- ## Course structure - ### Classical computation - Bits (W 1.1) - Logic gates (W 1.2) - Adders / CPU building blocks (W1.3) - Reversible vs irreversible logic gates (W 1.5) - How to make a gate reversible - Error correction (W 1.6) - Computational complexity (W 1.7, A) - Turing machines (W 1.8) - ### Quantum mechanics - Basic quantum mechanics - Schrödinger equation (ND 1.2) - Dirac notation, discrete Hilbert space, change of basis (ND 1.3) - Perturbation theory (ND 1.5) - Density matrix (ND 1.10, P 2.3) - Two-level systems - Bloch sphere - TLS Hamiltonian - Pauli matrices - Eigenenergies and eigenstates - Any Hamiltonian as a field - Dynamics - Static field: precession - Landau-Zener transitions - Rabi driving - Measurement - ### Quantum information and computation - Qubits, data storage capacity - Single-qubit gates: H, X, T - Two-qubit gates: SWAP, CNOT - Universal sets of gates (NC) - Important differences with classical information processing - Reversibility - No-cloning theorem - Quantum adder (W 4.5) - Concept and misunderstanding of parallellism - ### Entanglement as resource (W 6) - Entanglement - Bell inequalities - Superdense coding (KFM 5.1) - Quantum teleportation (KFM 5.2,5.3) - Quantum key distribution (W 6.6) - ### Quantum algorithms (W 7, KFM 7) - Deutsch-Jozsa - Simon's problem - Phase estimation - Cycle finding - Number theory to connect to factorizing (Hans) - Shor (TMA4160) - ### Quantum error correction - Operator formalism (NC) - No-cloning theorem - Bit-flip code - Remember equivalence of partial and probabilistic flip - Check working for partial flip (W 4.7.2) - Phase-flip code - Stabilizer formalism? - ### Physical qubit implementations - DiVincenzo criteria - Resonant driving vs baseband pulsing - TLS coupled to environment - Relaxation - Dephasing - Bloch-Redfield equations - Superconducting qubits - Spin qubits - ### Outlook: NISQ applications? - VQE (?) - ## Literature - W: Wong, Introduction to classical and quantum computing - A: Scott Aaronson - ND: Nazarov & Danon, Advanced quantum mechanics - P: Preskill, Lecture notes Ph219 - NC: Nielsen & Chuang, Quantum computation and quantum information - KFM: Kaye, Laflamme & Mosca, In introduction to quantum computing - More to consider - Bombin chapter in QEC - Rabi driving: https://physics.unm.edu/Courses/Deutsch/Phys566F19/Lectures/Phys566_Lect06.pdf - https://courses.cs.washington.edu/courses/cse599d/06wi/ - https://www.cs.cmu.edu/~odonnell/quantum18/ - Exercises: https://www.thp.uni-koeln.de/kastoryano/teaching.html - NISQ - https://www.cornell.edu/video/john-preskill-quantum-computing-nisq-era-beyond - https://quantum-journal.org/papers/q-2018-08-06-79/pdf/ - https://quantumfrontiers.com/2023/12/09/crossing-the-quantum-chasm-from-nisq-to-fault-tolerance/