C191: Syllabus


1. Basic QM (4 lectures)                 

F       Aug 29            Axioms

States, Hamiltonians, observables Hilbert space, tensor product, partial trace              

W    Sep 3               Qubits, multiple qubits, Bloch sphere  

Physical qubits                  

F       Sep 5               Bra-ket notation, density matrices         

W    Sep 10            Evolution, unitary maps, positive maps, representation frames (Heisenberg, Schrodinger, interaction, rotating)               


2. Circuit model QC (3 lectures)                 

F       Sep 12            Reversible computation                                 

                                    Circuits, elementary one- and two-qubit gates                  

W    Sep 17            Measurements, principle of deferred measurement    


F       Sep 19            Universality       

                                    Circuit simulation, Solvay-Kitaev, Clifford group               


3. CS complexity (1 lecture)        

W    Sep 24            Complexity classes, interpretation and motivation       

                                    BQP and its relation to BPP, P and NP    

                                    Oracle model    

                                    Hamiltonian complexity               


4. Quantum classical separations (1 lecture)        

F       Sep 26            No-cloning, uncertainty principle, superdense coding 

                                    Deutsch-Josza algorithm              


5. Foundations and Interpretations, entanglement (1 lecture)   

W    Oct 1               The notion of state         

                                    Classical formal mechanics       

                                    Notion of phase space distributions      

                                    Wave function as state (maximal knowledge and uncertainty)                  

                                    Wave function as distribution (non-positivity) 

                                    Interpretations: Copenhagen/operational, many-worlds, Bayesian,    

                                    EPR, Bell's theorem        


6. QKD, Cryptography (2 lectures)            

F       Oct 3               Classical cryptographic models (public, private)              

                                    Notions of security         

                                    Fundamental arguments for why quantum is more secure         

W    Oct 8               QKD protocols (BB84, GG02)      

                                    Postprocessing details, error correction, privacy amplification                


7. Measures on state space, distinguishability (1 lecture)               

F       Oct 10            POVMs 

Notions of distinguishability (mathematical, operational), distance measures for classical and quantum distributions

                                    State and process fidelity, diamond norm


8. Open quantum systems, decoherence, error correction, fault tolerance (5 lectures) 

W    Oct 15            Open systems, notion of decoherence and dephasing 

                                    Hamiltonian formulation, partial trace, master equations        

F       Oct 17            Kraus maps        

                                    Common error models for QC    

W    Oct 22            Classical and quantum error correction codes

F       Oct 24            Implementing ECC and fault tolerance theorem               

W    Oct 29            Error avoidance: decoherence free subspaces/subsystems      


9. Algorithms (4 lectures)             

F       Oct 31            Grover 

W    Nov 5              QFT                           

F       Nov 7              Phase estimation            

W    Nov 12           Period finding, Shor, factoring  


10. Implementations  (2 lectures)            

F       Nov 14           Superconducting circuits (Prof. Irfan Siddiqi)

W    Nov 19           Ion traps (Prof. Hartmut Haffner)


11. Entanglement (1 lecture)     

F       Nov 21           Notion of entanglement, EPR, Bell           

                                    Entanglement in bipartite pure states, measures           

                                    Multipartite pure state entanglement, measure             

                                    Mixed state entanglement, measures 

                                    Bound entanglement and discord           


12. Alternate QC models (1 lecture)       

W    Nov 26           Quantum simulation, analog and digital              

                                    Adiabatic QC


F       Nov 28           Thanksgiving holiday


13. Student Presentations (2 lectures)

W    Dec 3

F       Dec 5