- Product states and nonseparable states — Bruna placeholder
Add a worked tensor product with the basis order stated.
Contrast it with a normalized two-system state that cannot factor into a product. Use state vectors without circuit programming.
- Physical meaning of a subsystem — Bruna placeholder
Choose a physical two-level example. Identify the preparation and the measured observable for each subsystem.
Explain which assumptions let us model the pair as a tensor product.
- Preparation versus statistical mixture — Bruna placeholder
Develop one physical preparation of a superposition and one mixture with the same probabilities in a chosen basis.
Use a second measurement basis to distinguish them.
- A complete Born-rule example — Bruna placeholder
Specify a normalized state and a measurement basis. Calculate every outcome probability and the post-measurement state.
Include a student checkpoint with a different basis.
- Single-particle interference — Bruna placeholder
Add the experiment, preparation, and detection procedure.
Explain interference between indistinguishable alternatives for a single quantum system. Avoid describing it as photons needing to collide with one another.
- Which-path information and coherence — Bruna placeholder
Compare coherent alternatives with distinguishable paths. Connect the observed distributions to amplitude addition and probability addition.
Distinguish loss of local coherence from conditioning on a measurement outcome.
- Stern–Gerlach measurement model — Bruna placeholder
Develop the preparation, magnetic-field gradient, and readout.
Separate the Pauli observable with eigenvalues ±1 from physical spin angular momentum with eigenvalues ±ℏ/2.
- Sequential measurements — Bruna placeholder
Work through two measurement axes and conditional probabilities.
Explain the change of state and the difference between an observable, apparatus setting, and observed value.
- Hamiltonian and time evolution — Bruna placeholder
Derive the connection between the Schrödinger equation and U(t) for a time-independent Hermitian Hamiltonian.
State the assumptions and units. Replace the unfinished derivation in original Lecture 12, slides 41–42.
- Energy eigenstates and relative phase — Bruna placeholder
Use a two-level energy spectrum to calculate phase accumulation.
Distinguish a shared global phase from a relative phase observable in a suitable basis.
- Physics-to-computation boundary — Bruna placeholder
Finish with a worked physical evolution and its unitary matrix.
Q3 will treat selected transformations as allowed computational operations. Leave circuit software for M_Q.
- Entanglement and local statistics — Bruna placeholder
Define separability and entanglement with explicit joint states.
Calculate joint probabilities and each subsystem’s marginal probabilities. Explain why correlations do not permit faster-than-light messaging.
- Bell assumptions and an experimental test — Bruna placeholder
State the assumptions behind the chosen Bell inequality. Give measurement settings, a classical bound, and a quantum prediction.
Explain experimental limitations without claiming that the result proves faster-than-light communication.
- Q2 synthesis exercise — Bruna placeholder
Combine state preparation, tensor products, measurement bases, and physical evolution in one problem.
Students should explain the predicted evidence before Q3 introduces computational models.
- Density matrices and reduced states — Bruna placeholder
Develop pure states, statistical mixtures, and the partial trace with worked two-level examples.
Show how a pure entangled joint state gives a mixed local state.
- Entropy and physical information — Bruna placeholder
Calculate Shannon and von Neumann entropy in small examples.
Connect the eigenvalues of a density matrix to uncertainty, purity, and correlations. Define all conventions.
- A physical decoherence mechanism — Bruna placeholder
Develop one system–environment coupling model. Calculate the reduced state and the loss of off-diagonal coherence.
Distinguish decoherence, measurement conditioning, relaxation, and dephasing.
- Noise channels and time scales — Bruna placeholder
Introduce T₁ and T₂ with physical preparation and readout procedures.
Work through a simple channel and compare ideal and noisy output probabilities.
- Error mitigation and its limits — Bruna placeholder
Choose a mitigation method and state its calibration assumptions.
Compare bias, variance, and sampling overhead. Explain why mitigation alone does not provide fault tolerance.
- Current hardware comparison — Bruna placeholder
Update the illustrative platform and vendor examples with dated primary sources.
Compare encoding, control, readout, connectivity, coherence, and native operations. Separate physical and logical qubits.
- Logical qubits and syndrome measurement — Bruna placeholder
Develop one small code, its encoding, and a syndrome table.
Show which errors it corrects and which it cannot. Explain why syndrome measurement can preserve logical information.
- Fault tolerance and overhead — Bruna placeholder
Connect physical error rates, code distance, and logical failure probability.
State the assumptions behind a threshold claim and provide a worked resource example.
- An evidence-based hardware case study — Bruna placeholder
Choose a dated result from a primary source. Identify the task, classical comparison, accuracy, and total resources.
Distinguish a simulator demonstration, a query advantage, and useful hardware performance.
- Final synthesis assessment — Bruna placeholder
Trace one Q3 algorithm through state preparation, compilation, noisy execution, and readout.
Ask students to explain what would have to improve for the demonstration to become useful.