Quantum Computing

Study

• Basics of Quantum Information, lesson 1 (single systems): state vectors, Dirac notation, unitary operations, measurement probabilities.
• Install Qiskit; run your first circuits on the simulator.

Exercises

• In NumPy (no Qiskit), represent |0>, |1>, |+>, |-> as vectors; apply X, Z, H as matrices; compute measurement probabilities. Prove H applied twice is the identity.
• Repeat in Qiskit and confirm the simulator agrees with your NumPy math.
• Show numerically that X, Z, and H are unitary (Week 2 skill, now load-bearing).

Checkpoint

You can compute the outcome distribution of any single-qubit circuit by hand.

Study

• Basics of Quantum Information, lesson 2 (multiple systems): tensor products, CNOT, Bell states, why entangled states cannot be factored.

Exercises

• Build all four Bell states in Qiskit; verify the correlation statistics over many shots.
• In NumPy, show that the state (|00> + |11>)/sqrt(2) cannot be written as a tensor product of two single-qubit states (set up the equations and derive the contradiction).
• Implement the CHSH game in Qiskit and beat the classical bound of 75 percent.

Checkpoint

The CHSH experiment wins about 85 percent of the time and you can explain why no classical strategy does that.

Study

• Basics of Quantum Information, lesson on quantum protocols (teleportation, superdense coding, the no-cloning theorem).

Exercises

• Implement teleportation in Qiskit; verify with state tomography (or statevector simulation) that the state really moved.
• Prove no-cloning on paper: assume a unitary clones two distinct non-orthogonal states, take inner products, reach the contradiction.
• Implement superdense coding: two classical bits through one qubit.

Checkpoint

You can explain why teleportation does not violate no-cloning or send information faster than light.

Study

• IBM's Fundamentals of Quantum Algorithms course (same platform): Deutsch-Jozsa, then the Quantum Fourier Transform and phase estimation.
• The QFT deserves extra attention from you specifically - it is the quantum cousin of the FFT you met in Week 4, and it is the "Quantum Fourier Transform" item from your original list.

Exercises

• Implement Deutsch-Jozsa in Qiskit for a 3-bit oracle; confirm one query suffices.
• Build the QFT circuit for 3 qubits from H and controlled-phase gates by hand (no library call); verify against qiskit.circuit.library.QFT.
• Use phase estimation to extract an eigenphase you planted in a simple unitary.

Checkpoint

You can articulate what the QFT computes, and why that is not the same as "a faster FFT for your radio data" (input/output are amplitudes, not accessible arrays).

Study

• Grover's algorithm (same IBM course): amplitude amplification, the sqrt(N) speedup, why it is quadratic and not magic.
• NISQ reality: noise, decoherence, gate errors, transpilation. Skim IBM's material on error mitigation.

Exercises

• Implement Grover search over 3 qubits for a marked item; plot success probability vs number of iterations, including past the optimum.
• Run the same Bell-state circuit on the simulator and on a real IBM device (free tier). Compare the histograms; quantify the noise.
• Transpile a 3-qubit circuit for a real backend and look at what the hardware actually runs - count the gate overhead.

Checkpoint

You have run a circuit on a physical quantum computer, and you can name the two main reasons its output differs from the simulator's.

Exercises

• From memory: teleportation and 3-qubit QFT, on paper and in Qiskit.
• Write your one-page "quantum computing in my own words" summary. If a claim feels shaky, that is the topic to revisit.
• Where the written course felt thin, read the matching chapter of Nielsen & Chuang (ch. 1-2, 4-5 map to this phase). Programming Quantum Computers (O'Reilly) is a friendlier second angle if you bought it.