PROGRAM

Quantum Engineering is an interdisciplinary program that seeks to equip students for careers in emerging technologies based on quantum entanglement. It encompasses a wide range of disciplines that includes physics, materials science, computer science, electrical engineering, and mathematics, and is necessarily a collaborative effort among many Mines departments.
 

Two Master’s degrees and one professional certificate are offered. For both degrees and the professional certificate, Quantum Engineering has two tracks.

  • Quantum Engineering Hardware (QEH) track focuses on experimental techniques relevant to quantum technology.
  • Quantum Engineering Software (QES) track focuses on theory, algorithms, and simulation.
A track must be chosen to complete the program, but courses from both tracks may be taken provided that the prerequisite requirements are met.
 
Beginning this Fall 2021 semester, an interdisciplinary minor in Quantum Engineering will be offered. Details may be found on the Minor tab and in the course catalog.

Course InformationHours
Software Track (QES)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

CSCI581 Quantum Programming

CSCI581. Quantum Programming. This course serves as an introduction to programming quantum computers. Students will receive an in depth education in quantum algorithms and their design, and then break into teams to learn the API of a commercially available quantum computing system. They will use this system to write and test simple quantum algorithms, and debug their code to improve its performance against noise and other error sources. Prerequisite: PHGN519.
3

PHGN545 Quantum Many-Body Physics

PHGN545. This course offers an introduction to quantum many-body physics in a modern approach from the perspectives of quantum information science. Starting from the difference between classical and quantum correlations, this course introduces composite quantum systems and the concept of entanglement as the central theme in quantum many-body physics. A system of many spin-1/2s is then presented as the paradigmatic quantum many-body system, opening the realm of quantum phase transitions and quantum simulation experiments. Next, systems of non-interacting bosons or fermions are examined using the powerful canonical transformation. To understand what happens when particles interact, the well-known Hubbard model is brought in, together with its importance in quantum materials. Finally, topological ordered quantum matter is introduced and explained via the structure of quantum entanglement. The application of topological order to quantum computing will also be mentioned.
3
Elective #13
Elective #23
Elective #33
Elective #43
Thesis Credits9
30 Total
Hardware Track (QEH)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

PHGN435 Interdisciplinary Microelectronics Processing Laboratory/PHGN535 Interdisciplinary Silicon Processing Laboratory

PHGN435. INTERDISCIPLINARY MICROELECTRONICS PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN535, Application of science and engineering principles to the design, fabrication, and testing of microelectronic devices. Emphasis on specific unit operations and the interrelation among processing steps. Prerequisites: Senior standing in PHGN, CHGN, MTGN, or EGGN. 1.5 hours lecture, 4 hours lab; 3 semester hours.

PHGN535. INTERDISCIPLINARY SILICON PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN435, (II) Explores the application of science and engineering principles to the fabrication and testing of microelectronic devices with emphasis on specific unit operations and interrelation among processing steps. Teams work together to fabricate, test, and optimize simple devices. Prerequisite: none. 1 hour lecture, 4 hours lab; 3 semester hours.
3

EENG532 Low Temperature Microwave Measurements for Quantum Applications

EENG532. Low Temperature Microwave Measurements for Quantum Applications. The goal of the course is to provide hands on training in high-frequency, low-temperature measurements which are requisite for quantum information applications. This course introduces the fundamentals of high-frequency measurements, the latest techniques for accuracy-enhanced automated microwave measurements, low-temperature measurement techniques, low noise measurements, and common devices used in quantum information. The course will have three modules. The first module, basics of electronic measurements, will include chip layout, power measurements, ground loop testing, impedance measurements, noise fundamentals, cable and device fabrication and care. The second module, high frequency measurements, will include measurements of basic scattering parameters, accuracy enhancement and calibration, transmission line, amplifier, and oscillator characterization including noise measurements. The third module, low-temperature measurements, will cover critical parameters for superconductors and Josephson junctions, measurements of superconducting resonators, characterization of low-temperature electronic elements including amplifiers. At the end of this course the students will know how to use network analyzers, spectrum analyzers, cryostats, the software Eagle for chip design, amplifiers, and filters. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course.
3
Elective #13
Elective #23
Elective #33
Elective #43
Thesis Credits9
30 Total

Course InformationHours
Software Track (QES)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

CSCI581 Quantum Programming

CSCI581. Quantum Programming. This course serves as an introduction to programming quantum computers. Students will receive an in depth education in quantum algorithms and their design, and then break into teams to learn the API of a commercially available quantum computing system. They will use this system to write and test simple quantum algorithms, and debug their code to improve its performance against noise and other error sources. Prerequisite: PHGN519.
3

PHGN545 Quantum Many-Body Physics

PHGN545. This course offers an introduction to quantum many-body physics in a modern approach from the perspectives of quantum information science. Starting from the difference between classical and quantum correlations, this course introduces composite quantum systems and the concept of entanglement as the central theme in quantum many-body physics. A system of many spin-1/2s is then presented as the paradigmatic quantum many-body system, opening the realm of quantum phase transitions and quantum simulation experiments. Next, systems of non-interacting bosons or fermions are examined using the powerful canonical transformation. To understand what happens when particles interact, the well-known Hubbard model is brought in, together with its importance in quantum materials. Finally, topological ordered quantum matter is introduced and explained via the structure of quantum entanglement. The application of topological order to quantum computing will also be mentioned.
3
Elective #13
Elective #23
Elective #33
Elective #43
Elective #53
Elective #63
Elective #73
30 Total
Hardware Track (QEH)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

PHGN435 Interdisciplinary Microelectronics Processing Laboratory/PHGN535 Interdisciplinary Silicon Processing Laboratory

PHGN435. INTERDISCIPLINARY MICROELECTRONICS PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN535, Application of science and engineering principles to the design, fabrication, and testing of microelectronic devices. Emphasis on specific unit operations and the interrelation among processing steps. Prerequisites: Senior standing in PHGN, CHGN, MTGN, or EGGN. 1.5 hours lecture, 4 hours lab; 3 semester hours.

PHGN535. INTERDISCIPLINARY SILICON PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN435, (II) Explores the application of science and engineering principles to the fabrication and testing of microelectronic devices with emphasis on specific unit operations and interrelation among processing steps. Teams work together to fabricate, test, and optimize simple devices. Prerequisite: none. 1 hour lecture, 4 hours lab; 3 semester hours.
3

EENG532 Low Temperature Microwave Measurements for Quantum Applications

EENG532. Low Temperature Microwave Measurements for Quantum Applications. The goal of the course is to provide hands on training in high-frequency, low-temperature measurements which are requisite for quantum information applications. This course introduces the fundamentals of high-frequency measurements, the latest techniques for accuracy-enhanced automated microwave measurements, low-temperature measurement techniques, low noise measurements, and common devices used in quantum information. The course will have three modules. The first module, basics of electronic measurements, will include chip layout, power measurements, ground loop testing, impedance measurements, noise fundamentals, cable and device fabrication and care. The second module, high frequency measurements, will include measurements of basic scattering parameters, accuracy enhancement and calibration, transmission line, amplifier, and oscillator characterization including noise measurements. The third module, low-temperature measurements, will cover critical parameters for superconductors and Josephson junctions, measurements of superconducting resonators, characterization of low-temperature electronic elements including amplifiers. At the end of this course the students will know how to use network analyzers, spectrum analyzers, cryostats, the software Eagle for chip design, amplifiers, and filters. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course.
3
Elective #13
Elective #23
Elective #33
Elective #43
Elective #53
Elective #63
Elective #73
30 Total

Course InformationHours
Software Track (QES)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

CSCI581 Quantum Programming

CSCI581. Quantum Programming. This course serves as an introduction to programming quantum computers. Students will receive an in depth education in quantum algorithms and their design, and then break into teams to learn the API of a commercially available quantum computing system. They will use this system to write and test simple quantum algorithms, and debug their code to improve its performance against noise and other error sources. Prerequisite: PHGN519.
3

PHGN545 Quantum Many-Body Physics

PHGN545. This course offers an introduction to quantum many-body physics in a modern approach from the perspectives of quantum information science. Starting from the difference between classical and quantum correlations, this course introduces composite quantum systems and the concept of entanglement as the central theme in quantum many-body physics. A system of many spin-1/2s is then presented as the paradigmatic quantum many-body system, opening the realm of quantum phase transitions and quantum simulation experiments. Next, systems of non-interacting bosons or fermions are examined using the powerful canonical transformation. To understand what happens when particles interact, the well-known Hubbard model is brought in, together with its importance in quantum materials. Finally, topological ordered quantum matter is introduced and explained via the structure of quantum entanglement. The application of topological order to quantum computing will also be mentioned.
3
Elective3
12 Total
Hardware Track (QEH)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

PHGN435 Interdisciplinary Microelectronics Processing Laboratory/PHGN535 Interdisciplinary Silicon Processing Laboratory

PHGN435. INTERDISCIPLINARY MICROELECTRONICS PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN535, Application of science and engineering principles to the design, fabrication, and testing of microelectronic devices. Emphasis on specific unit operations and the interrelation among processing steps. Prerequisites: Senior standing in PHGN, CHGN, MTGN, or EGGN. 1.5 hours lecture, 4 hours lab; 3 semester hours.

PHGN535. INTERDISCIPLINARY SILICON PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN435, (II) Explores the application of science and engineering principles to the fabrication and testing of microelectronic devices with emphasis on specific unit operations and interrelation among processing steps. Teams work together to fabricate, test, and optimize simple devices. Prerequisite: none. 1 hour lecture, 4 hours lab; 3 semester hours.
3

EENG532 Low Temperature Microwave Measurements for Quantum Applications

EENG532. Low Temperature Microwave Measurements for Quantum Applications. The goal of the course is to provide hands on training in high-frequency, low-temperature measurements which are requisite for quantum information applications. This course introduces the fundamentals of high-frequency measurements, the latest techniques for accuracy-enhanced automated microwave measurements, low-temperature measurement techniques, low noise measurements, and common devices used in quantum information. The course will have three modules. The first module, basics of electronic measurements, will include chip layout, power measurements, ground loop testing, impedance measurements, noise fundamentals, cable and device fabrication and care. The second module, high frequency measurements, will include measurements of basic scattering parameters, accuracy enhancement and calibration, transmission line, amplifier, and oscillator characterization including noise measurements. The third module, low-temperature measurements, will cover critical parameters for superconductors and Josephson junctions, measurements of superconducting resonators, characterization of low-temperature electronic elements including amplifiers. At the end of this course the students will know how to use network analyzers, spectrum analyzers, cryostats, the software Eagle for chip design, amplifiers, and filters. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course.
3
Elective3
12 Total

Beyond the required courses for each track, students will take one or more additional electives chosen from an extensive list of relevant courses (courses meant for the other track can also be used for these electives). This list, which is continuously updated as the curricula of the participating departments evolves, is comprised of:

Course Information, 3 credit hours each course
Physics

PHGN440 Solid-State Physics/PHGN441 Solid State Physics Applications and Phenomena

PHGN440also a materials course. SOLID STATE PHYSICS. 3.0 SEMESTER HRS. An elementary study of the properties of solids including crystalline structure and its determination, lattice vibrations, electrons in metals, and semiconductors. (Graduate students in physics may register only for PHGN440.) Prerequisite: PHGN320. 3 hours lecture; 3 semester hours.

PHGN441also a materials course. SOLID STATE PHYSICS APPLICATIONS AND PHENOMENA.3.0 SEMESTER HRS. Continuation of PHGN440/ MLGN502 with an emphasis on applications of the principles of solid state physics to practical properties of materials including: optical properties, superconductivity, dielectric properties, magnetism, noncrystalline structure, and interfaces. (Graduate students in physics may register only for PHGN441.) Prerequisite: PHGN440 or MLGN502. 3 hours lecture; 3 semester hours.

PHGN466/566 Modern Optical Engineering

PHGN466 MODERN OPTICAL ENGINEERING. 3.0 SEMESTER HRS. Provides students with a comprehensive working knowledge of optical system design that is sufficient to address optical problems found in their respective disciplines. Topics include paraxial optics, imaging, aberration analysis, use of commercial ray tracing and optimization, diffraction, linear systems and optical transfer functions, detectors and optical system examples. Prerequisite: PHGN462. 3 hours lecture; 3 semester hours.

PHGN566. MODERN OPTICAL ENGINEERING. 3.0 SEMESTER HRS. Provides students with a comprehensive working knowledge of optical system design that is sufficient to address optical problems found in their respective disciplines. Topics include paraxial optics, imaging, aberration analysis, use of commercial ray tracing and optimazation, diffraction, linear systems and optical transfer functions, detectors, and optical system examples. Prerequisite: PHGN462. 3 hours lecture; 3 semester hours.

PHGN480 Laser Physics

PHGN480. LASER PHYSICS. 3.0 SEMESTER HRS.(I) Theory and application of the following: Interaction of light with atoms: absorption, gain, rate equations and line broadening. Propagation, control and measurement of light waves: Gaussian beams, optical resonators and wave guides, interferometers. Laser design and operation: pumping, oscillation, and dynamics (Q-switching and mode-locking). Introduction to ultrafast optics. Laboratory: alignment and characterization of laser systems. Prerequisites: PHGN320. Co-requisites: PHGN462. 3 hours lecture; 3 semester hours.

PHGN520/521 Quantum Mechanics

PHGN520. QUANTUM MECHANICS I. 3.0 SEMESTER HRS. (II) Schroedinger equation, uncertainty, change of representation, one-dimensonal problems, axioms for state vectors and operators, matrix mechanics, uncertainty relations, time-independent perturbation theory, time-dependent perturbations, harmonic oscillator, angular momentum; semiclassical methods, variational methods, two-level system, sudden and adiabatic changes, applications. Prerequisite: PHGN511 and PHGN320 or equivalent. 3 hours lecture; 3 semester hours.

PHGN521. QUANTUM MECHANICS II. 3.0 SEMESTER HRS. (I) Review of angular momentum, central potentials and applications. Spin; rotations in quantum mechanics. Formal scattering theory, Born series, partial wave analysis. Addition of angular momenta, Wigner-Eckart theorem, selection rules, identical particles. Prerequisite: PHGN520. 3 hours lecture; 3 semester hours.

PHGN530 Statistical Mechanics

PHGN530. STATISTICAL MECHANICS. 3.0 SEMESTER HRS. (I) Review of thermodynamics; equilibrium and stability; statistical operator and ensemblesl ideal systems; phase transitions; non-equilibrium systems. Prerequisite: PHGN341 or equivalent and PHGN520. Co-requisite: PHGN521. 3 hours lecture; 3 semester hours.

PHGN550 Physics and Technology

PHGN550. NANOSCALE PHYSICS AND TECHNOLOGY. 3.0 SEMESTER HRS. An introduction to the basic physics concepts involved in nanoscale phenomena, processing methods resulting in engineered nanostructures, and the design and operation of novel structures and devices which take advantage of nanoscale effects. Students will become familiar with interdisciplinary aspects of nanotechnology, as well as with current nanoscience developments described in the literature. Prerequisites: PHGN320, PHGN341, co-requisite: PHGN462. 3 hours lecture; 3 semester hours.

PHGN585 Nonlinear Optics

PHGN585. NONLINEAR OPTICS. 3.0 SEMESTER HRS. An exploration of the nonlinear response of a medium (semiclassical and quantum descriptions) and nonlinear wave mixing and propagation. Analytic and numeric techniques to treat nonlinear dynamics are developed. Applications to devices and modern research areas are discussed, including harmonic and parametric wave modulation, phase conjugation, electro-optic modulation. Prerequiste: PHGN462 or equivalent, PHGN520. 3 hours lecture; 3 semester hours.
Computer Science

CSCI542 Simulation

CSCI542. SIMULATION. 3.0 Semester Hrs. Equivalent with MACS542, (I) Advanced study of computational and mathematical techniques for modeling, simulating, and analyzing the performance of various systems. Simulation permits the evaluation of performance prior to the implementation of a system; it permits the comparison of various operational alternatives without perturbing the real system. Topics to be covered include simulation techniques, random number generation, Monte Carlo simulations, discrete and continuous stochastic models, and point/interval estimation. Offered every other year. Prerequisite: CSCI 262 (or equivalent) and MATH 323 (or MATH 530 or equivalent). 3 hours lecture; 3 semester hours.

CSCI563 Parallel Computing

CSCI563. PARALLEL COMPUTING FOR SCIENTISTS AND ENGINEERS. 3.0 Semester Hrs.(I) Students are taught how to use parallel computing to solve complex scientific problems. They learn how to develop parallel programs, how to analyze their performance, and how to optimize program performance. The course covers the classification of parallel computers, shared memory versus distributed memory machines, software issues, and hardware issues in parallel computing. Students write programs for state of the art high performance supercomputers, which are accessed over the network. Prerequisite: Programming experience in C. 3 hours lecture; 3 semester hours.

CSCI564 Computer Architecture

CSCI564. ADVANCED COMPUTER ARCHITECTURE. 3.0 Semester Hrs. The objective of this class is to gain a detailed understanding about the options available to a computer architect when designing a computer system along with quantitative justifications for the options. All aspects of modern computer architectures including instruction sets, processor design, memory system design, storage system design, multiprocessors, and software approaches will be discussed. Prerequisite: CSCI341. 3 hours lecture; 3 semester hours.

CSCI571 Artificial Intelligence

CSCI571. ARTIFICIAL INTELLIGENCE. 3.0 Semester Hrs. (I) Artificial Intelligence (AI) is the subfield of computer science that studies how to automate tasks for which people currently exhibit superior performance over computers. Historically, AI has studied problems such as machine learning, language understanding, game playing, planning, robotics, and machine vision. AI techniques include those for uncertainty management, automated theorem proving, heuristic search, neural networks, and simulation of expert performance in specialized domains like medical diagnosis. This course provides an overview of the field of Artificial Intelligence. Particular attention will be paid to learning the LISP language for AI programming. Prerequisite: CSCI262. 3 hours lecture; 3 semester hours.

CSCI474 Introduction to Cryptography

CSCI474. INTRODUCTION TO CRYPTOGRAPHY. 3.0 SEMESTER HRS. Equivalent with MATH474, (II) This course is primarily oriented towards the mathematical aspects of cryptography, but is also closely related to practical and theoretical issues of computer security. The course provides mathematical background required for cryptography, including relevant aspects of number theory and mathematical statistics. The following aspects of cryptography will be covered: symmetric and asymmetric encryption, computational number theory, quantum encryption, RSA and discrete log systems, SHA, steganography, chaotic and pseudo-random sequences, message authentication, digital signatures, key distribution and key management, and block ciphers. Many practical approaches and most commonly used techniques will be considered and illustrated with real-life examples. Prerequisites: CSCI262, CSCI358, MATH334 or MATH335 or MATH201. 3 hours lecture; 3 semester hours.

CSCI575 Machine Learning

CSCI575. MACHINE LEARNING. 3.0 Semester Hrs. Equivalent with MACS575, (II) The goal of machine learning research is to build computer systems that learn from experience and that adapt to their environments. Machine learning systems do not have to be programmed by humans to solve a problem; instead, they essentially program themselves based on examples of how they should behave, or based on trial and error experience trying to solve the problem. This course will focus on the methods that have proven valuable and successful in practical applications. The course will also contrast the various methods, with the aim of explaining the situations in which each is most appropriate. Prerequisites: CSCI262 and MATH201. 3 hours lecture; 3 semester hours.

CSCI580 High-Performance Computing

CSCI580. ADVANCED HIGH PERFORMANCE COMPUTING. 3.0 Semester Hrs. This course provides students with knowledge of the fundamental concepts of high performance computing as well as hands-on experience with the core technology in the field. The objective of this class is to understand how to achieve high performance on a wide range of computational platforms. Topics will include sequential computers including memory hierarchies, shared memory computers and multicore, distributed memory computers, graphical processing units (GPUs), cloud and grid computing, threads, OpenMP, message passing (MPI), CUDA (for GPUs), parallel file systems, and scientific applications. 3 hours lecture; 3 semester hours.

CSCI586 Fault Tolerant Computing

CSCI586. FAULT TOLERANT COMPUTING. 3.0 Semester Hrs.
Electrical Engineering

EENG509 Sparse Signal Processing

EENG509. SPARSE SIGNAL PROCESSING. 3.0 Semester Hrs. Equivalent with EGGN509, (II) This course presents a mathematical tour of sparse signal representations and their applications in modern signal processing. The classical Fourier transform and traditional digital signal processing techniques are extended to enable various types of computational harmonic analysis. Topics covered include time-frequency and wavelet analysis, filter banks, nonlinear approximation of functions, compression, signal restoration, and compressive sensing. Prerequisites: EENG411 and EENG515. 3 hours lecture; 3 semester hours.

EENG417/517 Advanced Control Systems

EENG417. MODERN CONTROL DESIGN. 3.0 SEMESTER HRS. Equivalent with EGGN417, (I) Control system design with an emphasis on observer-based methods, from initial open-loop experiments to final implementation. The course begins with an overview of feedback control design technique from the frequency domain perspective, including sensitivity and fundamental limitations. State space realization theory is introduced, and system identification methods for parameter estimation are introduced. Computerbased methods for control system design are presented. Prerequisite: EENG307. 3 lecture hours, 3 semester hours.

517. THEORY AND DESIGN OF ADVANCED CONTROL SYSTEMS. 3.0 Semester Hrs. Equivalent with EGGN517, (II) This course will introduce and study the theory and design of multivariable and nonlinear control systems. Students will learn to design multivariable controllers that are both optimal and robust, using tools such as state space and transfer matrix models, nonlinear analysis, optimal estimator and controller design, and multi-loop controller synthesis. Spring semester of even years. Prerequisites: EENG417. 3 hours lecture; 3 semester hours.

EENG526 Advanced Electromagnetics

EENG526. ADVANCED ELECTROMAGNETICS. 3.0 SEMESTER HRS. (II) In this course the fundamental theorems of electromagnetics are developed rigorously. Wave solutions are developed in Cartesian, cylindrical, and spherical coordinate systems for bounded and unbounded regions. Prerequisite: EENG386. 3 hours lecture; 3 semester hours.

EENG528 Computational Electromagnetics

EENG528. COMPUTATIONAL ELECTROMAGNETICS. 3.0 Semester Hrs. (II) In this course the fundamental theorems of electromagnetics are developed rigorously. Wave solutions are developed in Cartesian, cylindrical, and spherical coordinate systems for bounded and unbounded regions. Prerequisite: EENG386. 3 hours lecture; 3 semester hours.

EENG529 Active RF and Microwave Devices

EENG529. ACTIVE RF & MICROWAVE DEVICES. 3.0 Semester Hrs. (II) This course introduces the basics of active radio-frequency (RF) and microwave circuits and devices which are the building blocks of modern communication and radar systems. The topics that will be studied are RF and microwave circuit components, resonant circuits, matching networks, noise in active circuits, switches, RF and microwave transistors and amplifiers. Additionally, mixers, oscillators, transceiver architectures, RF and monolithic microwave integrated circuits (RFICs and MMICs) will be introduced. Moreover, students will learn how to model active devices using professional CAD software, how to fabricate printed active microwave devices, how a vector network analyzer (VNA) operates, and how to measure active RF and microwave devices using VNAs. Prerequisites: EEBG385. 3 hours lecture; 3 semester hours.

EENG530 Passive RF and Microwave Devices

EENG530. PASSIVE RF & MICROWAVE DEVICES. 3.0 Semester Hrs. (I) This course introduces the basics of passive radio-frequency (RF) and microwave circuits and devices which are the building blocks of modern communication and radar systems. The topics that will be studied are microwave transmission lines and waveguides, microwave network theory, microwave resonators, power dividers, directional couplers, hybrids, RF/microwave filters, and phase shifters. Students will also learn how to design and analyze passive microwave devices using professional CAD software. Moreover, students will learn how to fabricate printed passive microwave devices and test them using a vector network analyzer. Prerequisites: EENG386. 3 hours lecture; 3 semester hours.

EENG617 Intelligent Control Systems

EENG617. INTELLIGENT CONTROL SYSTEMS. 3.0 Semester Hrs. Equivalent with EGGN617, Fundamental issues related to the design on intelligent control systems are described. Neural networks analysis for engi neering systems are presented. Neural-based learning, estimation, and identification of dynamical systems are described. Qualitative control system analysis using fuzzy logic is presented. Fuzzy mathematics design of rule-based control, and integrated human-machine intelligent control systems are covered. Real-life problems from different engineering systems are analyzed. Prerequisite: EENG517. 3 hours lecture; 3 semester hours. Taught on demand.

EENG618 Nonlinear and Adaptive Control

EENG618. NONLINEAR AND ADAPTIVE CONTROL. 3.0 Semester Hrs. Equivalent with EGGN618, This course presents a comprehensive exposition of the theory of nonlinear dynamical systems and the applications of this theory to adaptive control. It will focus on (1) methods of characterizing and understanding the behavior of systems that can be described by nonlinear ordinary differential equations, (2) methods for designing controllers for such systems, (3) an introduction to the topic of system identification, and (4) study of the primary techniques in adaptive control, including model-reference adaptive control and model predictive control. Prerequisite: EENG517. 3 hours lecture; 3 semester hours. Spring, even numbered years.
Metallurgy and Material Engineering

MTGN456 Electron Microscopy

MTGN456. ELECTRON MICROSCOPY. 2.0 Semester Hrs. (I, II, S) Introduction to electron optics and the design and application of transmission and scanning electron microscopes. Interpretation of images produced by various contrast mechanisms. Electron diffraction analysis and the indexing of electron diffraction patterns. Prerequisites: MTGN211 or MTGN311. Corequisite: MTGN456L. 2 hours lecture; 2 semester hours.

MTGN505 Crystallography and Diffraction

MTGN505. CRYSTALLOGRAPHY AND DIFFRACTION. 3.0 SEMESTER HRS. (I) Introduction to point symmetry operations, crystal systems, Bravais lattices, point groups, space groups, Laue classes, stereographic projections, reciprocal lattice and Ewald sphere constructions, the new International Tables for Crystallography, and, finally, how certain properties correlate with symmetry. Subsequent to the crystallography portion, the course will move into the area of diffraction and will consider the primary diffraction techniques (x-rays, electrons and neutrons) used to determine the crystal structure of materials. Other applications of diffraction such as texture and residual stress will also be considered. Prerequisites: Graduate or Senior in good standing. 3 hours lecture, 3 semester hours.
Materials Science

MLGN593 Bonding, Structure, and Crystallography

MLGN593. BONDING, STRUCTURE, AND CRYSTALLOGRAPHY. 3.0 SEMESTER HRS. (I) This course will be an overview of condensed matter structure from the atomic scale to the mesoscale. Students will gain a perspective on electronic structure as it relates to bonding, long range order as it relates to crystallography and amorphous structures, and extend these ideas to nanostructure and microstructure. Examples relating to each hierarchy of structure will be stressed, especially as they relate to reactivity, mechanical properties, and electronic and optical properties. Prerequisites: A 300 level or higher course in thermodynamics. 3 semester hours.
Applied Mathematics and Statistics

MATH408 Computational Differential Equations

MATH408. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS. 3.0 Semester Hrs. (I) This course is designed to introduce computational methods to scientists and engineers for developing differential equations based computer models. Students in this course will be taught various numerical methods and programming techniques to simulate systems of nonlinear ordinary differential equations. Emphasis will be on implementation of various numerical and approximation methods to efficiently simulate several systems of nonlinear differential equations. Prerequisite: MATH307. 3 hours lecture, 3 semester hours.

MATH436 Advanced Statistical Modeling

MATH436. ADVANCED STATISTICAL MODELING. 3.0 Semester Hrs. (II) Modern methods for constructing and evaluating statistical models. Topics include generalized linear models, generalized additive models, hierarchical Bayes methods, and resampling methods. Time series models, including moving average, autoregressive, and ARIMA models, estimation and forecasting, confidence intervals. Prerequisites: MATH335 and MATH424. 3 hours lecture; 3 semester hours.

MATH438 Stochastic Models

MATH438. STOCHASTIC MODELS. 3.0 Semester Hrs. (II) An introduction to stochastic models applicable to problems in engineering, physical science, economics, and operations research. Markov chains in discrete and continuous time, Poisson processes, and topics in queuing, reliability, and renewal theory. Prerequisite: MATH334. 3 hours lecture, 3 semester hours.

MATH510 and Dynamical Systems

MATH510. ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS. 3.0 Semester Hrs. Equivalent with MACS510, (I) Topics to be covered: basic existence and uniqueness theory, systems of equations, stability, differential inequalities, Poincare-Bendixon theory, linearization. Other topics from: Hamiltonian systems, periodic and almost periodic systems, integral manifolds, Lyapunov functions, bifurcations, homoclinic points and chaos theory. Offered even years. Prerequisite: (MATH225 or MATH235) and (MATH332 or MATH342). 3 hours lecture; 3 semester hours.

MATH551 Computational Linear Algebra

MATH551. COMPUTATIONAL LINEAR ALGEBRA. 3.0 Semester Hrs. Equivalent with MACS551, (II) Numerical analysis of algorithms for solving linear systems of equations, least squares methods, the symmetric eigenproblem, singular value decomposition, conjugate gradient iteration. Modification of algorithms to fit the architecture. Error analysis, existing software packages. Prerequisites: MATH332, CSCI407/MATH407. 3 hours lecture; 3 semester hours.

The interdisciplinary minor in Quantum Engineering requires 18 credit hours.

QE minor students will be required to take Honors Linear Algebra (MATH342) or Linear Algebra (MATH332) and three of the following courses: Quantum Programming (CSCI481/CSCI581), Low Temperature Microwave Measurement (EENG432/EENG532), Quantum Many-Body Physics (PHGN441), Microelectronics Processing (PHGN435), and Fundamentals of Quantum Information (PHYS519).

Students may select an additional 2 courses from the list above, or from the list in the course catalog, to further increase specialization.

As with many other graduate programs, students enrolled in Mines’ combined undergraduate/graduate program (meaning uninterrupted registration from the time the student earns a Mines undergraduate degree to the time the student begins a Mines graduate degree) may double count up to six hours of credits which were used in fulfilling the requirements of their undergraduate degree at Mines, towards their quantum engineering MS degree. Any 400+ level courses that count towards the undergraduate degree requirements as “Elective Coursework” or any 500+ level course, may be used for the purposes of double counting at the discretion of the graduate advisor. These courses must have been passed with a “B-” or better, not be substitutes for required coursework, and meet all other University, Department, Division, and Program requirements for graduate credit.
BS Electrical Engineering / MS Quantum Engineering (please consult with your advisor)
REGISTRATION REQUIREMENTS FOR COMBINED STUDENTS

Q. Are GRE scores required to apply to the Quantum Engineering (QE) Master’s program?
A. No, GRE scores are not required for either the QE Master’s Thesis or QE Master’s Non-Thesis. Submission of GRE scores is entirely optional.

Q. To whom should I submit my academic credentials?
A. Please submit all academic credentials only via the online application.

Q. Are teaching and research assistantships available?
A. Yes, teaching and research assistantships are available to qualified MS and PhD candidates in Mines’ interdisciplinary programs.

Q. Does Mines offer a Quantum Engineering PhD?
A. No. Currently PhDs go only through the QE constituent departments.

Q. Does Mines offer a Quantum Engineering Minor?
A. Yes, beginning with the Fall 2021 semester.

Q. Would it be possible to schedule a Zoom conference to discuss the program?
A. Yes, you may schedule a Zoom meeting with Carolyn Freedman, the Interdisciplinary Graduate Programs Manager, for advice on the application process and the combined program.

Q. What types of courses should I take as an undergraduate that would allow myself to be viewed most favorably for admission to the Quantum Engineering program?
A. A science or engineering degree and successful completion of college-level linear algebra are required for admission. Successful completion of a number of elective courses is required for the QE MS Thesis, MS Non-Thesis, and Graduate Certificate options. Completion of prerequisites, or comparable courses, for the electives that you intend to take, prior to entering the program, is recommended. Please see the Electives tab of this document for information on the various elective courses including prerequisites.

For more information about admission to our program, application instructions, deadlines, selection criteria, and other aspects of the process, please see the Quantum Engineering Program Overview* page, refer to the FAQs and Grad Links tabs of this document, and/or contact us at quantum@mines.edu.

You may also schedule a Zoom meeting with Carolyn Freedman, the Interdisciplinary Graduate Programs Manager, for advice on the application process and the combined program.

Please submit credentials only via the online application.

*The information regarding GRE scores for the Master of Science Thesis option is incorrect. GRE scores are not required for admission to this program.

Quantum Engineering is an interdisciplinary program that seeks to equip students for careers in emerging technologies based on quantum entanglement. It encompasses a wide range of disciplines that includes physics, materials science, computer science, electrical engineering, and mathematics, and is necessarily a collaborative effort among many Mines departments.

Two Master’s degrees and one professional certificate are offered. For both degrees and the professional certificate, Quantum Engineering has two tracks.

  • Quantum Engineering Hardware (QEH) track focuses on experimental techniques relevant to quantum technology.
  • Quantum Engineering Software (QES) track focuses on theory, algorithms, and simulation.

A track must be chosen to complete the program, but courses from both tracks may be taken provided that the prerequisite requirements are met.

Beginning this Fall 2021 semester, an interdisciplinary minor in Quantum Engineering will be offered. Details may be found on the Minor tab and in the course catalog.

Course InformationHours
Software Track (QES)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

CSCI581 Quantum Programming

CSCI581. Quantum Programming. This course serves as an introduction to programming quantum computers. Students will receive an in depth education in quantum algorithms and their design, and then break into teams to learn the API of a commercially available quantum computing system. They will use this system to write and test simple quantum algorithms, and debug their code to improve its performance against noise and other error sources. Prerequisite: PHGN519.
3

PHGN545 Quantum Many-Body Physics

PHGN545. This course offers an introduction to quantum many-body physics in a modern approach from the perspectives of quantum information science. Starting from the difference between classical and quantum correlations, this course introduces composite quantum systems and the concept of entanglement as the central theme in quantum many-body physics. A system of many spin-1/2s is then presented as the paradigmatic quantum many-body system, opening the realm of quantum phase transitions and quantum simulation experiments. Next, systems of non-interacting bosons or fermions are examined using the powerful canonical transformation. To understand what happens when particles interact, the well-known Hubbard model is brought in, together with its importance in quantum materials. Finally, topological ordered quantum matter is introduced and explained via the structure of quantum entanglement. The application of topological order to quantum computing will also be mentioned.
3
Elective #13
Elective #23
Elective #33
Elective #43
Thesis Credits9
30 Total
Hardware Track (QEH)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

PHGN435 Interdisciplinary Microelectronics Processing Laboratory/PHGN535 Interdisciplinary Silicon Processing Laboratory

PHGN435. INTERDISCIPLINARY MICROELECTRONICS PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN535, Application of science and engineering principles to the design, fabrication, and testing of microelectronic devices. Emphasis on specific unit operations and the interrelation among processing steps. Prerequisites: Senior standing in PHGN, CHGN, MTGN, or EGGN. 1.5 hours lecture, 4 hours lab; 3 semester hours.

PHGN535. INTERDISCIPLINARY SILICON PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN435, (II) Explores the application of science and engineering principles to the fabrication and testing of microelectronic devices with emphasis on specific unit operations and interrelation among processing steps. Teams work together to fabricate, test, and optimize simple devices. Prerequisite: none. 1 hour lecture, 4 hours lab; 3 semester hours.
3

EENG532 Low Temperature Microwave Measurements for Quantum Applications

EENG532. Low Temperature Microwave Measurements for Quantum Applications. The goal of the course is to provide hands on training in high-frequency, low-temperature measurements which are requisite for quantum information applications. This course introduces the fundamentals of high-frequency measurements, the latest techniques for accuracy-enhanced automated microwave measurements, low-temperature measurement techniques, low noise measurements, and common devices used in quantum information. The course will have three modules. The first module, basics of electronic measurements, will include chip layout, power measurements, ground loop testing, impedance measurements, noise fundamentals, cable and device fabrication and care. The second module, high frequency measurements, will include measurements of basic scattering parameters, accuracy enhancement and calibration, transmission line, amplifier, and oscillator characterization including noise measurements. The third module, low-temperature measurements, will cover critical parameters for superconductors and Josephson junctions, measurements of superconducting resonators, characterization of low-temperature electronic elements including amplifiers. At the end of this course the students will know how to use network analyzers, spectrum analyzers, cryostats, the software Eagle for chip design, amplifiers, and filters. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course.
3
Elective #13
Elective #23
Elective #33
Elective #43
Thesis Credits9
30 Total

Course InformationHours
Software Track (QES)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

CSCI581 Quantum Programming

CSCI581. Quantum Programming. This course serves as an introduction to programming quantum computers. Students will receive an in depth education in quantum algorithms and their design, and then break into teams to learn the API of a commercially available quantum computing system. They will use this system to write and test simple quantum algorithms, and debug their code to improve its performance against noise and other error sources. Prerequisite: PHGN519.
3

PHGN545 Quantum Many-Body Physics

PHGN545. This course offers an introduction to quantum many-body physics in a modern approach from the perspectives of quantum information science. Starting from the difference between classical and quantum correlations, this course introduces composite quantum systems and the concept of entanglement as the central theme in quantum many-body physics. A system of many spin-1/2s is then presented as the paradigmatic quantum many-body system, opening the realm of quantum phase transitions and quantum simulation experiments. Next, systems of non-interacting bosons or fermions are examined using the powerful canonical transformation. To understand what happens when particles interact, the well-known Hubbard model is brought in, together with its importance in quantum materials. Finally, topological ordered quantum matter is introduced and explained via the structure of quantum entanglement. The application of topological order to quantum computing will also be mentioned.
3
Elective #13
Elective #23
Elective #33
Elective #43
Elective #53
Elective #63
Elective #73
30 Total
Hardware Track (QEH)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

PHGN435 Interdisciplinary Microelectronics Processing Laboratory/PHGN535 Interdisciplinary Silicon Processing Laboratory

PHGN435. INTERDISCIPLINARY MICROELECTRONICS PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN535, Application of science and engineering principles to the design, fabrication, and testing of microelectronic devices. Emphasis on specific unit operations and the interrelation among processing steps. Prerequisites: Senior standing in PHGN, CHGN, MTGN, or EGGN. 1.5 hours lecture, 4 hours lab; 3 semester hours.

PHGN535. INTERDISCIPLINARY SILICON PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN435, (II) Explores the application of science and engineering principles to the fabrication and testing of microelectronic devices with emphasis on specific unit operations and interrelation among processing steps. Teams work together to fabricate, test, and optimize simple devices. Prerequisite: none. 1 hour lecture, 4 hours lab; 3 semester hours.
3

EENG532 Low Temperature Microwave Measurements for Quantum Applications

EENG532. Low Temperature Microwave Measurements for Quantum Applications. The goal of the course is to provide hands on training in high-frequency, low-temperature measurements which are requisite for quantum information applications. This course introduces the fundamentals of high-frequency measurements, the latest techniques for accuracy-enhanced automated microwave measurements, low-temperature measurement techniques, low noise measurements, and common devices used in quantum information. The course will have three modules. The first module, basics of electronic measurements, will include chip layout, power measurements, ground loop testing, impedance measurements, noise fundamentals, cable and device fabrication and care. The second module, high frequency measurements, will include measurements of basic scattering parameters, accuracy enhancement and calibration, transmission line, amplifier, and oscillator characterization including noise measurements. The third module, low-temperature measurements, will cover critical parameters for superconductors and Josephson junctions, measurements of superconducting resonators, characterization of low-temperature electronic elements including amplifiers. At the end of this course the students will know how to use network analyzers, spectrum analyzers, cryostats, the software Eagle for chip design, amplifiers, and filters. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course.
3
Elective #13
Elective #23
Elective #33
Elective #43
Elective #53
Elective #63
Elective #73
30 Total

Course InformationHours
Software Track (QES)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

CSCI581 Quantum Programming

CSCI581. Quantum Programming. This course serves as an introduction to programming quantum computers. Students will receive an in depth education in quantum algorithms and their design, and then break into teams to learn the API of a commercially available quantum computing system. They will use this system to write and test simple quantum algorithms, and debug their code to improve its performance against noise and other error sources. Prerequisite: PHGN519.
3

PHGN545 Quantum Many-Body Physics

PHGN545. This course offers an introduction to quantum many-body physics in a modern approach from the perspectives of quantum information science. Starting from the difference between classical and quantum correlations, this course introduces composite quantum systems and the concept of entanglement as the central theme in quantum many-body physics. A system of many spin-1/2s is then presented as the paradigmatic quantum many-body system, opening the realm of quantum phase transitions and quantum simulation experiments. Next, systems of non-interacting bosons or fermions are examined using the powerful canonical transformation. To understand what happens when particles interact, the well-known Hubbard model is brought in, together with its importance in quantum materials. Finally, topological ordered quantum matter is introduced and explained via the structure of quantum entanglement. The application of topological order to quantum computing will also be mentioned.
3
Elective3
12 Total
Hardware Track (QEH)

PHGN519 Fundamentals of Quantum Information

PHGN519. Fundamentals of Quantum Information. This course serves as a broad introduction to quantum information science, open to students from many backgrounds. The basic structure of quantum mechanics (Hilbert spaces, operators, wavefunctions, entanglement, superposition, time evolution) is presented, as well as a number of important topics relevant to current quantum hardware (including oscillating fields, quantum noise, and more). Finally, we will survey the gate model of quantum computing, and study the critical subroutines which provide the promise of a quantum speedup in future quantum computers.
3

PHGN435 Interdisciplinary Microelectronics Processing Laboratory/PHGN535 Interdisciplinary Silicon Processing Laboratory

PHGN435. INTERDISCIPLINARY MICROELECTRONICS PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN535, Application of science and engineering principles to the design, fabrication, and testing of microelectronic devices. Emphasis on specific unit operations and the interrelation among processing steps. Prerequisites: Senior standing in PHGN, CHGN, MTGN, or EGGN. 1.5 hours lecture, 4 hours lab; 3 semester hours.

PHGN535. INTERDISCIPLINARY SILICON PROCESSING LABORATORY. 3.0 SEMESTER HRS. Equivalent with CBEN435, CBEN535, CHEN435, CHEN535, MLGN535, PHGN435, (II) Explores the application of science and engineering principles to the fabrication and testing of microelectronic devices with emphasis on specific unit operations and interrelation among processing steps. Teams work together to fabricate, test, and optimize simple devices. Prerequisite: none. 1 hour lecture, 4 hours lab; 3 semester hours.
3

EENG532 Low Temperature Microwave Measurements for Quantum Applications

EENG532. Low Temperature Microwave Measurements for Quantum Applications. The goal of the course is to provide hands on training in high-frequency, low-temperature measurements which are requisite for quantum information applications. This course introduces the fundamentals of high-frequency measurements, the latest techniques for accuracy-enhanced automated microwave measurements, low-temperature measurement techniques, low noise measurements, and common devices used in quantum information. The course will have three modules. The first module, basics of electronic measurements, will include chip layout, power measurements, ground loop testing, impedance measurements, noise fundamentals, cable and device fabrication and care. The second module, high frequency measurements, will include measurements of basic scattering parameters, accuracy enhancement and calibration, transmission line, amplifier, and oscillator characterization including noise measurements. The third module, low-temperature measurements, will cover critical parameters for superconductors and Josephson junctions, measurements of superconducting resonators, characterization of low-temperature electronic elements including amplifiers. At the end of this course the students will know how to use network analyzers, spectrum analyzers, cryostats, the software Eagle for chip design, amplifiers, and filters. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course. Prerequisite: EENG385, PHGN215, or equivalent Electronics Devices & Circuits course.
3
Elective3
12 Total

Beyond the required courses for each track, students will take one or more additional electives chosen from an extensive list of relevant courses (courses meant for the other track can also be used for these electives). This list, which is continuously updated as the curricula of the participating departments evolves, is comprised of:

Course Information, 3 credit hours each course
Physics

PHGN440 Solid-State Physics/PHGN441 Solid State Physics Applications and Phenomena

PHGN440also a materials course. SOLID STATE PHYSICS. 3.0 SEMESTER HRS. An elementary study of the properties of solids including crystalline structure and its determination, lattice vibrations, electrons in metals, and semiconductors. (Graduate students in physics may register only for PHGN440.) Prerequisite: PHGN320. 3 hours lecture; 3 semester hours.

PHGN441also a materials course. SOLID STATE PHYSICS APPLICATIONS AND PHENOMENA.3.0 SEMESTER HRS. Continuation of PHGN440/ MLGN502 with an emphasis on applications of the principles of solid state physics to practical properties of materials including: optical properties, superconductivity, dielectric properties, magnetism, noncrystalline structure, and interfaces. (Graduate students in physics may register only for PHGN441.) Prerequisite: PHGN440 or MLGN502. 3 hours lecture; 3 semester hours.

PHGN466/566 Modern Optical Engineering

PHGN466 MODERN OPTICAL ENGINEERING. 3.0 SEMESTER HRS. Provides students with a comprehensive working knowledge of optical system design that is sufficient to address optical problems found in their respective disciplines. Topics include paraxial optics, imaging, aberration analysis, use of commercial ray tracing and optimization, diffraction, linear systems and optical transfer functions, detectors and optical system examples. Prerequisite: PHGN462. 3 hours lecture; 3 semester hours.

PHGN566. MODERN OPTICAL ENGINEERING. 3.0 SEMESTER HRS. Provides students with a comprehensive working knowledge of optical system design that is sufficient to address optical problems found in their respective disciplines. Topics include paraxial optics, imaging, aberration analysis, use of commercial ray tracing and optimazation, diffraction, linear systems and optical transfer functions, detectors, and optical system examples. Prerequisite: PHGN462. 3 hours lecture; 3 semester hours.

PHGN480 Laser Physics

PHGN480. LASER PHYSICS. 3.0 SEMESTER HRS.(I) Theory and application of the following: Interaction of light with atoms: absorption, gain, rate equations and line broadening. Propagation, control and measurement of light waves: Gaussian beams, optical resonators and wave guides, interferometers. Laser design and operation: pumping, oscillation, and dynamics (Q-switching and mode-locking). Introduction to ultrafast optics. Laboratory: alignment and characterization of laser systems. Prerequisites: PHGN320. Co-requisites: PHGN462. 3 hours lecture; 3 semester hours.

PHGN520/521 Quantum Mechanics

PHGN520. QUANTUM MECHANICS I. 3.0 SEMESTER HRS. (II) Schroedinger equation, uncertainty, change of representation, one-dimensonal problems, axioms for state vectors and operators, matrix mechanics, uncertainty relations, time-independent perturbation theory, time-dependent perturbations, harmonic oscillator, angular momentum; semiclassical methods, variational methods, two-level system, sudden and adiabatic changes, applications. Prerequisite: PHGN511 and PHGN320 or equivalent. 3 hours lecture; 3 semester hours.

PHGN521. QUANTUM MECHANICS II. 3.0 SEMESTER HRS. (I) Review of angular momentum, central potentials and applications. Spin; rotations in quantum mechanics. Formal scattering theory, Born series, partial wave analysis. Addition of angular momenta, Wigner-Eckart theorem, selection rules, identical particles. Prerequisite: PHGN520. 3 hours lecture; 3 semester hours.

PHGN530 Statistical Mechanics

PHGN530. STATISTICAL MECHANICS. 3.0 SEMESTER HRS. (I) Review of thermodynamics; equilibrium and stability; statistical operator and ensemblesl ideal systems; phase transitions; non-equilibrium systems. Prerequisite: PHGN341 or equivalent and PHGN520. Co-requisite: PHGN521. 3 hours lecture; 3 semester hours.

PHGN550 Physics and Technology

PHGN550. NANOSCALE PHYSICS AND TECHNOLOGY. 3.0 SEMESTER HRS. An introduction to the basic physics concepts involved in nanoscale phenomena, processing methods resulting in engineered nanostructures, and the design and operation of novel structures and devices which take advantage of nanoscale effects. Students will become familiar with interdisciplinary aspects of nanotechnology, as well as with current nanoscience developments described in the literature. Prerequisites: PHGN320, PHGN341, co-requisite: PHGN462. 3 hours lecture; 3 semester hours.

PHGN585 Nonlinear Optics

PHGN585. NONLINEAR OPTICS. 3.0 SEMESTER HRS. An exploration of the nonlinear response of a medium (semiclassical and quantum descriptions) and nonlinear wave mixing and propagation. Analytic and numeric techniques to treat nonlinear dynamics are developed. Applications to devices and modern research areas are discussed, including harmonic and parametric wave modulation, phase conjugation, electro-optic modulation. Prerequiste: PHGN462 or equivalent, PHGN520. 3 hours lecture; 3 semester hours.
Computer Science

CSCI542 Simulation

CSCI542. SIMULATION. 3.0 Semester Hrs. Equivalent with MACS542, (I) Advanced study of computational and mathematical techniques for modeling, simulating, and analyzing the performance of various systems. Simulation permits the evaluation of performance prior to the implementation of a system; it permits the comparison of various operational alternatives without perturbing the real system. Topics to be covered include simulation techniques, random number generation, Monte Carlo simulations, discrete and continuous stochastic models, and point/interval estimation. Offered every other year. Prerequisite: CSCI 262 (or equivalent) and MATH 323 (or MATH 530 or equivalent). 3 hours lecture; 3 semester hours.

CSCI563 Parallel Computing

CSCI563. PARALLEL COMPUTING FOR SCIENTISTS AND ENGINEERS. 3.0 Semester Hrs.(I) Students are taught how to use parallel computing to solve complex scientific problems. They learn how to develop parallel programs, how to analyze their performance, and how to optimize program performance. The course covers the classification of parallel computers, shared memory versus distributed memory machines, software issues, and hardware issues in parallel computing. Students write programs for state of the art high performance supercomputers, which are accessed over the network. Prerequisite: Programming experience in C. 3 hours lecture; 3 semester hours.

CSCI564 Computer Architecture

CSCI564. ADVANCED COMPUTER ARCHITECTURE. 3.0 Semester Hrs. The objective of this class is to gain a detailed understanding about the options available to a computer architect when designing a computer system along with quantitative justifications for the options. All aspects of modern computer architectures including instruction sets, processor design, memory system design, storage system design, multiprocessors, and software approaches will be discussed. Prerequisite: CSCI341. 3 hours lecture; 3 semester hours.

CSCI571 Artificial Intelligence

CSCI571. ARTIFICIAL INTELLIGENCE. 3.0 Semester Hrs. (I) Artificial Intelligence (AI) is the subfield of computer science that studies how to automate tasks for which people currently exhibit superior performance over computers. Historically, AI has studied problems such as machine learning, language understanding, game playing, planning, robotics, and machine vision. AI techniques include those for uncertainty management, automated theorem proving, heuristic search, neural networks, and simulation of expert performance in specialized domains like medical diagnosis. This course provides an overview of the field of Artificial Intelligence. Particular attention will be paid to learning the LISP language for AI programming. Prerequisite: CSCI262. 3 hours lecture; 3 semester hours.

CSCI474 Introduction to Cryptography

CSCI474. INTRODUCTION TO CRYPTOGRAPHY. 3.0 SEMESTER HRS. Equivalent with MATH474, (II) This course is primarily oriented towards the mathematical aspects of cryptography, but is also closely related to practical and theoretical issues of computer security. The course provides mathematical background required for cryptography, including relevant aspects of number theory and mathematical statistics. The following aspects of cryptography will be covered: symmetric and asymmetric encryption, computational number theory, quantum encryption, RSA and discrete log systems, SHA, steganography, chaotic and pseudo-random sequences, message authentication, digital signatures, key distribution and key management, and block ciphers. Many practical approaches and most commonly used techniques will be considered and illustrated with real-life examples. Prerequisites: CSCI262, CSCI358, MATH334 or MATH335 or MATH201. 3 hours lecture; 3 semester hours.

CSCI575 Machine Learning

CSCI575. MACHINE LEARNING. 3.0 Semester Hrs. Equivalent with MACS575, (II) The goal of machine learning research is to build computer systems that learn from experience and that adapt to their environments. Machine learning systems do not have to be programmed by humans to solve a problem; instead, they essentially program themselves based on examples of how they should behave, or based on trial and error experience trying to solve the problem. This course will focus on the methods that have proven valuable and successful in practical applications. The course will also contrast the various methods, with the aim of explaining the situations in which each is most appropriate. Prerequisites: CSCI262 and MATH201. 3 hours lecture; 3 semester hours.

CSCI580 High-Performance Computing

CSCI580. ADVANCED HIGH PERFORMANCE COMPUTING. 3.0 Semester Hrs. This course provides students with knowledge of the fundamental concepts of high performance computing as well as hands-on experience with the core technology in the field. The objective of this class is to understand how to achieve high performance on a wide range of computational platforms. Topics will include sequential computers including memory hierarchies, shared memory computers and multicore, distributed memory computers, graphical processing units (GPUs), cloud and grid computing, threads, OpenMP, message passing (MPI), CUDA (for GPUs), parallel file systems, and scientific applications. 3 hours lecture; 3 semester hours.

CSCI586 Fault Tolerant Computing

CSCI586. FAULT TOLERANT COMPUTING. 3.0 Semester Hrs.
Electrical Engineering

EENG509 Sparse Signal Processing

EENG509. SPARSE SIGNAL PROCESSING. 3.0 Semester Hrs. Equivalent with EGGN509, (II) This course presents a mathematical tour of sparse signal representations and their applications in modern signal processing. The classical Fourier transform and traditional digital signal processing techniques are extended to enable various types of computational harmonic analysis. Topics covered include time-frequency and wavelet analysis, filter banks, nonlinear approximation of functions, compression, signal restoration, and compressive sensing. Prerequisites: EENG411 and EENG515. 3 hours lecture; 3 semester hours.

EENG417/517 Advanced Control Systems

EENG417. MODERN CONTROL DESIGN. 3.0 SEMESTER HRS. Equivalent with EGGN417, (I) Control system design with an emphasis on observer-based methods, from initial open-loop experiments to final implementation. The course begins with an overview of feedback control design technique from the frequency domain perspective, including sensitivity and fundamental limitations. State space realization theory is introduced, and system identification methods for parameter estimation are introduced. Computerbased methods for control system design are presented. Prerequisite: EENG307. 3 lecture hours, 3 semester hours.

517. THEORY AND DESIGN OF ADVANCED CONTROL SYSTEMS. 3.0 Semester Hrs. Equivalent with EGGN517, (II) This course will introduce and study the theory and design of multivariable and nonlinear control systems. Students will learn to design multivariable controllers that are both optimal and robust, using tools such as state space and transfer matrix models, nonlinear analysis, optimal estimator and controller design, and multi-loop controller synthesis. Spring semester of even years. Prerequisites: EENG417. 3 hours lecture; 3 semester hours.

EENG526 Advanced Electromagnetics

EENG526. ADVANCED ELECTROMAGNETICS. 3.0 SEMESTER HRS. (II) In this course the fundamental theorems of electromagnetics are developed rigorously. Wave solutions are developed in Cartesian, cylindrical, and spherical coordinate systems for bounded and unbounded regions. Prerequisite: EENG386. 3 hours lecture; 3 semester hours.

EENG528 Computational Electromagnetics

EENG528. COMPUTATIONAL ELECTROMAGNETICS. 3.0 Semester Hrs. (II) In this course the fundamental theorems of electromagnetics are developed rigorously. Wave solutions are developed in Cartesian, cylindrical, and spherical coordinate systems for bounded and unbounded regions. Prerequisite: EENG386. 3 hours lecture; 3 semester hours.

EENG529 Active RF and Microwave Devices

EENG529. ACTIVE RF & MICROWAVE DEVICES. 3.0 Semester Hrs. (II) This course introduces the basics of active radio-frequency (RF) and microwave circuits and devices which are the building blocks of modern communication and radar systems. The topics that will be studied are RF and microwave circuit components, resonant circuits, matching networks, noise in active circuits, switches, RF and microwave transistors and amplifiers. Additionally, mixers, oscillators, transceiver architectures, RF and monolithic microwave integrated circuits (RFICs and MMICs) will be introduced. Moreover, students will learn how to model active devices using professional CAD software, how to fabricate printed active microwave devices, how a vector network analyzer (VNA) operates, and how to measure active RF and microwave devices using VNAs. Prerequisites: EEBG385. 3 hours lecture; 3 semester hours.

EENG530 Passive RF and Microwave Devices

EENG530. PASSIVE RF & MICROWAVE DEVICES. 3.0 Semester Hrs. (I) This course introduces the basics of passive radio-frequency (RF) and microwave circuits and devices which are the building blocks of modern communication and radar systems. The topics that will be studied are microwave transmission lines and waveguides, microwave network theory, microwave resonators, power dividers, directional couplers, hybrids, RF/microwave filters, and phase shifters. Students will also learn how to design and analyze passive microwave devices using professional CAD software. Moreover, students will learn how to fabricate printed passive microwave devices and test them using a vector network analyzer. Prerequisites: EENG386. 3 hours lecture; 3 semester hours.

EENG617 Intelligent Control Systems

EENG617. INTELLIGENT CONTROL SYSTEMS. 3.0 Semester Hrs. Equivalent with EGGN617, Fundamental issues related to the design on intelligent control systems are described. Neural networks analysis for engi neering systems are presented. Neural-based learning, estimation, and identification of dynamical systems are described. Qualitative control system analysis using fuzzy logic is presented. Fuzzy mathematics design of rule-based control, and integrated human-machine intelligent control systems are covered. Real-life problems from different engineering systems are analyzed. Prerequisite: EENG517. 3 hours lecture; 3 semester hours. Taught on demand.

EENG618 Nonlinear and Adaptive Control

EENG618. NONLINEAR AND ADAPTIVE CONTROL. 3.0 Semester Hrs. Equivalent with EGGN618, This course presents a comprehensive exposition of the theory of nonlinear dynamical systems and the applications of this theory to adaptive control. It will focus on (1) methods of characterizing and understanding the behavior of systems that can be described by nonlinear ordinary differential equations, (2) methods for designing controllers for such systems, (3) an introduction to the topic of system identification, and (4) study of the primary techniques in adaptive control, including model-reference adaptive control and model predictive control. Prerequisite: EENG517. 3 hours lecture; 3 semester hours. Spring, even numbered years.
Metallurgy and Material Engineering

MTGN456 Electron Microscopy

MTGN456. ELECTRON MICROSCOPY. 2.0 Semester Hrs. (I, II, S) Introduction to electron optics and the design and application of transmission and scanning electron microscopes. Interpretation of images produced by various contrast mechanisms. Electron diffraction analysis and the indexing of electron diffraction patterns. Prerequisites: MTGN211 or MTGN311. Corequisite: MTGN456L. 2 hours lecture; 2 semester hours.

MTGN505 Crystallography and Diffraction

MTGN505. CRYSTALLOGRAPHY AND DIFFRACTION. 3.0 SEMESTER HRS. (I) Introduction to point symmetry operations, crystal systems, Bravais lattices, point groups, space groups, Laue classes, stereographic projections, reciprocal lattice and Ewald sphere constructions, the new International Tables for Crystallography, and, finally, how certain properties correlate with symmetry. Subsequent to the crystallography portion, the course will move into the area of diffraction and will consider the primary diffraction techniques (x-rays, electrons and neutrons) used to determine the crystal structure of materials. Other applications of diffraction such as texture and residual stress will also be considered. Prerequisites: Graduate or Senior in good standing. 3 hours lecture, 3 semester hours.
Materials Science

MLGN593 Bonding, Structure, and Crystallography

MLGN593. BONDING, STRUCTURE, AND CRYSTALLOGRAPHY. 3.0 SEMESTER HRS. (I) This course will be an overview of condensed matter structure from the atomic scale to the mesoscale. Students will gain a perspective on electronic structure as it relates to bonding, long range order as it relates to crystallography and amorphous structures, and extend these ideas to nanostructure and microstructure. Examples relating to each hierarchy of structure will be stressed, especially as they relate to reactivity, mechanical properties, and electronic and optical properties. Prerequisites: A 300 level or higher course in thermodynamics. 3 semester hours.
Applied Mathematics and Statistics

MATH408 Computational Differential Equations

MATH408. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS. 3.0 Semester Hrs. (I) This course is designed to introduce computational methods to scientists and engineers for developing differential equations based computer models. Students in this course will be taught various numerical methods and programming techniques to simulate systems of nonlinear ordinary differential equations. Emphasis will be on implementation of various numerical and approximation methods to efficiently simulate several systems of nonlinear differential equations. Prerequisite: MATH307. 3 hours lecture, 3 semester hours.

MATH436 Advanced Statistical Modeling

MATH436. ADVANCED STATISTICAL MODELING. 3.0 Semester Hrs. (II) Modern methods for constructing and evaluating statistical models. Topics include generalized linear models, generalized additive models, hierarchical Bayes methods, and resampling methods. Time series models, including moving average, autoregressive, and ARIMA models, estimation and forecasting, confidence intervals. Prerequisites: MATH335 and MATH424. 3 hours lecture; 3 semester hours.

MATH438 Stochastic Models

MATH438. STOCHASTIC MODELS. 3.0 Semester Hrs. (II) An introduction to stochastic models applicable to problems in engineering, physical science, economics, and operations research. Markov chains in discrete and continuous time, Poisson processes, and topics in queuing, reliability, and renewal theory. Prerequisite: MATH334. 3 hours lecture, 3 semester hours.

MATH510 and Dynamical Systems

MATH510. ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS. 3.0 Semester Hrs. Equivalent with MACS510, (I) Topics to be covered: basic existence and uniqueness theory, systems of equations, stability, differential inequalities, Poincare-Bendixon theory, linearization. Other topics from: Hamiltonian systems, periodic and almost periodic systems, integral manifolds, Lyapunov functions, bifurcations, homoclinic points and chaos theory. Offered even years. Prerequisite: (MATH225 or MATH235) and (MATH332 or MATH342). 3 hours lecture; 3 semester hours.

MATH551 Computational Linear Algebra

MATH551. COMPUTATIONAL LINEAR ALGEBRA. 3.0 Semester Hrs. Equivalent with MACS551, (II) Numerical analysis of algorithms for solving linear systems of equations, least squares methods, the symmetric eigenproblem, singular value decomposition, conjugate gradient iteration. Modification of algorithms to fit the architecture. Error analysis, existing software packages. Prerequisites: MATH332, CSCI407/MATH407. 3 hours lecture; 3 semester hours.

 

The interdisciplinary minor in Quantum Engineering requires 18 credit hours.

QE minor students will be required to take Honors Linear Algebra (MATH342) or Linear Algebra (MATH332) and three of the following courses: Quantum Programming (CSCI481/CSCI581), Low Temperature Microwave Measurement (EENG432/EENG532), Quantum Many-Body Physics (PHGN441), Microelectronics Processing (PHGN435), and Fundamentals of Quantum Information (PHYS519).

Students may select an additional 2 courses from the list above, or from the list in the course catalog, to further increase specialization.

As with many other graduate programs, students enrolled in Mines’ combined undergraduate/graduate program (meaning uninterrupted registration from the time the student earns a Mines undergraduate degree to the time the student begins a Mines graduate degree) may double count up to six hours of credits which were used in fulfilling the requirements of their undergraduate degree at Mines, towards their quantum engineering MS degree. Any 400+ level courses that count towards the undergraduate degree requirements as “Elective Coursework” or any 500+ level course, may be used for the purposes of double counting at the discretion of the graduate advisor. These courses must have been passed with a “B-” or better, not be substitutes for required coursework, and meet all other University, Department, Division, and Program requirements for graduate credit.
BS Electrical Engineering / MS Quantum Engineering (please consult with your advisor)
REGISTRATION REQUIREMENTS FOR COMBINED STUDENTS

Q. Are GRE scores required to apply to the Quantum Engineering (QE) Master’s program?
A. No, GRE scores are not required for either the QE Master’s Thesis or QE Master’s Non-Thesis. Submission of GRE scores is entirely optional.

Q. To whom should I submit my academic credentials?
A. Please submit all academic credentials only via the online application.

Q. Are teaching and research assistantships available?
A. Yes, teaching and research assistantships are available to qualified MS and PhD candidates in Mines’ interdisciplinary programs.

Q. Does Mines offer a Quantum Engineering PhD?
A. No. Currently PhDs go only through the QE constituent departments.

Q. Does Mines offer a Quantum Engineering Minor?
A. Yes, beginning with the Fall 2021 semester.

Q. Would it be possible to schedule a Zoom conference to discuss the program?
A. Yes, you may schedule a Zoom meeting with Carolyn Freedman, the Interdisciplinary Graduate Programs Manager, for advice on the application process and the combined program.

Q. What types of courses should I take as an undergraduate that would allow myself to be viewed most favorably for admission to the Quantum Engineering program?
A. A science or engineering degree and successful completion of college-level linear algebra are required for admission. Successful completion of a number of elective courses is required for the QE MS Thesis, MS Non-Thesis, and Graduate Certificate options. Completion of prerequisites, or comparable courses, for the electives that you intend to take, prior to entering the program, is recommended. Please see the Electives tab of this document for information on the various elective courses including prerequisites.

For more information about admission to our program, application instructions, deadlines, selection criteria, and other aspects of the process, please see the Quantum Engineering Program Overview* page, refer to the FAQs and Grad Links tabs of this document, and/or contact us at quantum@mines.edu.

You may also schedule a Zoom meeting with Carolyn Freedman, the Interdisciplinary Graduate Programs Manager, for advice on the application process and the combined program.

Please submit credentials only via the online application.

*The information regarding GRE scores for the Master of Science Thesis option is incorrect. GRE scores are not required for admission to this program.