[PS1] The version of Problem #2 that was handed out in class contains an error. Equation (8) should have parentheses around the sum of three terms: H_{0} = (1/3)(E_{12} + E_{23} + E_{31}). Also, you may find it helpful to use mathematics software such as Mathematica or MATLAB to solve this problem.
[PS1] Problem #5 is problematic and will not be graded. However, it is insightful to try it and you are encouraged to do so anyway.
[PS3] In Problem #3, you may treat gamma as a small quantity (gamma is much less than one).
Advanced graduate course on quantum computation and quantum information. Topics include quantum circuits, quantum Fourier transform and search algorithms, physical implementations, the quantum operations formalism, quantum error correction, stabilizer and CalderbankShorSteane codes, fault tolerant quantum computation, quantum data compression, entanglement, and proof of the security of quantum cryptography. Prior knowledge of quantum mechanics and basic information theory is required.This class will be of interest to students in Physics, Electrical Engineering, Computer Science, and Chemistry. It will be closely coordinated with Seth Lloyd's MIT 2.111 introduction to quantum computation.

Course Textbook 
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[R 06Sep]  Entrance exam  
[T 11Sep]  Lecture 1: Review  
[R 13Sep]  Lecture 2: Quantum circuits; universal gate sets; SolovayKitaev theorem  [PS#1 out]  
[T 18Sep]  Lecture 3: Quantum Fourier transform and phase estimation algorithms, orderfinding and factoring  
[R 20Sep]  Lecture 4: Hidden subgroup algorithms; quantum simulation  
[T 25Sep]  Guest lecture (Andrew Childs: Quantum computation in continuous time)  
[R 27Sep]  Lecture 5: Quantum search algorithms; quantum counting  [PS#2 out, PS#1 due]  
[T 02Oct]  Lecture 6: Hamiltonians and physical implementations; JaynesCummings model  
[R 04Oct]  Lecture 7: Quantum operations formalism; decoherence; open quantum systems  
[T 09Oct]  MIT Holiday  
[R 11Oct]  Lecture 8: Generalized measurements; distance measurements for quantum information  [PS#3 out, PS#2 due]  
[T 16Oct]  Lecture 9: Quantum error correction; Shor code; quantum Hamming bound  
[R 18Oct]  Lecture 10: CalderbankShorSteane codes; stabilizer codes  
[T 23Oct]  Lecture 11: Faulttolerant quantum computation  
[R 25Oct]  Guest lecture (Debbie Leung, IBM Watson Research Center)  [PS#4 out, PS#3 due]  
[T 30Oct]  Lecture 12: Quantum information theory; Holevo theorem; quantum data compression  
[R 01Nov]  Lecture 13: Distributed quantum computation; cryptographic primitives; quantum bit escrow  
[T 06Nov]  Lecture 14: Entanglement, PPT criterion, Schmidt number, HillWootters measure  
[R 08Nov]  Guest lecture (Aram Harrow): Entanglement of pure states  [PS#5 out]  
[T 13Nov]  Guest lecture (Aram Harrow): distillation & dilution; entanglement of mixed states  [PS#4 due]  
[R 15Nov]  Lecture 15: Quantum cryptography; BB84, Ekert protocol, privacy and coherent information  
[T 20Nov]  Lecture 16: Informationtheoretic proof of the security of the BennettBrassard 84 protocol  
[R 22Nov]  MIT Holiday, Thanksgiving  
[T 27Nov]  Guest lecture (Andrew Childs)  [PS#5 due]  
[R 29Nov]  Project meetings  
[T 04Dec]  Project meetings  
[R 06Dec]  Project meetings  
[T 11Dec]  Final project paper due 
Syllabus (pdf)  
entrance exam (ps, pdf)  solutions (ps, pdf) 
problem set 1 (ps, pdf)  solutions (ps, pdf) 
problem set 2 (ps, pdf)  solutions (ps, pdf) 
problem set 3 (ps, pdf)  solutions (ps, pdf) 
problem set 4 (ps, pdf)  solutions (ps, pdf) 
problem set 5 (ps, pdf)  solutions (ps, pdf) 