Quantum Information Science and Technology Minor
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Ben Zwickl, Associate Professor
Offered within the
School of Physics and Astronomy
School of Physics and Astronomy
Overview for Quantum Information Science and Technology Minor
The minor in quantum information science and technology provides an introduction to the foundational concepts of quantum information science. Topics focus on how quantum devices are designed and operate and how they are being applied in emerging technologies, such as quantum computing, cryptography, and sensing.
Notes about this minor:
- Posting of the minor on the student's academic transcript requires a minimum GPA of 2.0 in the minor.
- Notations may appear in the curriculum chart below outlining pre-requisites, co-requisites, and other curriculum requirements (see footnotes).
The plan code for Quantum Information Science and Technology Minor is QUANTUM-MN.
Curriculum for Quantum Information Science and Technology Minor
|Choose one of the following:|
This is the second course in three-course sequence (COS-MATH-171, -172, -173). The course includes Riemann sums, the Fundamental Theorem of Calculus, techniques of integration, and applications of the definite integral. The techniques of integration include substitution and integration by parts. The applications of the definite integral include areas between curves, and the calculation of volume. (Prerequisites: C- or better in MATH-171 or 1016-171T or 1016-281 or 1016-231 or equivalent course.) Lecture 5 (Fall, Spring).
This is the second in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers techniques of integration including integration by parts, partial fractions, improper integrals, applications of integration, representing functions by infinite series, convergence and divergence of series, parametric curves, and polar coordinates. (Prerequisites: C- or better in (MATH-181 or MATH-173 or 1016-282) or (MATH-171 and MATH-180) or equivalent course(s).) Lecture 6 (Fall, Spring, Summer).
|Choose one of the following:|
College Physics I
This is an introductory course in algebra-based physics focusing on mechanics and waves. Topics include kinematics, planar motion, Newton’s laws, gravitation; rotational kinematics and dynamics; work and energy; momentum and impulse; conservation laws; simple harmonic motion; waves; data presentation/analysis and error propagation. The course is taught using both traditional lectures and a workshop format that integrates material traditionally found in separate lecture, recitation, and laboratory settings. Lab 4 (Fall, Spring, Summer).
University Physics I
This is a course in calculus-based physics for science and engineering majors. Topics include kinematics, planar motion, Newton's Laws, gravitation, work and energy, momentum and impulse, conservation laws, systems of particles, rotational motion, static equilibrium, mechanical oscillations and waves, and data presentation/analysis. The course is taught in a workshop format that integrates the material traditionally found in separate lecture and laboratory courses. (Prerequisites: C- or better in MATH-181 or equivalent course. Co-requisites: MATH-182 or equivalent course.) Lec/Lab 6 (Fall, Spring).
University Physics IA
University Physics I: Physics Majors
This is a course in calculus-based physics for physics majors. Topics include kinematics, planar motion, Newton’s Laws, gravitation, work and energy, momentum and impulse, conservation laws, systems of particles, rotational motion, static equilibrium, mechanical oscillations and waves, and data presentation/analysis. Calculus and basic numerical techniques will be applied throughout the course to analyze non-idealized complex systems. The course is taught in a workshop format that integrates the material traditionally found in separate lecture and laboratory courses. The course will also include enrichment activities connecting current developments in the field of physics. (Prerequisites: C- or better in MATH-181 or MATH-181A or MATH-172 or equivalent course. Co-requisites: MATH-182 or MATH-182A or MATH-172 or equivalent course.) Lec/Lab 7.5 (Fall, Spring).
Introduction to Quantum Computing and Information Science
Principles and Applications of Quantum Technology
This course will provide an introduction to principles of quantum mechanics, hardware platforms, and applications of quantum technology. Two state systems, such as photon polarization, will be used to introduce mathematical formalism including Dirac notation for quantum states, operators, observables, measurements, composite systems and entanglement. The course will overview different platforms for physically realizing quantum bits (qubits) and operations on quantum bits. Real-world effects on quantum systems, including coherence and decoherence and reducing classical noise in quantum hardware will be discussed. Quantum limits on precision of sensors and imaging as well quantum simulations will be primary applications. (Prerequisites: (PHYS-111 or PHYS-211 or PHYS-211A or PHYS-216) and (MATH-172 or MATH-182 or MATH-182A) or equivalent courses.) Lecture 3 (Fall).
Physical Chemistry II
This course provides fundamental concepts, and organizing principles of quantum chemistry, applied in all aspects of chemistry and related fields. A rigorous and detailed explanation of central, unifying concepts in quantum chemistry will be developed. Mathematical models will be described, which contain the underpinnings to concepts applied in analytical, inorganic, organic, and biochemistry courses, as well as more advanced topics in chemistry. The course will cover: Postulates and formulation of Schrödinger equations, Operators and matrix elements, Solutions for the particle-in-a-box, simple harmonic oscillators, the rigid rotor and angular momentum, the hydrogen atom; spin, the Pauli principle. Approximation methods will be described for the helium atom, the hydrogen molecule ion, the hydrogen molecule, Diatomic molecules. Linear combinations of atomic orbitals and computational chemistry will be introduced and quantum chemistry applications will be provided. In addition this course will cover standard thermodynamic functions expressed in partition functions and spectroscopy and light-matter interaction (Prerequisite: CHMP-441 and (MATH-233 or (MATH-231 and MATH-241)) or equivalent courses.) Lecture 3 (Fall, Spring).
This course is a study of the concepts and mathematical structure of non-relativistic quantum mechanics. Topics for the course include wave functions and the Schrodinger equation, solutions to the one-dimensional and three-dimensional time-independent Schrodinger equation, stationary states and their superposition to produce time-dependent states, quantum-mechanical operators, commutators, and uncertainty principles, solutions to general central potential problems and the hydrogen atom, and the quantum theory of angular momentum. (Prerequisites: PHYS-213, PHYS-320 and (PHYS-330 or 1017-402) or equivalent courses. Students in the PHYS-BS program are also required to complete PHYS-275 before taking this course.) Lecture 3 (Fall).
Advanced Quantum Mechanics
This course is a continued study of the concepts and mathematical structure of quantum mechanics presented in Quantum Mechanics (PHYS-414), with an emphasis on applications to real physical systems. Topics covered include the quantum theory of spin, effect of magnetic fields on spin-1/2 particles, many-particle systems, variational principle, time-independent and time-dependent perturbation theory, absorption and emission of radiation by atoms, quantum theory of scattering, and interpretations and paradoxes of quantum mechanics. (Prerequisites: PHYS-414 or equivalent course.) Lecture 3 (Spring).
This course explores the fundamental nature of electromagnetic radiation. This course will introduce the student to the second quantized description of light with special attention to its role in a modern understanding of and far reaching utility in emerging technologies. Starting with an appropriate formulation for the quantum mechanical electromagnetic radiation field, we will study quantum mechanical models for interactions with matter, and we will test these models through a series of experiments. (Prerequisites: PHYS-411 and PHYS-414 or equivalent course or Graduate standing.) Lab 3 (Spring).
Discrete Mathematics for Computing
This course introduces students to ideas and techniques from discrete mathematics that are widely used in Computer Science. Students will learn about the fundamentals of propositional and predicate calculus, set theory, relations, recursive structures and counting. This course will help increase students’ mathematical sophistication and their ability to handle abstract problems. (Co-requisites: MATH-182 or MATH-182A or MATH-172 or equivalent courses.) Lecture 3 (Fall, Spring).
Discrete Mathematics and Introduction to Proofs
This course prepares students for professions that use mathematics in daily practice, and for mathematics courses beyond the introductory level where it is essential to communicate effectively in the language of mathematics. It covers various methods of mathematical proof, starting with basic techniques in propositional and predicate calculus and set theory, and then moving to applications in advanced mathematics. (Prerequisite: MATH-173 or MATH-182 or MATH-182A or equivalent course.) Lecture 3 (Fall).
This course is an introduction to the basic concepts of linear algebra, and techniques of matrix manipulation. Topics include linear transformations, Gaussian elimination, matrix arithmetic, determinants, vector spaces, linear independence, basis, null space, row space, and column space of a matrix, eigenvalues, eigenvectors, change of basis, similarity and diagonalization. Various applications are studied throughout the course. (Prerequisites: MATH-190 or MATH-200 or MATH-219 or MATH-220 or MATH-221 or MATH-221H or equivalent course.) Lecture 3 (Fall, Spring).
Honors Linear Algebra
Digital System Design I
This course covers the specification, analysis, modeling and design of digital systems. Standard modules, such as decoders, multiplexers, shifter registers, adders, and counters, will be analyzed. Lectures will discuss fundamental design methodologies, state machines, and digital system modeling with the use of VHDL as a hardware description language. The laboratory provides hands-on experiences of the design, modeling, implementation, and testing of digital systems using commercial IC components as well as CAD tools. (Co-requisite: CSCI-105 or CSCI-140 or CSCI-141 or equivalent course.) Lab 2 (Fall, Spring).
Digital System Design II
This course presents modern approaches to the design, modeling and testing of digital system. Topics covered are: VHDL and Verilog HDL as hardware description languages (HDLs), simulation techniques, design synthesis, verification methods, and implementation with field programmable gate arrays (FPGAs). Combinational and both the synchronous and asynchronous sequential circuits are studied. Testing and design for testability techniques are emphasized and fault tolerant and fail safe design concepts are introduced. Laboratory projects that enable students gain hands-on experience are required. The projects include complete design flow: design of the system, modeling using HDLs, simulation, synthesis and verification. (Prerequisites: CMPE-160 or CMPE-161 or equivalent courses. Co-requisites: PHYS-212 or PHYS-208 or EEEE-281 or equivalent courses.) Lab 2 (Fall, Spring).
The course covers the important aspects of the design, organization, and performance evaluation of modern computer systems. Topics include computer performance measures, instruction set architecture classification, input/output organization, CPU datapath and control unit design, microprogramming, arithmetic and logic unit design, and the memory hierarchy, including cache levels and virtual memory. (Prerequisites: CMPE-250 or equivalent course.) Lecture 3 (Fall, Spring).
The objective of this course is to present the foundations of reconfigurable computing methodologies from both hardware and software perspectives. Topics covered are: architectures of modern field programmable gate arrays (FPGAs), digital system design methodologies using FPGAs, hardware-software co-design with embedded processors, hardware optimization techniques, system level integration under operating system, dynamic reconfiguration. Laboratory projects in which students will acquire a solid capability of Xilinx CAD tools and FPGA devices are required. The projects include the whole design flow: design of the system, VHDL modeling, software and hardware development, FPGA verification. (Prerequisites: CMPE-260 or equivalent course or graduate standing in the CMPE-MS program.) Studio 3 (Fall).
Embedded Systems Design I
This is an embedded systems architecture and design course. Microprocessor, as well as system level design principles will be analyzed from both a hardware and software perspective. Assembly language and C are used to develop software applications for a 32-bit embedded processor. Application software emphasizes interrupt driven operation and peripheral interfacing. A hardware description language is used to design and debug embedded components for an FPGA-based system. During the course’s laboratory component, students will be design and debug hardware and software systems, evaluate design trade-offs and choose the best design solution, and perform functional and timing analysis of an embedded system. Student must register for BOTH the Lecture and Laboratory components of this course. (Prerequisites: (CPET-253 or (CPET-251 and CPET-252)) and (CPET-343 or (CPET-341 and CPET-342)) with grades of C- or better or equivalent courses.) Lab 2 (Fall).
Embedded Systems Design II
This project-based course is the culmination of the curriculum capstone experience for the computer engineering technology major. This course will be focused around a project that includes product ideation, project/resource management techniques, and best practices; system level specification, modeling, partition, and design; team collaboration and communication; best documentation practices; industry level coding practices; hardware and software co-design methodologies; design reuse and intellectual property creation; design verification and validation; and design sign-off. (Prerequisites: CPET-561 or equivalent course.) Lab 2 (Spring).
Embedded Systems Design
The purpose of this course is to expose students to both the hardware and the software components of a digital embedded system. It focuses on the boundary between hardware and software operations. The elements of microcomputer architecture are presented, including a detailed discussion of the memory, input-output, the central processing unit (CPU) and the busses over which they communicate. C and assembly language level programming concepts are introduced, with an emphasis on the manipulation of microcomputer system elements through software means. Efficient methods for designing and developing C and assembly language programs are presented. Concepts of program controlled input and output are studied in detail and reinforced with extensive hands-on lab exercises involving both software and hardware, hands-on experience. (Prerequisites: EEEE-220 or equivalent course.) Lab 3 (Fall, Spring).
Modern Optics for Engineers
This course provides a broad overview of modern optics in preparation for more advanced courses in the rapidly developing fields of optical fiber communications, image processing, super-resolution imaging, optical properties of materials, and novel optical materials. Topics covered: geometrical optics, propagation of light, diffraction, interferometry, Fourier optics, optical properties of materials, polarization and liquid crystals, and fiber optics. In all topics, light will be viewed as signals that carry information (data) in the time or spatial domain. After taking this course, the students should have a firm foundation in classical optics. (Prerequisites: EEEE-374 or equivalent course and not in EEEE-BS/MS program. Students in EEEE-BS/MS must take 600 or 700 level course.EEEE-374 Pre +not EEEE-BS/MS.) Lecture 3 (Spring).
Signals, Systems, and Transforms
Develops the analytical skills to design, develop, and simulate analog and digital filters, control systems, and advanced electronic circuits such as those used in robotics, digital communications, and wireless systems. Continuous-time and discrete-time linear, time-invariant, casual systems are examined throughout the course. Topics include Fourier series, the Laplace transform, signal sampling, and the z-transform. Advanced circuit analysis techniques include circuit characterization in the s-plane. (Prerequisites: (EEET-125 and EEET-126) or (EEET-121 and EEET-122) or (EEET-215 and EEET-216) and (MATH-211 or MATH-231) or equivalent courses. Co-requisites: EEET-332 or equivalent course.) Lecture 3 (Fall).
Signals, Systems and Transforms Lab
MATLAB is introduced and used extensively to analyze circuits on continuous-time and discrete-time systems. PSPICE is utilized for circuit simulation. (Prerequisites: (EEET-125 and EEET-126) or (EEET-121 and EEET-122) or (EEET-215 and EEET-216) and (MATH-171 or MATH-181 or MATH-181A) or equivalent courses. Corequisites: EEET-331 or equivalent course.) Lab 1 (Fall).
Fiber Optics Technology
This course presents the basic technologies of fiber-optic telecommunications systems including optical fiber, light sources and modulators, photodetectors and receivers, and passive components such as optical mux/demux and couplers. Students will learn the principle of operation of these technologies as well as gain practical hands-on experience in the laboratory. Students will also learn how to design and assess a fiber-optic link impaired by attenuation and dispersion. (Prerequisites: EEET-331 and EEET-332 or equivalent courses.) Lecture 3 (Fall or Spring).
An introduction to the basics of integrated circuit fabrication. The electronic properties of semiconductor materials and basic device structures are discussed, along with fabrication topics including photolithography diffusion and oxidation, ion implantation, and metallization. The laboratory uses a four-level metal gate PMOS process to fabricate an IC chip and provide experience in device design - and layout (CAD), process design, in-process characterization and device testing. Students will understand the basic interaction between process design, device design and device layout. (This course is restricted to EEEE-BS or MCEE-BS students with at least 2nd year standing or with instructor approval.) Lab 3 (Fall, Spring).
This course focuses on the deposition and etching of thin films of conductive and insulating materials for IC fabrication. A thorough overview of vacuum technology is presented to familiarize the student with the challenges of creating and operating in a controlled environment. Physical and Chemical Vapor Deposition (PVD & CVD) are discussed as methods of film deposition. Plasma etching and Chemical Mechanical Planarization (CMP) are studied as methods for selective removal of materials. Applications of these fundamental thin film processes to IC manufacturing are presented. (Prerequisites: MCEE-201 or equivalent course.) Lab 3 (Fall).
Lithography Materials and Processes
Microlithography Materials and Processes covers the chemical aspects of microlithography and resist processes. Fundamentals of polymer technology will be addressed and the chemistry of various resist platforms including novolac, styrene, and acrylate systems will be covered. Double patterning materials will also be studied. Topics include the principles of photoresist materials, including polymer synthesis, photochemistry, processing technologies and methods of process optimization. Also advanced lithographic techniques and materials, including multi-layer techniques for BARC, double patterning, TARC, and next generation materials and processes are applied to optical lithography. (Prerequisites: CHMG-131 and CHMG-141 or equivalent courses.) Lab 3 (Fall).
An advanced course covering the physical aspects of micro- and nano-lithography. Image formation in projection and proximity systems are studied. Makes use of optical concepts as applied to lithographic systems. Fresnel diffraction, Fraunhofer diffraction, and Fourier optics are utilized to understand diffraction-limited imaging processes and optimization. Topics include illumination, lens parameters, image assessment, resolution, phase-shift masking, and resist interactions as well as non-optical systems such as EUV, maskless, e-beam, and nanoimprint. Lithographic systems are designed and optimized through use of modeling and simulation packages. Lab 3 (Spring).
Advanced Concepts in Semiconductor Packaging
The advanced course in semiconductor packaging will provide a thorough coverage of the materials, processes, failure, and reliability of chip level packaging. Specific topics include single-chip, multi-chip, wafer level and 3D stacked packaging, photonic integrated chip (PIC), smaller passives and embedded passive component technology, advanced substrates and microvia technology, solder technologies, metallurgy and joint formation, thermal management, thermal and mechanical behavior of packaging, failure analysis, and reliability testing. This course is cross listed with MFET-656 students may receive credit for MFET-556 or MFET-656, not both. (Prerequisites: MFET-545 or equivalent course. Students cannot take and receive credit for this course if they have taken MFET-656.) Lecture 3 (Spring).
In this course light waves having both amplitude and phase will be described to provide a foundation for understanding key optical phenomena such as interference, diffraction, and propagation. Starting from Maxwell's equations the course advances to the topic of Fourier optics. (Prerequisites: (PHYS-212 or PHYS-209 or PHYS-217) and PHYS-225, PHYS-283, PHYS-320 and (MATH-219 or MATH-221 or MATH-221H) or equivalent courses. Students in the PHYS-BS program are also required to complete PHYS-275 before taking this course.) Lab 3 (Spring).
This course covers the semi-classical theory of the operation of a laser, characteristics and practical aspects of various laser systems, and some applications of lasers in scientific research. (Prerequisites: PHYS-365 or equivalent course. Students in the PHYS-BS program are also required to complete PHYS-275 prior to taking this course.) Lecture 3 (Fall).
Solid State Physics
This course is an introduction to the physics of the solid state including crystal structure, x-ray diffraction by crystals, crystal binding, elastic waves and lattice vibrations, thermal properties, the free electron model of solids, and band theory and its applications. (Prerequisites: PHYS-214 and PHYS-320 or equivalent courses. Students in the PHYS-BS program are also required to complete PHYS-275 prior to taking this course.) Lecture 3 (Fall).
Hardware and Software Design for Cryptographic Applications
The objective of this course is to build knowledge and skills necessary for efficient implementations of cryptographic primitives on reconfigurable hardware. The implementation platform will be a field programmable gate array (FPGA) containing a general purpose processor and additional reconfigurable fabric for implementations of custom hardware accelerators. In the studio format, team projects require design of selected cryptographic primitives followed by comparison and contrast of various implementation alternatives, such as software, custom FPGA hardware, and hybrid hardware-software co-design. Project teams are ideally composed of one Computer Engineering student and one Software Engineering or Computer Science student. Computer Engineering students lead the hardware design portions of each project, and Software Engineering and Computer Science students lead the software development portions. Topics may include binary finite field arithmetic, block ciphers, hash functions, counter mode of operation for block ciphers, public key cryptosystems, hardware/software co-design methodologies with FPGAs, software development and profiling, high level synthesis, on-chip buses, hardware/software interfaces, custom hardware accelerators and side channel attacks. (Prerequisites: CMPE-260 or CMPE-240 or equivalent course or graduate standing in the CMPE-MS program.) Studio 2 (Spring).
Introduction to Artificial Intelligence
An introduction to the theories and algorithms used to create artificial intelligence (AI) systems. Topics include search algorithms, logic, planning, machine learning, and applications from areas such as computer vision, robotics, and natural language processing. Programming assignments are an integral part of the course. (Prerequisites: (CSCI-243 or SWEN-262) and (MATH-251 or STAT-205) or equivalent courses. Students cannot take and receive credit for this course if they have taken CSCI-630.) Lecture 3 (Fall, Spring, Summer).
Principles of Cybersecurity
This course provides a broad introduction to cybersecurity principles and practices, and emphasizes policies and mechanisms for building secure and trusted computer systems. It will cover cybersecurity principles, policies and mechanisms; core knowledge areas of data, software, component, connection, system, human, organizational and societal security; and crosscutting concepts of confidentiality, integrity, availability, risk, adversarial thinking, and systems thinking. Topics in privacy, and legal and ethical aspects will also be emphasized. Presentations, reports and projects are required. This course requires the knowledge of computer science theory and concepts of computer systems. (Prerequisites: CSCI-250 and (CSCI-262 or CSCI-263) or equivalent courses.) Lecture 3 (Spring).
Introduction to Cryptography
This course provides an introduction to cryptography, its mathematical foundations, and its relation to security. It covers classical cryptosystems, private-key cryptosystems (including DES and AES), hashing and public-key cryptosystems (including RSA). The course also provides an introduction to data integrity and authentication. (Prerequisites: (CSCI-243 or SWEN-262 or CSEC-202) and (MATH-190 or MATH-200) or equivalent courses.) Lecture 3 (Fall, Spring, Summer).
Introduction to Machine Learning
This course offers an introduction to supervised machine learning theories and algorithms, and their application to classification and regression tasks. Topics include: Mathematical background of machine learning (e.g. statistical analysis and visualization of data), neural models (e.g. Convolutional Neural Networks, Recurrent Neural Networks), probabilistic graphical models (e.g. Bayesian networks, Markov models), and reinforcement learning. Programming assignments are required. (Prerequisites: CSCI-630 or CSCI-331 or equivalent course. Students may not take and receive credit for CSCI-635 and CSCI-335.) Lecture 3 (Fall, Spring).
Codes and Ciphers
This course will introduce, explain and employ both the classical and modern basic techniques of cryptography. Topics will include the Vignère cipher, affine ciphers, Hill ciphers, one-time pad encryption, Enigma, public key encryption schemes (RSA, Diffie-Hellman, El-Gamal, elliptic curves), and hash functions. The course will include an introduction to algebraic structures and number theoretic tools used in cryptography. (Prerequisites: MATH-190 or MATH-200 or equivalent course.) Lecture 3 (Spring).
Photonic Integrated Circuits
This course focuses on photonic integrated circuits (PICs) - an emerging technology where photonic chips (consisting of waveguides, lasers, detectors, modulators and more) are manufactured using integrated circuit technology and closely integrated with microelectronics. The circuits are finding applications in high performance communication, computing and sensing systems. The technology is rapidly growing in complexity and demand, and as the advantages of using photons are realized and the manufacturing hurdles are overcome, photonic circuits will become ubiquitous in future microsystems. Course topics include, fundamental concepts (waveguides, interference, light-matter interaction), PIC component modeling, schematic and layout driven design, PIC fabrication techniques, and PIC testing to round out the students understanding of integrated photonics. (Prerequisite: EEEE-374 or MCEE-320 or equivalent course or graduate standing in MCSE-PHD or ENGR-PHD or EEEE-MS or CMPE-MS or MCEE-MS.) Lecture 3 (Spring).
Integrated Optical Devices and Systems
This course discusses basic goals, principles and techniques of integrated optical devices and systems, and explains how the various optoelectronic devices of an integrated optical system operate and how they are integrated into a system. Emphasis in this course will be on planar passive optical devices. Topics include optical waveguides, optical couplers, micro-optical resonators, surface plasmons, photonic crystals, modulators, design tools and fabrication techniques, and the applications of optical integrated circuits. Some of the current state-of-the-art devices and systems will be investigated by reference to journal articles. Lecture 3 (Fall).
* The remaining four courses must come from at least two of the four focus areas.