor="start">Scientific value</text>183<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>184<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>185<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>186</g></svg>187