CMSC 657: Introduction to Quantum Information Processing (Fall 2024)

The behavior of individual atoms and objects of similar size are governed by the laws of quantum mechanics rather than the familiar rules of classical mechanics, which apply to macroscopic objects. Quantum information is the study of the properties of information encoded in quantum objects, and quantum computers can take advantage of quantum properties to solve some problems much faster than any classical computer. This course will give an overview of the major results in the field of quantum information.

This is an interdisciplinary subject, so the only necessary background is a good understanding of linear algebra.

Problem Sets

• Problem Set 1 (LaTeX): Due Sep. 5, 2024 at 5 PM
• Problem Set 2 (LaTeX): Due Sep. 12, 2024 at 5 PM
• Problem Set 3 (LaTeX): Due Sep. 19, 2024 at 5 PM
• Problem Set 4 (LaTeX): Due Sep. 26, 2024 at 5 PM
• Problem Set 5 (LaTeX): Due Oct. 3, 2024 at 5 PM
• Problem Set 6 (LaTeX): Due Oct. 10, 2024 at 5 PM
• Problem Set 7 (LaTeX): Due Oct. 17, 2024 at 5 PM
• Problem Set 8 (LaTeX): Due Oct. 24, 2024 at 5 PM
• Problem Set 9 (LaTeX): Due Nov. 7, 2024 at 5 PM
• Problem Set 10 (LaTeX): Due Nov. 21, 2024 at 5 PM

Lecture Notes

• Lecture 1: Introduction to the class; pure states, unitary operators, no-cloning theorem
• Lecture 2: Tensor products and unitaries, measurements, and introduction to density matrices
• Lecture 3: More on density matrices
• Lecture 4: CP maps, POVMs, purification, Bloch sphere
• Lecture 5: Reversible computation, quantum circuits
• Lecture 6: Universal gate sets, Bell measurement, quantum teleportation
• Lecture 7: Teleportation, superdense coding, introduction to computational complexity
• Lecture 8: Church-Turing thesis, P, BPP, BQP, and NP.
• Lecture 9: NP-completeness, oracle problems, Deutsch-Jozsa algorithm.
• Lecture 10: Classical cryptography: one-time pad, RSA
• Lecture 11: Shor's algorithm
• Lecture 12: Shor's algorithm concluded, Grover's algorithm for one marked element
• Lecture 13: Grover's algorithm for multiple marked elements, introduction to Hamiltonian simulation
• Lecture 14: Hamiltonian simulation
• Lecture 15: DiVincenzo criteria, Ion traps: qubits and one-qubit gates
• Lecture 16: Ion traps: two-qubit gates and scaling up
• Lecture 17: Superconducting quantum computers, brief discussion of photonic and cold atom quantum computers
• Lecture 18: 3-qubit codes, 9-qubit code
• Lecture 19: Stabilizer codes, 5-qubit code
• Lecture 20: 7-qubit code, toric code, tranversal gates, magic states
• Lecture 21: Fault-tolerant error correction, threshold theorem, fidelity
• Lecture 22: Fidelity, trace distance, and diamond norm
• Lecture 23: Entropy, classical data compression
• Lecture 24: Quantum data compression and channel capacity
• Lecture 25: Examples of quantum channel capacity, entanglement monotones, entanglement entropy, entanglement of formation, distillable entanglement
• Lecture 26: Negativity, one- and two-way quantum capacities, Holevo capacity, Bell inequalities
• Lecture 27: Bell inequalities, quantum communication complexity
• Lecture 28: Quantum Key Distribution: BB84
• Lecture 29: Man-in-the-middle attack on QKD, Ekert 91 QKD, Bit commitment

Supplementary notes on basic group theory.

Contact Information

Lectures: Tuesday, Thursday 12:30-1:45 PM, IRB 2107
Textbook (Optional): Nielsen & Chuang, Quantum Computation and Quantum Information
Course Web Page: https://www.cs.umd.edu/class/fall2024/cmsc657/
Gradescope: https://www.gradescope.com/courses/837001
Piazza: https://piazza.com/umd/fall2024/cmsc657

Instructor: Daniel Gottesman (dgottesm@umd.edu)
Office hours: Tuesday 11 AM-12 noon, Atlantic 3251

TA: Suchetan Dontha (sdontha@umd.edu)
Office hours: Thursday 2-3 PM, Atlantic 3373

Course Requirements and Grading

Your grade will be determined by the following components:

• Weekly problem sets (60%)
• Take-home final exam (40%)

There will also be an optional final project that can substitute for your two lowest problem set grades.

Problem Set Rules

• Roughly one per week, due Thursdays at 5 PM.
• The problem sets will be turned in on Gradescope.
• For the problem sets, if you use any external material to solve it (other than the lectures and the textbook), cite the source and indicate what you took from it. This includes AI tools: Explain how you used the AI tool to contribute to your problem set.
• You may discuss problem sets with other students, but you must understand and write up your solution by yourself. If you do collaborate, indicate who you talked to on your assignment.
• There is no late penalty for problem sets up to 24 hours late. Beyond that, you will need to request an extension before the deadline.

Final Exam

• Take-home final exam
• Exam is open-book for class materials, but you must not discuss with other students or use other outside sources including AI tools.
• The exam will be available on Gradescope from sometime on Thursday, Dec. 12 until 11:59 PM on Monday, Dec. 16, and you will be able to choose a window of 4 hours within this period in which to take the exam. Once you access the exam, you must upload your solutions within the time window.
• You will need internet access to download the exam and upload your solutions.

Final Project

The final project is optional. It can be done individually or in groups of up to 4 people. Groups of 3-4 will need more material than the baselines listed below.

If you want to do the project, note the following important deadlines:

• Proposal: October 29, 5 PM (by email).
• Outline: November 19, 5 PM (by email).
• Project final due date: December 6, 11:59 PM (submitted on Gradescope).

The proposal consists of a topic and the group of people that will be involved in the project. The outline consists of a more detailed breakdown of what will be included in the project.

The final project will be a choice:

• Term paper, 5--10 pages long, based on your reading of 1-2 research articles.
• Learn a quantum programming language and implement a quantum algorithm or protocol on a quantum computer and/or simulator.
• Another comparable project, with instructor approval.

In case of a programming project, you will turn in a writeup on Gradescope including the source code and an analysis of the behavior of your code with and without noise. For a group project, the final project should include a description of what each group member contributed to the project.

More information about the project is available here.

Topics Covered

• Introduction to quantum mechanics (Hilbert spaces, unitary operators, density matrices, CP maps, measurements)
• Quantum circuits (quantum gates, universality, teleportation, superdense coding)
• Complexity theory (Complexity classes, oracles, Deutsch-Jozsa algorithm)
• Shor's algorithm (RSA, factoring, Shor's algorithm)
• Other algorithms (Grover's algorithm, simulation of quantum systems)
• Implementations (DiVincenzo criteria, ion traps, superconductors)
• Quantum error correction (quantum error-correcting codes, fault tolerant circuits, threshold theorem)
• Quantum information theory (distance measures, entropy, quantum compression and channel capacity, entanglement, non-locality)
• Quantum key distribution

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