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Fault-tolerant quantum computing

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Fault-tolerant quantum computing
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This is a tutorial on fault-tolerant quantum computing, with an emphasis on concatenated-coding and topological-coding approaches in the quantum circuit model. The tutorial will cover key protocols used in fault-tolerant quantum computing schemes, including syndrome extraction, syndrome decoding, and encoded computation with magic states. It will also cover well-established analysis techniques, including extended rectangles and Monte Carlo simulation. A basic familiarity with stabilizer-based quantum error correction is assumed.
Quantum computerExecution unitEmailSeries (mathematics)VotingSource codeEndliche ModelltheorieNoise (electronics)Fault-tolerant systemQuantum computerSet (mathematics)Natural numberLocal ringError messageProcess (computing)FamilySelf-organizationLoginFehlererkennungOrder (biology)Limit of a functionEvent horizonCodeBitLevel (video gaming)Database normalizationInformationPoint (geometry)Thresholding (image processing)SoftwareGame controllerForm (programming)Bit rateComputerField (computer science)ExpressionQuantum mechanicsTelecommunicationCodeCommunications protocolMathematical analysisHard disk driveQuicksortCombinational logicSocial classSemiconductor memorySurfaceData structureData miningType theoryFunctional (mathematics)Ideal (ethics)Reading (process)Electronic data processingSystem callAreaTheoryLecture/ConferenceComputer animation
Maxima and minimaClassical physicsFault-tolerant systemClassical physicsComputer simulationThresholding (image processing)SimulationError messageMereologyComputerQuicksortQuantum computerLogic gateSoftware developerComputer hardwareWell-formed formulaTheoremOrder (biology)Limit of a functionEndliche ModelltheorieNoise (electronics)Functional (mathematics)Social classDigital electronicsParameter (computer programming)Bit rateoutputFunction (mathematics)Numbering schemeMoment (mathematics)Sinc functionCalculationConnectivity (graph theory)Expert systemLine (geometry)Physical systemMultiplication signVapor barrierOperator (mathematics)Game controllerScaling (geometry)Basis <Mathematik>Power (physics)Process (computing)InformationMechanism designArithmetic meanSmartphoneBitDefault (computer science)Key (cryptography)FehlererkennungTheoryCrash (computing)ExistenceExtension (kinesiology)Point (geometry)Overhead (computing)Instance (computer science)AreaCASE <Informatik>Bound stateObservational studyField (computer science)Form (programming)1 (number)Computer animation
Quantum computerExecution unitMaxima and minimaParallel portCrash (computing)Order (biology)Physical systemLogic gateMultiplication signError messageCommunications protocolState of matterNumberFunctional (mathematics)Digital electronicsDegree (graph theory)Noise (electronics)Endliche ModelltheorieQubitMaxima and minimaFault-tolerant systemFamilyMessage passingClassical physicsOnline helpComputerAlgorithmData structureRevision controlInfinityCodeCartesian coordinate systemResultantSet (mathematics)Descriptive statisticsSlide ruleBasis <Mathematik>Arrow of timeInformationMeasurementFinitismusConnectivity (graph theory)Latent heatTheoremInverse elementCodierung <Programmierung>Quantum computerTouchscreenTuring-MaschineQuicksortTuring testDifferent (Kate Ryan album)Virtual machineObject (grammar)Uniformer RaumDimensional analysisScaling (geometry)Fourier transformFehlererkennungQuantum information scienceEnergy levelComputer simulationRow (database)Local ringGame controllerSinc functionGoodness of fitLibrary (computing)HolonomiegruppeBit rateCodeStability theoryLeakDatabase normalizationBit1 (number)Source codeIndependence (probability theory)Operator (mathematics)Two-dimensional spaceExecution unitMathematical analysisDemonPropagation of uncertaintySound effectCubeFigurate numberGame theoryQuantum circuitPropagatorSocial classPattern recognitionGraph coloringCASE <Informatik>DemosceneSummierbarkeitTowerThresholding (image processing)DatabaseConstructor (object-oriented programming)Computer hardwareComputer animation
Logic gateDegree (graph theory)Power (physics)Digital electronicsApproximationFinitismusRotationNumberLimit of a functionInteractive televisionInformationFourier seriesBitAlgorithmLocal ringQuantum computerDescriptive statisticsFunctional (mathematics)Compilation albumSequenceMultiplication signSpeech synthesisLoginOrder (biology)LogarithmSimulationBasis <Mathematik>MereologyFault-tolerant systemPolygonProxy serverCopyright infringementQuicksortComputer simulationLecture/Conference
Grand Unified TheoryExecution unitFluidHill differential equationMIDIMoving averageLogic gateQuicksortBasis <Mathematik>Set (mathematics)State of matterCodeOperator (mathematics)MeasurementGame controllerComplete metric spaceInformationTheoremMultiplication signPhase transitionMereologyBitQuantum computerSurfaceHadamard matrixCodeImplementationDigital electronicsCodierung <Programmierung>Entire functionFinitismusUniverse (mathematics)Clifford algebraReal numberMilitary baseConstructor (object-oriented programming)Standard deviationDatabaseNumberAlgorithmInverter (logic gate)PlanningPositional notationCausalityComputerGroup actionFrequencyAngleBit rateACIDCopyright infringementEuler anglesDisk read-and-write headCategory of beingSpiralInversion (music)Classical physicsComputer animation
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InfinityCodeCodeSpacetimeHomologieConnected spaceDifferent (Kate Ryan album)Closed setBoundary value problemFault-tolerant systemCodeComputer hardwareInfinityFormal languageTesselationFamilyGoodness of fitComputerThree-dimensional spaceElectronic mailing listTheoryCommunications protocolAreaStability theoryContext awarenessGraph coloringOperator (mathematics)Lattice (group)MeasurementNetwork topologyCollaborationismLocal ringThresholding (image processing)Denial-of-service attackDimensional analysisComputer animation
CodeFamilyInfinityCodeStatistical mechanicsFault-tolerant systemInflection pointRenormalization groupCodeWechselseitige InformationSurfaceCurveLevel (video gaming)Graph coloringThresholding (image processing)Reading (process)Asymptotic analysisFamilyRight angleNoise (electronics)Scaling (geometry)Endliche ModelltheorieFehlererkennungFunctional (mathematics)outputElementary arithmeticPoint (geometry)Physical systemFitness function1 (number)Goodness of fitPointer (computer programming)WebsiteComputer simulationBitComputer animation
Endliche ModelltheorieMappingEndliche ModelltheorieCodeLogic gateUniform resource locatorNoise (electronics)Functional (mathematics)BitMeasurementCodierung <Programmierung>QuicksortInvariant (mathematics)Phase transitionError messageParameter (computer programming)Artificial neural networkResultantStatistical mechanicsNatural numberEstimatorExterior algebraHamiltonian (quantum mechanics)Physical systemTerm (mathematics)MetreBinary multiplierThresholding (image processing)Identity managementGoodness of fitLocal ringWordSet (mathematics)Computer simulationSummierbarkeitStandard ModelGraphics tabletDigital electronicsProcess (computing)HypermediaCross-correlationDimensional analysisOperator (mathematics)Key (cryptography)Numeral (linguistics)Context awarenessNetwork topologyComputer animation
Execution unitDigital electronicsAdditionPolygonError messageOperator (mathematics)State of matterBitNumberQubitStability theoryCodierung <Programmierung>CASE <Informatik>Electric generatorLogic gateCodeGame controllerSound effectMultiplication signFault-tolerant systemQuicksortInformationKnotCross-correlationFehlererkennungBell and HowellCodeClassical physicsIndependence (probability theory)Pointer (computer programming)Process (computing)Single-precision floating-point formatTransverse waveBound stateNoise (electronics)Network topologyDistanceLevel (video gaming)CircleArrow of timeIdeal (ethics)Dirac delta functionComputer-assisted translationFraction (mathematics)TrailForceCommunications protocolComputer animationProgram flowchart
Theory of everythingExecution unitError messageCodePropagatorQubitBitVertex (graph theory)Lattice (group)Fault-tolerant systemArithmetic meanNetwork topologyCodeEigenvalues and eigenvectorsOrder (biology)Element (mathematics)Multiplication signDistanceData structureScheduling (computing)QuicksortGoodness of fitMereologyCommunications protocolStability theoryLocal ringMultilaterationRevision controlGame theorySurfaceFehlererkennungForceGame controllerEntire functionPropagation of uncertaintyCASE <Informatik>Execution unitCategory of beingMetreCubeComputer animation
Theory of everythingFormal verificationCodeMultiplication signHadamard matrixFormal verificationResultantDistanceState of matterGame controllerNumberFigurate numberProcess (computing)Communications protocolComputer-assisted translationType theoryLattice (group)Procedural programmingDifferent (Kate Ryan album)BitCodeError messageScheduling (computing)Degree (graph theory)Single-precision floating-point formatMereologyDigital electronicsLogic gateCodierung <Programmierung>Latin squareCellular automatonInformationDemosceneWordParticle systemEntire functionHypothesisForceComputer animation
Formal verificationExecution unitCodeMessage passingDifferent (Kate Ryan album)Data recoveryFormal verificationMathematical optimizationSoftwareExecution unitProgrammer (hardware)PropagatorMultiplication signIterationLevel (video gaming)Error messageComputer architectureObservational studyDistanceElectric generatorCodeForcing (mathematics)CalculationSurfaceSystem callAlgorithmLogical constantCollaborationism4 (number)GodComputerInformationComputer scienceCodierung <Programmierung>CASE <Informatik>Phase transitionThresholding (image processing)Matching (graph theory)LoginBitMappingLinear programmingGeometryComplex (psychology)Cross-correlationSocial classOrder (biology)Quantum computerProcedural programmingWeightPerfect groupLogarithmQuicksortNP-hardStability theoryPolynomialFault-tolerant systemEndliche ModelltheorieMaxima and minimaRenormalization groupScaling (geometry)Statistical mechanicsComputer animation
Quantum computerGoodness of fitCodeFault-tolerant systemCodeOperator (mathematics)QubitComplex (psychology)ResultantPlanningError messageUniverse (mathematics)Multiplication signAdditionLogic gateTransformation (genetics)Codierung <Programmierung>Strategy gameForm (programming)ComputerFehlererkennungProcess (computing)Block (periodic table)QuicksortWordTwo-dimensional spaceOcean currentPlotterInformationPairwise comparisonGame controllerComputer animation
12 (number)Logic gateIdentical particlesStability theoryLocal ringSpacetimeMeasurementOperator (mathematics)Transverse waveSystem callOptical disc driveThree-dimensional spaceQubitBitHadamard matrixMatching (graph theory)CodePhase transitionError messageLength1 (number)Digital electronicsQuantum computerWordSet (mathematics)Eigenvalues and eigenvectorsModulo (jargon)FehlererkennungCodeLogicCommunications protocolTheoremGame controllerQuicksortWeightCase moddingMultiplicationACIDMatrix (mathematics)Process (computing)Block (periodic table)Mechanism designLink (knot theory)Power (physics)Fiber (mathematics)State of matterSource codeSigma-algebraComputerEscape characterComputer architectureHypermediaStudent's t-testSingle-precision floating-point formatForm (programming)Computer animation
CodeHill differential equationQuantum computerSurfaceQubitLogicCodeState of matterService (economics)MeasurementInjektivitätLevel (video gaming)Web crawlerNoise (electronics)Communications protocolProcess (computing)Codierung <Programmierung>FehlererkennungComputer animation
Execution unitFault-tolerant systemBound stateComputer programmingThresholding (image processing)Quantum computerExtension (kinesiology)Endliche ModelltheorieMathematical analysisReverse engineeringTerm (mathematics)Digital electronicsNoise (electronics)Operator (mathematics)AreaOverhead (computing)Sinc functionCodierung <Programmierung>Numeral (linguistics)Form (programming)Game theoryRevision controlWordLevel (video gaming)Physical lawFile archiverEstimatorState of matterCopyright infringementPower (physics)Reading (process)Shared memoryType theoryRectangleGraph coloringLecture/Conference
Personal identification numberQuantum computerBitProcess (computing)AlgorithmConnectivity (graph theory)Communications protocolDigital electronicsOverhead (computing)Fraction (mathematics)View (database)Latent heatControl flowNumberAnalytic continuationIdeal (ethics)Nichtlineares GleichungssystemComputer architectureCellular automatonComputer simulationFocus (optics)Particle systemLecture/ConferenceMeeting/Interview
Transcript: Englisch(auto-generated)