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Week 165: Quantum Complexity Theory

Week 165 of 288~56 min read

Learning Objectives

•Define BQP precisely and explain its relationship to classical complexity classes
•Define QMA and explain the significance of QMA-complete problems
•Prove the Local Hamiltonian problem is QMA-complete (proof sketch)
•Apply the polynomial method to derive quantum query lower bounds
•Prove Grover's algorithm is optimal using the polynomial method
•Analyze oracle problems and quantum-classical query separations
•Explain the oracle evidence for P ≠ BQP and BQP ≠ NP

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