Quantum Computing: Programs and Systems will be structured around reading and discussing several foundational research papers in realizing quantum computers. Students will also complete programming assignments to implement algorithms in open-source quantum frameworks. The goal of the course is to bring students up-to-speed on recent developments in realizing quantum computers, which will be a strong foundation for pursuing research or to be a subject expert in industry.
Basic course information
- Canvas: https://rutgers.instructure.com/courses/385586
- In-person attendance: We meet Tuesdays 12:10 PM – 1:30 PM and Fridays 12:10 PM – 1:30 PM in TIL-226
- Recitation: The undergraduate 443 section has recitation Tuesdays 2:15 PM – 3:10 PM in BE-011
Instructor information
- Yipeng Huang
- Email: yipeng.huang@rutgers.edu
- Students can expect a 2-day turnaround from me on emails.
- Office hours: TBA
- Please see Canvas site for office hour Zoom info.
- Office: CoRE 317
Prerequisites
- Courses in or experience in Python programming, computer architecture, algorithms, linear algebra, probability.
- Taking first an introductory class in quantum computing such as Rutgers ECE 493 Intro to Quantum Information Science (Prof. Emina Soljanin) or Rutgers Physics 421 Introduction to Quantum Computing (Prof. Ananda Roy) is ideal but not required.
- Senior undergraduates interested in quantum computing have successfully taken this class in the past.
Course components and grading rubric
- Assignments (42% for 558 section; 60% for 443 section)
- We will practice the mathematics for understanding quantum algorithms via graded problem sets consisting of derivations and proofs.
- We will discuss a mix of introductory, foundational, and recent research articles on realizing quantum computing systems. Participation in reading discussions on the forum and in-class discussions will be important.
- We will practice implementing and analyzing several quantum algorithms via programming assignments.
- The logistics of the selection of assignment problems, the policy on leveraging artificial intelligience for problem solving, and the points rewarding system for verifying and demonstrating understanding of the solutions is described on the class Canvas, under the Assignments tab.
- Exams (28% for 558 section; 40% for 443 section)
- Midterm 1 (8.4% for 558 section; 12% for 443 section) is scheduled for Friday, February 20 12:10 PM – 1:30 PM in TIL-226
- Midterm 2 (8.4% for 558 section; 12% for 443 section) is scheduled for Friday, March 27 12:10 PM – 1:30 PM in TIL-226
- Final exam (11.2% for 558 section; 16% for 443 section) is scheduled for the standard final exam time in TIL-226
- The goal of the exams is to demonstrate understanding of the assignments. The exam questions will draw on the assignment problems.
- Project (30% for 558 section; 0% for 443 section)
- The class culminates in a final project to be completed in three person teams. The open-ended final project will be of students’ design. Typical projects include implementation and simulation of a quantum algorithm. The final project deliverables include a project proposal, interim report, final report, and oral presentation.
Syllabus
| Date | Theme | Contents | Assignments and exams deliverables | Project deliverables |
|---|---|---|---|---|
| Tue. 1/20 | Spring Semester Begins | |||
| Tue. 1/20 | Introduction [slides] [slides] | Preview of the syllabus, course objectives & activities. | Harrow. Why now is the right time to study quantum computing. XRDS. 2012. Assignment stage 1 released. | |
| Fri. 1/23 | Postulate 1. State space [slides] | The state of a single qubit 1. Superposition 2. Bloch sphere | ||
| Tue. 1/27 | Postulate 2. Composition [slides] | The state of multiple qubits 1. Tensor product 2. Entanglement 3. No-cloning theorem | ||
| Fri. 1/30 | Postulate 3. Evolution [slides] | 1. The state of multiple qubits • Tensor product 2 The evolution of qubit states | ||
| Tue. 2/3 | Basic quantum algorithms: dense coding, teleportation [slides] | 1. The evolution of qubit states • No-cloning theorem 2. The measurement of qubit states | Rieffel and Polak. An Introduction to Quantum Computing for Non-Physicists. (Up to and just short of section 6. Shor’s algorithm). | |
| Fri. 2/6 | Basic quantum algorithms: BB84, dense coding, teleportation [slides] | 1. Quantum cryptography / quantum key exchange / BB84 2. Entanglement protocol: Quantum superdense coding | ||
| Tue. 2/10 | Basic quantum algorithms: Deutsch, Deutsch-Jozsa [slides] | 1. The universe does not obey local realism • EPR paradox • CHSH game • Hardy’s paradox 2. Deutsch-Jozsa algorithm: simplest quantum algorithm showing advantage vs. classical • Problem description • Circuit diagram and what is in the oracle • Demonstration of Deutsch-Jozsa for the n = 1 case • Deutsch-Jozsa programs and systems | ||
| Fri. 2/13 | ||||
| Tue. 2/17 | Basic quantum algorithms: Deutsch-Jozsa, Bernstein-Vazirani [slides] | 1. Basic quantum algorithms: Deutsch-Jozsa, Bernstein-Vazirani • Deutsch’s algorithm: simplest quantum algorithm showing advantage vs. classical • Problem description • Circuit diagram and what is in the oracle • Demonstration of Deutsch-Jozsa for the n = 1 case • Deutsch-Jozsa programs and systems 2. Deutsch-Jozsa algorithm: extending Deutsch’s algorithm to more qubits • The state after applying oracle U • Lemma: the Hadamard transform • The state after the final set of Hadamards • Probability of measuring upper register to get 0 | ||
| Fri. 2/20 | Midterm exam 1 | All states, gates, detection codes, protocols, and algorithms involving one or two qubits. | Assignment stage 2 released. | Final project parameters released. |
| Tue. 2/24 | Quantum algorithms: Shor’s integer factoring classical part [slides] | |||
| Fri. 2/27 | Quantum algorithms: Shor’s integer factoring quantum part [slides] | 1. The factoring problem 2. Shor’s algorithm classical part: converting factoring to period finding • Factoring to modular square root • Modular square root to discrete logarithm • Discrete logarithm to order finding • Order finding to period finding 2. Shor’s algorithm quantum part: period finding using quantum Fourier transform • Calculate modular exponentiation • Measurement of target (bottom, ancillary) qubit register | ||
| Tue. 3/3 | Quantum algorithms: Shor’s integer factoring quantum part [slides] | Shor’s algorithm quantum part: period finding using quantum Fourier transform 1. Calculate modular exponentiation 2. Measurement of target (bottom, ancillary) qubit register 3. Quantum Fourier transform to obtain period 4. How to construct the Quantum Fourier transform 5. Evaluation of Shor’s as a fault-tolerant quantum algorithm | ||
| Fri. 3/6 | Final project proposals due. | |||
| Tue. 3/10 | Quantum algorithms: Noisy intermediate-scale quantum (NISQ) [slides] | • Density matrices and quantum noise • Noisy intermediate scale quantum (NISQ) | ||
| Fri. 3/13 | Quantum noise [slides] Quantum algorithms: Quantum approximate optimization algorithm [slides] | 1. NISQ (Noisy Intermediate Scale Quantum) vs FTQC (Fault Tolerant Quantum Computation) • NISQ algorithms: attributes, examples 2. Quantum Approximate Optimization Algorithm for MAX-CUT • The MAX-CUT problem • Encoding the vertices | ||
| Tue. 3/17 | Spring Recess | |||
| Fri. 3/20 | Spring Recess | |||
| Tue. 3/24 | A systems view of quantum computer engineering [slides] | |||
| Fri. 3/27 | Midterm exam 2 | All quantum error codes and algorithms involving few qubits. | Assignment stage 3 released. | Final project interim reports due. |
| Tue. 3/31 | Languages and representations for quantum computing: Stabilizer formalism [slides] | |||
| Fri. 4/3 | Emerging languages and representations for quantum computing: Tensor networks [slides] Tensor Network Simplification [slides] | 1. Tensor networks • Tensors • Tensor networks • Tensor network contraction • Tensor network contraction order 2. Unification of stabilizers and tensors • Example: inverting a CNOT • Splitting a CNOT into network of two rank-3 tensors • Tensor simplification rules • Automatic simplification of circuits | ||
| Tue. 4/7 | ||||
| Fri. 4/10 | ||||
| Tue. 4/14 | Quantum Chemistry [slides] | 1. Motivation for quantum chemistry 2. Ground state estimation 3. Simplification of problem representation 4. Qubit representation of orbitals 5. Variational quantum eigensolver 6. VQE ansatz | ||
| Fri. 4/17 | Quantum architecture [slides] Quantum microarchitecture [slides] | • Challenges of quantum computer architecture 1. Scheduling 2. Qubit mapping 3. Topological constraints resolving 4. Physical-gate decomposition 5. Physical-level optimization • Anatomy of a quantum computer 1. Essential hardware components of a quantum computer 2. DiVincenzo’s criteria • Device technologies 1. Trapped ion quantum computers 2. Superconducting quantum computers 3. Other technologies | ||
| Tue. 4/21 | Final project presentations | |||
| Fri. 4/24 | Final project presentations | |||
| Tue. 4/28 | Final project presentations | |||
| Fri. 5/1 | Final project presentations | |||
| Tue. 5/5 | Reading Day | |||
| Wed. 5/6 | Reading Day | |||
| Thu. 5/7 | Spring Exams Begin | |||
| Wed. 5/13 | Spring Exams End | Final project reports due. |
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