Practice
Exercises
All interactive exercises grouped by chapter. Each exercise links back to its chapter for theory.
Chapter 1
Qubit
QubitBasis stateComputational basisProbability amplitude
- Check your understandingNot startedClassical bit versus qubitDistinguish classical bits from qubit state vectors.
- Interactive exampleNot startedAmplitude and normalizationShape probability amplitudes and satisfy normalization.
- Guided exerciseNot startedComputational-basis measurementApply the Born rule in the computational basis.
- Chapter reviewNot startedChapter 1 reviewCombine basis states, normalization, and Born-rule reasoning.
Chapter 2
Superposition
SuperpositionRelative phase|+> and |->Hadamard gate
- Check your understandingNot startedCoherent superpositionDistinguish superposition from classical uncertainty.
- Interactive exampleNot startedRelative phaseExplore how relative phase affects interference.
- Guided exerciseNot startedHadamard transformationConnect computational and X-basis states via H.
- Chapter reviewNot startedChapter 2 reviewCombine superposition, phase, Hadamard, and interference.
Chapter 3
Measurement
Measurement basisBorn ruleProjective measurementPost-measurement state
- Check your understandingNot startedBorn ruleConvert amplitudes to measurement probabilities.
- Interactive exampleNot startedFresh preparation statisticsInterpret finite-shot frequencies from fresh preparations.
- Guided exerciseNot startedMeasurement basisCompare computational-basis and X-basis measurement.
- Chapter reviewNot startedChapter 3 reviewCombine Born rule, post-measurement state, and basis dependence.
Chapter 4
Quantum Gates
Unitary operatorPauli-X gatePauli-Z gateHadamard gate
- Check your understandingNot startedGates versus measurementDistinguish pulling a gate lever from taking a measurement.
- Interactive exampleNot startedZ and relative phaseSee how the Z gate turns |+⟩ into |-⟩.
- Guided exerciseNot startedUnitarity and reversibilityConfirm that ideal unitary gates preserve total probability.
- Chapter reviewNot startedChapter 4 reviewCombine gate matrices, unitarity, and the gate-versus-measurement distinction.
Chapter 5
Multi-Qubit States and Entanglement
Tensor productBasis orderingCNOTBell state
- Check your understandingNot startedTensor-product mapMap one-qubit states into a two-qubit basis order.
- Interactive exampleNot startedCNOT loomTrack H and CNOT as they create a Bell state.
- Guided exerciseNot startedBell correlation auditSeparate entangled correlation from signaling or hidden independent states.
- Chapter reviewNot startedChapter 5 assessmentSynthesize tensor products, CNOT, Bell states, and no-signaling interpretation.
- Guided exerciseNot startedSeparability testUse the two-qubit amplitude criterion to distinguish product and entangled pure states.
- Check your understandingNot startedLocal-state lensReason about random local outcomes and definite joint correlations.
- Interactive exampleNot startedBell correlations across basesTrack how a Bell state behaves when both qubits are measured in the X basis.
- Chapter reviewNot startedCorrelation without signalingDiagnose claims that confuse correlation, causation, and controllable communication.
Chapter 6
Quantum Circuits and Protocols
Circuit notationControlled gatesNo-cloningTeleportation
- Check your understandingNot startedCircuit reading roomRead wires, controls, measurement, and time order correctly.
- Guided exerciseNot startedNo-cloning crossroadsUse linearity to see why arbitrary unknown states cannot be copied.
- Interactive exampleNot startedTeleportation relayFollow Bell measurement, two classical bits, and correction gates.
- Chapter reviewNot startedChapter 6 assessmentSynthesize circuit notation, no-cloning, teleportation, and superdense coding.
- Guided exerciseNot startedCircuit order traceCompare noncommuting gate orders by evolving a state step by step.
- Interactive exampleNot startedTeleportation correction tableMap Bell-measurement bits to Bob's correction under a stated convention.
- Check your understandingNot startedDense-coding resource ledgerAccount for the entangled pair, transmitted qubit, and recovered classical bits.
- Chapter reviewNot startedProtocol resource auditCorrect incomplete claims about teleportation, cloning, and dense coding.
Chapter 7
Algorithms as Engineered Interference
OraclePhase kickbackDeutsch-JozsaGrover search
- Check your understandingNot startedOracle promise gateState what an oracle problem promises and what it does not promise.
- Guided exerciseNot startedKickback mirrorTrack a sign flip as information becomes relative phase.
- Interactive exampleNot startedGrover amplitude forgeCompute a four-item amplitude amplification step.
- Chapter reviewNot startedChapter 7 assessmentSynthesize oracle promises, kickback, Deutsch-Jozsa, and Grover limits.
- Guided exerciseNot startedDeutsch-Jozsa traceTrace the promised constant-versus-balanced decision through phase and interference.
- Check your understandingNot startedOracle cost ledgerSeparate oracle-query complexity from implementation and data-access costs.
- Interactive exampleNot startedGrover iteration countEstimate the useful number of amplitude-amplification iterations.
- Chapter reviewNot startedSpeedup claim auditRewrite exaggerated algorithm claims with model, baseline, and resource caveats.
Chapter 8
Noise, Error Correction, and Useful Quantum Computing
NoiseDecoherenceError correctionFault tolerance
- Check your understandingNot startedNoise channel clinicIdentify bit-flip, phase-flip, depolarizing, damping, and measurement-error effects.
- Guided exerciseNot startedSyndrome workshopUse repetition-code intuition to detect a simple bit flip.
- Interactive exampleNot startedHardware reality checkEvaluate a quantum advantage claim against resources and noise.
- Chapter reviewNot startedChapter 8 assessmentSynthesize noise, error correction, hardware limits, and responsible claims.
- Guided exerciseNot startedPhase-flip diagnosisExpose a phase error by changing measurement basis.
- Check your understandingNot startedRepetition-code limitsIdentify which errors the three-qubit bit-flip code does and does not correct.
- Interactive exampleNot startedStabilizer syndrome mapMap parity-check outcomes to a single bit-flip location.
- Chapter reviewNot startedFault-tolerance claim auditState the threshold idea with its assumptions and overhead.