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Interactive lab

Quantum Labs

Visual, mathematical, simulation, and coding activities that turn the written course into durable skill.

30 minFreeAvailable

Bloch State Studio

Map amplitudes and relative phase to a Bloch-sphere picture without treating the picture as the definition.

Activity

Visualization

Concepts

state vectornormalizationrelative phaseBloch sphere

Prompt

Choose three normalized states, predict Z-basis probabilities, then explain what changes when only relative phase changes.

Deliverable

A short state table with amplitudes, probabilities, and a one-sentence phase explanation.

Quality checks

  • Probabilities sum to 1.
  • Global phase is not counted as a distinct physical state.
  • Relative phase is tied to later interference.
25 minFreeAvailable

Measurement Sampler

Compare exact Born-rule probabilities with finite-shot samples from fresh preparations.

Activity

Simulation

Concepts

Born ruleshot statisticsbasis dependence

Prompt

Run 20, 100, and 1000-shot thought experiments for the same state and explain why frequencies move but probabilities do not.

Deliverable

A frequency table and a distinction between model probability and observed frequency.

Quality checks

  • Uses fresh preparations.
  • Does not claim one system is measured repeatedly unchanged.
  • Mentions sampling variation.
40 minFreeAvailable

Gate Composer

Compose single-qubit gates as matrices and predict the resulting state before drawing the circuit.

Activity

Mathematical derivation

Concepts

unitary matrixPauli gatesHadamard gate

Prompt

Compute HZH|0> and XH|0>, then identify which differences are measurable in the Z basis.

Deliverable

Matrix steps, final states, and Z-basis probabilities.

Quality checks

  • Matrix multiplication order is correct.
  • Final state is normalized.
  • Probabilities follow the final state.
45 minFreeAvailable

Entanglement Workbench

Build a Bell state from H and CNOT, then test why it cannot be factored into independent qubit states.

Activity

Mathematical derivation

Concepts

tensor productBell statemeasurement correlation

Prompt

Derive the state after each gate and attempt a separable factorization; explain where the attempt fails.

Deliverable

A two-column derivation showing circuit step and state after that step.

Quality checks

  • Uses tensor-product basis order consistently.
  • Shows the failed factorization.
  • Explains correlated measurements without faster-than-light signaling.
55 minProAvailable

Interference Algorithm Studio

Trace how algorithmic advantage appears through amplitude cancellation and reinforcement.

Activity

Simulation

Concepts

interferenceoraclephase kickback

Prompt

Trace a two-bit Deutsch-Jozsa oracle and mark which amplitudes cancel after the final Hadamards.

Deliverable

Amplitude trace with a claim about the promised property, not a general-purpose speedup.

Quality checks

  • States the promise clearly.
  • Tracks signs, not only probabilities.
  • Avoids overclaiming practical advantage.
60 minProAvailable

Circuit Coding Kata

A coding path for constructing circuits, checking statevectors, and comparing simulated counts with theory.

Activity

Coding

Concepts

circuit APIstatevectormeasurement counts

Prompt

Implement a Bell-state circuit, assert the expected statevector up to global phase, then sample measurement counts.

Deliverable

A reproducible notebook or script with assertions and a short interpretation of counts.

Quality checks

  • Statevector test allows global phase.
  • Shot counts are interpreted statistically.
  • Code separates construction, simulation, and explanation.
70 minProAvailable

Noise Model Clinic

Inspect how simple depolarizing and measurement noise change counts without changing the ideal algorithm.

Activity

Simulation

Concepts

noisedepthmeasurement error

Prompt

Compare an ideal Bell circuit with noisy variants and identify which errors create which count patterns.

Deliverable

A table linking noise assumptions to count changes and confidence limits.

Quality checks

  • Separates ideal circuit from noisy observation.
  • Mentions finite-shot uncertainty.
  • Does not infer hardware performance from a toy model.
75 minProAvailable

Hamiltonian Reading Room

Learn to read a small chemistry Hamiltonian and connect Pauli terms to expectation-value estimation.

Activity

Mathematical derivation

Concepts

HamiltonianVQEexpectation value

Prompt

Annotate a two-qubit Hamiltonian, group compatible Pauli terms, and explain what a variational circuit is trying to minimize.

Deliverable

Annotated Hamiltonian terms and a plain-language VQE objective.

Quality checks

  • Distinguishes operator terms from measured samples.
  • Describes an expectation value.
  • Avoids claiming chemical advantage without resource analysis.