Monday and Wednesday, 17:3018:45, P&A 184
The course is shared with CS 591.003 and NSMS 595.002
Professor Akimasa Miyake
office: P&A 25, email: amiyake_at_unm.edu, office hours: Thursday and Friday afternoon (preferably by appointment)
Adrian Chapman
office: P&A graduate students office 38, email: akchapman_at_unm.edu
M. A. Nielsen and I. L. Chuang, "Quantum Computation and Quantum Information" (required)
J. Preskill, "Quantum Information and Computation," available free online (optional)
A.Y. Kitaev, A.H. Shen, and M.N. Vyalyi,"Classical and Quantum Computation" (optional)
This advanced graduate course is a sequel to PHYC 572 "Quantum Information Theory," taught by Professor Caves in Fall 2012. The main subjects are quantum information, quantum computation, and "quantum supremacy" over classical information processing. While basic knowledge about quantum mechanics and related mathematics like linear algebra is assumed, the course will be taught in a selfcontained manner. Even if one has missed the prequel, it would be still possible to follow the lectures by reading the Chapter 2 of the textbook by Nielsen and Chuang supplementarily.
The course has two objectives. One is, following the previous course PHYC 572, to enlighten the basic concepts of quantum information, which are expected to be useful regardless of research fields everyone chooses. The other is to help preparing the ground to work in quantum information if one is interested in contributing to its research frontiers.
Similarly with PHYC 572, there will be no final exam. Students
adopting the graded track will be graded on their attendance and
performance on the homework assignments. To receive a grade of CR on
the ungraded track, students need to attend the lectures and show
interest. Students who plan to work in quantum information or
relevant research fields are highly encouraged to be in the graded
track.
0.1 Qubit
0.2 Pauli operators
0.3 Mixed states
0.4 Quantum operations
0.5 Two qubits: tensor product
0.6 Purification and complete positivity
0.7 ChoiJamiołkowski isomorphism
0.8 Schmidt decomposition of quantum states
0.9 Schmidt decomposition of quantum unitary operations
1.1 Definition
1.2 Conversions under LOCC: single copy
1.3 Schmidt rank and a coarsegrained characterization
1.4 Conversions under LOCC: identically many copies
1.5 Entanglement in mixed states
1.6 Key protocols: entanglement concentration, dilution, and distillation
1.7 Entanglement measures
1.8 Multipartite entanglement → to be taught with 2.4, 2.5, 4.1, and 4.2
2.1 ChurchTuring thesis
2.2 Quantum circuit model
2.3 Quantum teleportationbased model
2.4 Entanglementbased model
2.5 Graph states and their usage in quantum computation
3.1 Oracle problems: exponential speedup over classical computer
3.2 Grover's algorithm: amplitude amplification
3.3 Shor's integer factorization algorithm
3.4 Quantum simulation
4.1 Classical repetition code for error correction
4.2 Quantum 3qubit bitflip code
4.3 Quantum 9qubit error correction code
4.4 Stabilizer codes
4.5 Faulttolerance of quantum computation
Dates 
Subjects 
Lecture notes 
Jan. 14 Mon 
Course overview 
Quiz
1 
Jan. 16 Wed 
0. Review of quantum information theory I 
Lecture
note, Sec. 0 Nielsen & Chuang, Chap. 2 
Jan. 21 Mon 
Martin Luther King
Jr. Holiday 

Jan. 23 Wed 
0. Review of quantum information theory
II 
Lecture
note, Sec. 0 Nielsen & Chuang, Chap. 2 and 8 
Jan. 28 Mon 
0. Review of quantum information theory III  Lecture
note, Sec. 0 Nielsen & Chuang, Chap. 2 and 8 
Jan. 30 Wed 
1. Entanglement theory I 
Lecture
note, Sec. 1 Nielsen & Chuang, Chap. 12.5 
Feb. 4 Mon 
1. Entanglement theory II 1.21.3 
Lecture
note, Sec. 1 Nielsen & Chuang, Chap. 12.5 
Feb. 6 Wed 
1. Entanglement theory III 1.41.6 
Lecture
note, Sec. 1 Nielsen & Chuang, Chap. 12.5 
Feb. 11 Mon 
1. Entanglement theory IV 1.41.6  Lecture
note, Sec. 1 Nielsen & Chuang, Chap. 12.5 
Feb. 13 Wed 
1. Entanglement theory V 1.51.6 Homework Sec.0 is due 
Lecture
note, Sec. 1 Nielsen & Chuang, Chap. 12.5 
Feb. 18 Mon 
1. Entanglement theory VI 1.51.7  Lecture
note, Sec. 1 Nielsen & Chuang, Chap. 12.5 
Feb. 20 Wed 
cancelled by SQuInT
Workshop 

Feb. 25 Mon 
cancelled by SQuInT Workshop  
Feb. 27 Wed 
1. Entanglement theory VI 1.7  Lecture
note, Sec. 1 Nielsen & Chuang, Chap. 12.5 
Mar. 4 Mon 
2. Quantum computational models I 2.12.2 
Lecture
note, Sec. 2 Nielsen & Chuang, Chap. 3.1 and 4 PHYC 572 QIT, Sec. 810 
Mar. 6 Wed 
2. Quantum computational models II 2.2  Lecture
note, Sec. 2 Nielsen & Chuang, Chap. 4 PHYC 572 QIT, Sec. 810 
Mar. 11 Mon 
spring break 

Mar. 13 Wed 
spring break 

Mar. 18 Mon 
2. Quantum computational models III 2.22.3  Lecture
note, Sec. 2 Nielsen & Chuang, Chap. 4 PHYC 572 QIT, Sec. 810 
Mar. 20 Wed 
2. Quantum computational models IV 2.22.3  Lecture
note, Sec. 2 Nielsen & Chuang, Chap. 4 PHYC 572 QIT, Sec. 810 
Mar. 25 Mon 
2. Quantum computational models V 2.3  Lecture
note, Sec. 2 
Mar. 27 Wed 
2. Quantum computational models VI 2.32.4  Lecture
note, Sec. 2 
Apr. 1 Mon 
2. Quantum computational models VII 2.4  Lecture note, Sec. 2 
Apr. 3 Wed 
2. Quantum computational models VIII 2.5  Lecture
note, Sec. 2 
Apr. 8 Mon 
3.
Quantum algorithms I 3.1 Homework Sec.1 is due after the extension 
Lecture note, Sec.3 Nielsen & Chuang, Sec. 1.4.4 
Apr. 10 Wed 
3. Quantum algorithms II 3.2  Lecture
note, Sec.3 Nielsen & Chuang, Chap. 6 
Apr. 15 Mon 
cancelled  
Apr. 17 Wed 
3. Quantum algorithms III 3.3 
Nielsen & Chuang,
Chap. 5

Apr. 22 Mon 
3. Quantum algorithms IV 3.3  Lecture
note, Sec.3 Nielsen & Chuang, Chap. 5 
Apr. 24 Wed 
3.
Quantum algorithms V 3.3 Homework Sec.2 is due 
Lecture
note, Sec.3 Nielsen & Chuang, Chap. 5 
Apr. 29 Mon 
4. Quantum error correction
I 4.14.2 
Lecture note, Sec.4 Nielsen & Chuang, Chap. 10 
May 1 Wed 
4. Quantum error correction II 4.24.3  Lecture
note, Sec.4 Nielsen & Chuang, Chap. 10 
May 6 Mon 
4. Quantum error correction III 4.34.4  Lecture
note, Sec.4 Nielsen & Chuang, Chap. 10 
May 8 Wed 
4. Quantum error correction
IV 4.44.5 Homework Sec.3+4 is due 
Lecture
note, Sec.4 Nielsen & Chuang, Chap. 10 
0. Homework due on February 13 (Wed) [ Problems, Solutions ]
1. Homework due on April 1 (Mon) April 8 (Mon) [ Problems,
Solutions
]
2. Homework due on April 24 (Wed) April 29 (Mon) [
Problems,
Solutions
]
3+4. Homework due on May 8 (Wed) May 10 (Fri) [ Problems,
Solutions
]