Monday and Wednesday, 17:3018:45, P&A 5
The course is crosslisted with CS 591.004 and NSMS 595.004.
Professor Akimasa Miyake
office: P&A 25, email: amiyake_at_unm.edu, office hours: Monday 14:0016:00, otherwise you may arrange a meeting by appointment.
Gopikrishnan Muraleedharan
office: P&A 30, email: gopu90_at_unm.edu, office hours: Monday and Wednesday afternoon before the lecture.
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)
The main subjects of this advanced graduate course are quantum information, quantum computation, and quantum advantage 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. It is expected that comprehensive understanding is obtained, when another graduate course PHYC 572 "Quantum Information Theory," taught by Professor Caves in Fall 2014 was taken together. However, 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. There is a timely introduction to the subject, "Why now is the right time to study quantum computing," written by Harrow particularly for students of computer science department.
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.
There will be no exam, while there might be a final project about
what you learn from the course. 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.
1 Probabilistic information processing
2 Quantum information processing
3 Dirac notation in quantum mechanics
0.1 Qubit
0.2 Pauli operators and their eigenstates
0.3 Density operator formalism
0.4 Quantum operations
0.5 Two qubits: tensor product
0.6 Entanglement theory 101
0.7 Purification and complete positivity
0.8 ChoiJamioĊkowski isomorphism
1.1 ChurchTuring thesis
1.2 Quantum circuit model
1.3 Oracle problems: exponential speedup over classical computer
1.4 Grover's algorithm: amplitude amplification
1.5 Shor's integer factorization algorithm
1.6 Quantum complexity theory 101
2.1 Classical repetition code for error correction
2.2 Quantum 3qubit bitflip code
2.3 Quantum 9qubit error correction code
2.4 Stabilizer codes
2.5 Faulttolerance of quantum computation
Dates 
Subjects 
Assignments 
Jan. 12 Mon 
Course overview 

Jan. 14 Wed 
Crash course in quantum mechanics: 12 

Jan. 19 Mon 
Martin Luther King Jr. Holiday  
Jan. 21 Wed 
Crash course in quantum mechanics: 23  
Jan. 26 Mon 
0. Review of quantum information theory:
0.1 

Jan. 28 Wed 
0. Review of quantum information theory: 0.2  
Feb. 2 Mon 
0. Review of quantum information theory: 0.2  
Feb. 4 Wed 
0. Review of quantum information theory: 0.20.3  
Feb. 9 Mon 
0. Review of quantum information theory: 0.3  
Feb. 11 Wed 
0. Review of quantum information theory: 0.4  assignment 1 is posted 
Feb. 16 Mon 
0. Review of quantum information theory: 0.40.5 

Feb. 18 Wed 
canceled by SQuInT Workshop  
Feb. 23 Mon 
0. Review of quantum information theory: 0.50.6  
Feb. 25 Wed 
0. Review of quantum information theory: 0.6  
Mar. 2 Mon 
0. Review of quantum information theory: 0.7 
assignment 1 is due 
Mar. 4 Wed 
Review of assignment 1 

Mar. 9 Mon 
spring break 

Mar. 11 Wed 
spring break  
Mar. 16 Mon 
1. Quantum computation and
algorithms: 1.1 

Mar. 18 Wed 
1. Quantum computation and algorithms: 1.2  
Mar. 23 Mon 
1. Quantum computation and algorithms: 1.2 

Mar. 25 Wed 
1. Quantum computation and algorithms: 1.3  
Mar. 30 Mon 
1. Quantum computation and algorithms: 1.3  
Apr. 1 Wed 
1. Quantum computation and algorithms: 1.4  
Apr. 6 Mon 
1. Quantum computation and algorithms: 1.4  
Apr. 8 Wed 
1. Quantum computation and algorithms: 1.5  
Apr. 13 Mon 
1. Quantum computation and algorithms: 1.5  assignment 2 is posted 
Apr. 15 Wed 
2. Quantum error correction:
2.1 

Apr. 20 Mon 
2. Quantum error correction: 2.2  
Apr. 22 Wed 
2. Quantum error correction: 2.2  
Apr. 27 Mon 
2. Quantum error correction:2.3 
assignment 2 is due assignment 3 is posted 
Apr. 29 Wed 
2. Quantum error correction:2.42.5  
May 48 
final week  assignment
3 is due 
Students may study subjects of assignments together, but everyone is expected to prepare his/her original answer sheets.
1. Assignment due at 5:30 pm on March 2 (Mon) [Problems Solutions]
2. Assignment due at 5:30 pm on April 27 (Mon) [Problems Solutions]
3. Assignment due at 5:00 pm on May 8 (Fri), to be submitted to my mailbox [Problems Solutions]
Attempts to tackle following advanced assignments may be recognized towards additional credit in the final grade. Similarly with the rule of standard assignments, students may study together and look for hints in literature, but have to submit his/her own original answer sheets. These are due at 5:00 pm on May 8 (Fri), too.
1. What is a necessary and sufficient condition for the 2qubit Hermitian operator to be positive semidefinite in the Pauli basis?
2. Given an exact universal set of elementary gates, what is the minimal number of 1qubit and 2qubit gates respectively to implement an arbitrary 2qubit unitary time evolution given by SU(4)?