MIT MAS.961: Quantum Information Science

MIT MAS.961: Quantum Information Science

Course Homepage

Isaac Chuang

Fall, 2001


  • Announcements
  • Course Description
  • General Course Information
  • Mailing List
  • Syllabus
  • Handouts
  • Useful Resources


    [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: H0 = (-1/3)(E12 + E23 + E31). 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).

    Course Description

    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 Calderbank-Shor-Steane 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.

    General Information

    Units: 3-0-9
    Prerequisites: 2.111; 8.05; 6.401 or MAS.862
    Lectures: Tuesday & Thursday 2-3:30pm, Room 24-307
    Textbook: Quantum Computation and Quantum Information, by Nielsen and Chuang
    Grading: Homework (5 problem sets) 60%, Project paper 40%
    Schedule: Entrance quiz on Thursday, Sep. 6; Final project paper due on Dec. 11.

    Instructor: Prof. Isaac Chuang E15-424
    Office Hours: Tue. 3:30-4:30pm
    Teaching Assistants: Andrew Childs 6-409A
    Office Hours: Wed. 2-3pm
    Aram Harrow E15-430
    Office Hours: Wed. 3:30-4:30pm
    Course secretary: Murray Whitehead E15-435

    Course Textbook

    Mailing List

  • To join the class mailing list, send email to with the word "subscribe" in the body of the message.

  • Syllabus (tentative)

    [R 06-Sep] Entrance exam
    [T 11-Sep] Lecture 1: Review
    [R 13-Sep] Lecture 2: Quantum circuits; universal gate sets; Solovay-Kitaev theorem [PS#1 out]
    [T 18-Sep] Lecture 3: Quantum Fourier transform and phase estimation algorithms, order-finding and factoring
    [R 20-Sep] Lecture 4: Hidden subgroup algorithms; quantum simulation
    [T 25-Sep] Guest lecture (Andrew Childs: Quantum computation in continuous time)
    [R 27-Sep] Lecture 5: Quantum search algorithms; quantum counting [PS#2 out, PS#1 due]
    [T 02-Oct] Lecture 6: Hamiltonians and physical implementations; Jaynes-Cummings model
    [R 04-Oct] Lecture 7: Quantum operations formalism; decoherence; open quantum systems
    [T 09-Oct] MIT Holiday
    [R 11-Oct] Lecture 8: Generalized measurements; distance measurements for quantum information [PS#3 out, PS#2 due]
    [T 16-Oct] Lecture 9: Quantum error correction; Shor code; quantum Hamming bound
    [R 18-Oct] Lecture 10: Calderbank-Shor-Steane codes; stabilizer codes
    [T 23-Oct] Lecture 11: Fault-tolerant quantum computation
    [R 25-Oct] Guest lecture (Debbie Leung, IBM Watson Research Center) [PS#4 out, PS#3 due]
    [T 30-Oct] Lecture 12: Quantum information theory; Holevo theorem; quantum data compression
    [R 01-Nov] Lecture 13: Distributed quantum computation; cryptographic primitives; quantum bit escrow
    [T 06-Nov] Lecture 14: Entanglement, PPT criterion, Schmidt number, Hill-Wootters measure
    [R 08-Nov] Guest lecture (Aram Harrow): Entanglement of pure states [PS#5 out]
    [T 13-Nov] Guest lecture (Aram Harrow): distillation & dilution; entanglement of mixed states [PS#4 due]
    [R 15-Nov] Lecture 15: Quantum cryptography; BB84, Ekert protocol, privacy and coherent information
    [T 20-Nov] Lecture 16: Information-theoretic proof of the security of the Bennett-Brassard 84 protocol
    [R 22-Nov] MIT Holiday, Thanksgiving
    [T 27-Nov] Guest lecture (Andrew Childs) [PS#5 due]
    [R 29-Nov] Project meetings
    [T 04-Dec] Project meetings
    [R 06-Dec] Project meetings
    [T 11-Dec] 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)

    Useful Resources

  • Seth Lloyd's Introduction to Quantum Computation course 2.111 at MIT
  • John Preskill's Quantum Computation Course at Caltech
  • Umesh Vazirani's Quantum Computation course at Berkeley
  • quant-ph preprint archive at Los Alamos

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