Monday and Wednesday, 17:30-18:45, P&A 184
The course is cross-listed with CS 591 and NSMS 595.
Professor Akimasa Miyake
office: P&A 25, email: amiyake_at_unm.edu, office hours: Monday 14:00-16:00, otherwise you may arrange a meeting by appointment.
Students educate and peer-review 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 self-contained manner. We adopt modern pedagogy of active learning and engagement in the class. In particular, students are encouraged to educate and peer-review 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 Choi-Jamiołkowski isomorphism
1.1 Church-Turing thesis
1.2 Quantum circuit model
1.3 Oracle problems: exponential speed-up 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 3-qubit bit-flip code
2.3 Quantum 9-qubit error correction code
2.4 Stabilizer codes
2.5 Fault-tolerance of quantum computation
3.1 Stabilizer states and classical simulation of stabilizer circuits
3.2 Cluster states, teleportation, and measurement-based 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 |
0.1-0.2 |
|
| Jan. 24 Wed |
0.2 |
|
| Jan. 29 Mon |
0.2-0.3 |
|
| Jan. 31 Wed |
0.3-0.4 |
Assignment 1 is due |
| Feb. 5 Mon |
0.4 |
|
| Feb. 7 Wed |
0.4-0.6 |
Assignment 2 is due |
| Feb. 12 Mon |
0.6 |
|
| Feb. 14 Wed |
0.6-0.7 |
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 |
1.1-1.2 |
|
| Feb. 28 Wed |
1.2 |
Assignments 6 and 7 are due |
| Mar. 5 Mon |
1.2 |
|
| Mar. 7 Wed |
1.2-1.3 |
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 |
1.3-1.4 |
|
| Mar. 26 Mon |
1.4-1.5 |
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 |
2.1-2.2 |
|
| Apr. 9 Mon |
2.2 |
Assignments 14 and 15 are due |
| Apr. 11 Wed |
2.2-2.3 |
|
| Apr. 16 Mon |
2.3 |
Assignment 16 is due |
| Apr. 18 Wed |
2.3-2.4 |
|
| Apr. 23 Mon |
2.4 |
Assignment 17 is due |
| Apr. 25 Wed |
2.4-2.5 |
Assignment 18 is due |
| Apr. 30 Mon |
3.2 |
|
| May 2 Wed |
3.2 |
Advanced project is due on
May 4 |
| May 7-11 |
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 [Peer-review 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 [Peer-review 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 [Peer-review of Assignments 6 and 7 Solutions]
9. Challenging assignment due on Mar. 19 [Problem: Prove the exact universality of the gate set by all 1-qubit rotations and the 2-qubit Controlled-NOT gate for a 2-qubit register. Solutions]
10. Assignment due on Mar. 26 [Peer-review 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 [Peer-review 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 [Peer-review 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 [Peer-review of Assignment 15 Solutions]
17. Assignment due on Apr. 23 [Problem: Consider a noisy rotational error channel \(\Lambda'(\rho)=(1-p)\rho + p R^x (\epsilon) \rho R^{x \dagger}(\epsilon)\), where \(R^x(\epsilon)= \cos \epsilon 1 + i\sin \epsilon X = e^{i\epsilon X}\). Analyze the performance of the 3-qubit repetition code on it, and obtain the corresponding encoded error probability. Solutions]
18. Assignment due on Apr. 25 [Problem: Prove that any single-qubit Pauli error operator is correctable for (1) the Steane 7-qubit code (2) the 5-qubit code. Solutions]
19. Assignment due on Apr. 30 [Peer-review of Assignment 17 Solutions]
20. Assignment due on May 2 [Peer-review 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?]