ECE 405

https://ece.illinois.edu/academics/courses/ece405

1. Quantum technology overview

2. Quantum formalism

3. Quantum levels and hybridization

4. Two-level quantum systems

5. Interactions of quantum systems

6. Quantum information primer

7. Photons

8. Trapped neutral atoms

9. Trapped ions

10. Superconducting qubits

The principal goal of this course is to introduce students to current issues in quantum tech-nology and the physical realizations of quantum systems, including quantum processors, networks, sensors, and simulators. We will examine the use of physical systems such as single photons, su-perconducting qubits, neutral atoms, and ions to encode and manipulate quantum information at the elementary level. Using a semi-formal approach and classical analogies wherever they are rel-evant, we will introduce each platform's key metrics and limitations and show examples of state-of-the-art realizations. An overarching theme of the course is the universality of quantum formal-ism and its ability to describe diverse physical systems within the same framework.

Students will turn in several homeworks in the first half of the course and take a written midterm exam. The course will end with a literature review project. Students will make a final presentation and a written report, critically assessing a scientific quantum technology paper of their choice based on the knowledge acquired in class.

The course will consist of three parts:

PART I - Quantum physics primer, introducing the concepts of two-level systems, their interaction with fields, harmonic oscillators, relaxation, decoherence, and entanglement.

PART II - Quantum information basics, including basic architectures and protocols for quantum key distribution, quantum computing, and error correction.

PART III - Discussion of elementary quantum systems, their physical implementation, degrees of freedom, basic physical characteristics (interaction rates, dephasing rates), in-itialization, implementation of single and two-qubit gates, measurement and transduction mechanisms

Students will select a scientific paper of their choice either from a list of suggested papers or autonomously. The paper must deal with the physical issues of qubit fabrication/design/control/pro-tection/transmission/transduction/storage/measurement, be published after the year 2000, and make transformative impact on the field [e.g. Knill, Laflamme and Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 49 (2001)]. Students are encouraged to favor recently published papers over older ones. Students will prepare a 5 min presentation + 5 min Q&A discussing the context of the paper, its significance for the field, the opportunities it creates, and offer a critical discussion of how it could (or has) transform(ed) the field. In addition, students will prepare a written, illustrated report of about three to five pages, summarizing the paper and explaining its significance for a non-specialized reader.

ECE 305 or equivalent basic Quantum Mechanics class (for example, PHYS 486) or instructor consent

Main text: "Introduction to Quantum Computing", R. LaPierre, Springer, The Materials Research Society Series, 2021

Additional recommended texts:

1. "Introduction to Quantum Optics", G. Grynberg, A. Aspect, C. Fabre, Cambridge University Press, 2010

2. "Introduction to optical quantum information processing", P. Kok and B. Lovett, Cambridge University Press, 2010

3. "Optical resonance and two-level atoms", L. Allen and J.H. Eberly, Dover Publications, Inc., 1987

Selected Elective

This course is designed primarily for third and fourth year undergraduate students and starting graduate students interested in pursuing a career in a field, where quantum mechanical descriptions of systems are relevant. The overarching course goal is for students to learn and practice the language of quantum mechanics in engineering settings.

By the midterm, the students should be able to do the following:

• Define a basis of quantum states for a quantum mechanical system (1, 6)
• Propose a Hamiltonian for simple quantum mechanical systems, including composite systems and interactions with the environment (1, 7)
• Solve the time-dependent Schrodinger equation for all 2x2 Hamiltonians (1)
• Write the time evolution of a quantum harmonic oscillator starting in a Fock state, a coherent state, or any superposition thereof (1)
• Label quantum states of a qubit on a Bloch sphere and discuss their physical interpretation and time evolution (1)
• Derive the time evolution of Rabi oscillations in quantum dipoles and understand how it scales with qubit and control parameters (1)
• Calculate the effects of relaxation and dephasing on a single-qubit rotation (1)
• Explain how entanglement can be generated and removed in a system of two interacting quantum dipoles (electric or magnetic) (1, 2)
• Calculate the second-order nonlinear interaction of three classical optical beams (with at least one being undepleted), including phase matching effects (1)
• Understand the operation of single-qubit and two-qubit gates, write their matrix form and compute the effect of their composition (1)
• Understand the basic principles behind the Grover search, quantum error correction, quantum key distribution and qubit-based sensing (1, 2, 7)

By the end of the course, the students also should be able to do the following:

• Understand the various qubit implementations for single photons, superconducting qubits, single atoms and trapped ions (1, 2, 7)
• Understand the basic qubit initialization, control and readout mechanisms available in the photonic, superconducting, atomic and ionic quantum information platforms (1, 2, 7)
• Understand the basic implementation of single-qubit and two-qubit gates for single photons, superconducting qubits, single atoms and trapped ions (1, 2, 7)
• Discuss the fundamental strengths and weaknesses of photonic, superconducting, atomic and ionic quantum information platforms (1, 2, 7)
• Conduct literature review to compare the results of an experimental scientific paper to previous achievements (6, 7)
• Present a summary of an experimental scientific paper the in front of a non-specialized audience. (3, 5, 6, 7)
• Write a summary report with a critical discussion of the main contribution of an experimental scientific paper in the context of the modern challenges in quantum information processing (3, 4, 7)