Monday and Wednesday, 17:3018:45, P&A 184
The course is crosslisted with CS 591 and NSMS 595.
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.
Students educate and peerreview each other under supervision of the instructor.
M. A. Nielsen and I. L. Chuang, "Quantum Computation and Quantum Information" (optional)
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. We adopt modern pedagogy of active learning and engagement in the class. In particular, students are encouraged to educate and peerreview each other, so that they can also learn valuable skills as researchers to explain and communicate well.
The course has two objectives. One is 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. It is expected that comprehensive understanding is obtained, when another graduate course PHYC 572 "Quantum Information Theory," in Spring 2017 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.
Students adopting the graded track will be graded on their attendance and performance on the assignments and projects. 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 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 ChoiJamiołkowski 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
3.1 Stabilizer states and classical simulation of stabilizer circuits
3.2 Cluster states, teleportation, and measurementbased quantum computation
3.3 Matrix product states and simulations using MPS
3.4 Tensor network states and topologically ordered states
Dates 
Subjects 
Assignments 
Jan. 15 Mon 
Martin Luther King Jr. Holiday  
Jan. 17 Wed 
Course overview 

Jan. 22 Mon 
0.10.2 

Jan. 24 Wed 
0.2 

Jan. 29 Mon 
0.20.3 

Jan. 31 Wed 
0.30.4 
Assignment 1 is due 
Feb. 5 Mon 
0.4 

Feb. 7 Wed 
0.40.6 
Assignment 2 is due 
Feb. 12 Mon 
0.6 

Feb. 14 Wed 
0.60.7 
Assignment 3 and 4 are due 
Feb. 19 Mon 
1.1 
Assignment 5 is due 
Feb. 21 Wed 
no class due to SQuInT  
Feb. 26 Mon 
1.11.2 

Feb. 28 Wed 
1.2 
Assignments 6 and 7 are due 
Mar. 5 Mon 
1.2 

Mar. 7 Wed 
1.21.3 
Assignments 8 is due 
Mar. 12 Mon 
spring break 

Mar. 14 Wed 
spring break  
Mar. 19 Mon 
1.3 
Assignments 9 is due 
Mar. 21 Wed 
1.31.4 

Mar. 26 Mon 
1.41.5 
Assignments 10 and 11 are due 
Mar. 28 Wed 
1.5 

Apr. 2 Mon 
1.5 
Assignments 12 and 13 are due 
Apr. 4 Wed 
2.12.2 

Apr. 9 Mon 
2.2 
Assignments 14 and 15 are due 
Apr. 11 Wed 
2.22.3 

Apr. 16 Mon 
2.3 
Assignment 16 is due 
Apr. 18 Wed 
2.32.4 

Apr. 23 Mon 
2.4 
Assignment 17 is due 
Apr. 25 Wed 
2.42.5 
Assignment 18 is due 
Apr. 30 Mon 
3.2 

May 2 Wed 
3.2 
Advanced project is due on
May 4 
May 711 
no exam 
Assignments are as follows.
1. Assignment due on Jan. 31 [Problems: What are algebraic relations enough to derive a matrix representation of Pauli operators? What are the freedoms which remain in the representation? Solutions]
2. Assignment due on Feb. 7 [Problems: Any quantum pure state of 1 qubit should be able to be characterized as an eigenstate of a Pauli operator along an arbitrary axis. By parameterizing the axis in terms of the spherical coordinate, describe its 2 eigenstates. Solutions]
3. Assignment due on Feb. 14 [Peerreview of Assignment 2 Solutions]
4. Assignment due on Feb. 14 [Problem: Prove \(\tfrac{1}{2}(\Phi^+\rangle \langle\Phi^++\Psi^\rangle \langle\Psi^)\) is separable. Solutions]
5. Assignment due on Feb. 19 [Peerreview of Assignment 4 Solutions]
6. Assignment due on Feb. 28 [Prove the necessary and sufficient condition for a Bell diagonal state to be separable. You may use the positive partial transposition (PPT) criterion without a proof if you like. Solutions]
7. Assignment due on Feb. 28 [Essay: Explain to what extent reversible computation is possible? Solutions]
8. Assignment due on Mar. 7 [Peerreview of Assignments 6 and 7 Solutions]
9. Challenging assignment due on Mar. 19 [Problem: Prove the exact universality of the gate set by all 1qubit rotations and the 2qubit ControlledNOT gate for a 2qubit register. Solutions]
10. Assignment due on Mar. 26 [Peerreview of Assignment 9 Solutions]
11. Assignment due on Mar. 26 [Problem: Analyze Deutsch's algorithm in the Heisenberg picture instead of the Schrödinger picture. Solutions]
12. Assignment due on Apr. 2 [Peerreview of Assignment 11 Solutions]
13. Assignment due on Apr. 2 [Problem: Generalize Grover's algorithm to the case of multiple target states, and analyze its performance. Solutions]
14. Assignment due on Apr. 9 [Peerreview of Assignment 13 Solutions]
15. Assignment due on Apr. 9 [Problem: Analyze in details Shor's algorithm to factorize \(N=15\), with 2 different choices of coprime integers \(a=11\) and \(a=7\). Solutions]
16. Assignment due on Apr. 16 [Peerreview of Assignment 15 Solutions]
17. Assignment due on Apr. 23 [Problem: Consider a noisy rotational error channel \(\Lambda'(\rho)=(1p)\rho + p R^x (\epsilon) \rho R^{x \dagger}(\epsilon)\), where \(R^x(\epsilon)= \cos \epsilon 1 + i\sin \epsilon X = e^{i\epsilon X}\). Analyze the performance of the 3qubit repetition code on it, and obtain the corresponding encoded error probability. Solutions]
18. Assignment due on Apr. 25 [Problem: Prove that any singlequbit Pauli error operator is correctable for (1) the Steane 7qubit code (2) the 5qubit code. Solutions]
19. Assignment due on Apr. 30 [Peerreview of Assignment 17 Solutions]
20. Assignment due on May 2 [Peerreview of Assignment 18 Solutions]
Advanced projects are optional. Additional credit is granted for diligent reports.
1. Project due on May 4 [Problem: Access the IBM Q Experience and run a quantum algorithm or information protocol of your choice. Report (i) details of the algorithm and data you obtained, (ii) the original points you elaborated, and (iii) analysis and validation of the outcome. In particular, what sets the limitation of quantum computation in the current implementation?]