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From physics to computation. Translate quantum mechanics into computational building blocks: qubits, gates, circuits, and the no-cloning theorem.
Build intuition for qubits, the Bloch sphere, density matrices, and the partial trace. Based on Nielsen & Chuang \u00a71.2, \u00a71.3, and \u00a72.4.
Master the fundamental single-qubit gates: Pauli, Hadamard, phase, and general rotations. Based on Nielsen & Chuang \u00a74.2.
Explore the foundations of multi-qubit quantum mechanics: tensor product spaces, the CNOT gate, Bell states, the EPR paradox, and Bell's theorem with the CHSH inequality.
Study multi-qubit gate constructions, universal gate sets, the Solovay-Kitaev theorem, and important circuit identities for quantum computation.
Learn the quantum circuit model, projective measurements and POVMs, the deferred measurement principle, and how classical circuits can be simulated quantumly. Covers Nielsen & Chuang §4.1–4.4 and §2.2.3.
Study the four postulates of quantum mechanics in the N&C formulation, quantum operations, completely positive trace-preserving maps, the Kraus operator representation, and common quantum channels including depolarizing, dephasing, and amplitude damping. Covers Nielsen & Chuang §8.1–8.4.
Explore how quantum systems lose coherence through interaction with their environment. This module covers quantum channel models including bit-flip, phase-flip, amplitude damping, and depolarizing channels, as well as fidelity and trace distance as measures of state distinguishability.
Discover how quantum information can be protected against noise through quantum error correction. This module covers the bit-flip code, phase-flip code, Shor's 9-qubit code, the stabilizer formalism, and the threshold theorem for fault-tolerant quantum computing.