Bachelor of Science in Quantum Systems Engineering

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• Recall derivatives and antiderivatives of algebraic, trigonometric, exponential, and log functions.
• Compute limits using algebraic techniques and L’Hôpital’s rule. Compute derivatives using the power, product, quotient, and chain rule. Compute integrals using the Fundamental Theorem of Calculus, power rule, and u-substitution.
• Interpret the meaning of a limit, derivative, and integral in both geometric and physical contexts.
• Approximate functions, derivatives, and integrals using tangent lines, secant lines, and Riemann sums.
• Apply definitions and theorems to draw mathematical conclusions and justify computational results.
• Identify and apply techniques to solve problems from science, engineering, and economics.
• Communicate written mathematical arguments and statements that use standard notation and terminology, are logically ordered, and are clear and complete.

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• Design and conduct experiments to predict and explain simple chemical and physical processes.
• Calculate or measure quantities using the correct precision and units.
• Explain the general quantum mechanical model for an atom and perform simple spectroscopy calculations.
• Predict the products and calculate amounts of substances in a chemical reaction.
• Describe the trends in periodic properties of elements and explain why they occur.
• Identify the primary types of bonds in a substance, and types of intermolecular forces, if present.
• Explain molecular-level differences between solids, liquids, gases for pure ionic and covalent substances.
• Calculate amount of energy flow during a chemical reaction or phase change, classifying it as heat or work.
• Determine 3D shape and polarity of small molecules and polyatomic ions to predict trends in properties.
• Explain in basic terms how each concept above applies to modern science or engineering issues.

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• Demonstrate understanding of major ethical theories and concepts and apply them to current and past debates on technology, resource use, and environmental issues.
• Read and think critically about course reading assignments and lecture topics; discover personal biases and values, diverse perspectives, and rhetorical strategies.
• Construct original written and oral arguments about course topics that are supported by relevant experts and accurately cited evidence.
• Find and employ relevant research to writing assignments on engineering, ethics, and the environment; consistently and correctly cite use of sources in-text and in bibliographies.
• Develop clear, readable, grammatical written work through a process of drafting and revision to produce strong summaries, analyses of texts, and researched arguments.
• Demonstrate understanding of the impact of engineering and applied science in social, ethical, and environmental contexts.
• Develop habits of mind while completing the coursework, such as curiosity, openness, engagement, creativity, persistence, responsibility, academic integrity, flexibility, and metacognition to help in a variety of learning contexts.

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• Analyze a simple empirical problem, break it down into smaller more manageable components, and design algorithmic solutions to these subproblems
• Implement an existing prompt, plan, or design into programmatically correct Python code that produces the expected text, file, or graph output
• Communicate in the language of programming with a computer and other programmers through code reading, writing, and critique
• Critically discuss and reflect on the role technology has in modern society, and the positive and negative impacts their software may have on future users
• Model how basic numeric and non-numeric data is represented in a computer; identify when, why, and how these physical representations diverge from their conceptual equivalents
• Navigate and utilize a computer file system through a GUI, the text console, and code
• Demonstrate effective debugging practices in an IDE to find, characterize, and correct code errors

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• COMPUTATIONS: Perform computations with integrals, sequences, series, vectors, vector-valued functions, and polar coordinates.
• APPLICATIONS: Construct and interpret mathematical objects (integrals, sequences, series, vectors, vector-valued functions, parameterizations, and polar coordinate representations) to describe physical or mathematical quantities.
• REASONING: Apply definitions and theorems to draw mathematical conclusions and justify computational results.
• WRITING: Communicate written mathematical arguments and statements that are complete and logically ordered through the use of standard notion and terminology.

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• L1. Design an algorithm to solve a problem by breaking the overarching problem into smaller modular components using abstraction and object-oriented design with inheritance.
• L2. Translate the algorithm into a program using proper C++ syntax and fundamental programming constructs (e.g. control structures, I/O, classes).
• L3. Recite & apply frequently used Linux command line commands and compile a program using a command line build system.
• L4. Diagram memory usage, dynamically allocate & deallocate objects at run-time using "The Big Three," and trace the call stack of a program’s run-time.
• L5. Define recursion and construct common recursive data structures (e.g. linked list, stack, queue) & algorithms (e.g. search & sort).
• L6. Diagram & construct dynamically allocated data structures (e.g. array, vector, string), recursive data structures, (e.g. linked list, stack, queue), and implement common list operations (e.g. traversal, insertion, removal)
• L7. Define "Big-O" notation, list complexities in increasing order, and analyze an algorithm to compute its run-time performance & memory complexities

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• EXPLORATION: Explore and pursue academic interests and passions.
• VALUES IDENTIFICATION: Reflect on different learning experiences to integrate new learning with prior personal interests, needs, background, and prior experiences to enhance their own personal Mines journey and post-Mines career
• INTERDISCIPLINARY INTEGRATION: Integrate perspectives and tools from the sciences, engineering, design, business, humanities, arts, and social sciences to enhance disciplinary and professional awareness.
• BUILDING COMMUNITY & CONVERSATION: Collaborate effectively with and be supportive of communities and individuals with diverse perspectives, experiences, and backgrounds.
• DEFINE CHALLENGES & OPPORTUNITIES: Identify interconnections among technical and societal dimensions of problem identification and solution.
• PERSPECTIVE TAKING: Explore challenges from a variety of perspectives and through multiple representational modalities.
• FUTURE ORIENTATION: Practice envisioning future possibilities in science and engineering while using relevant foundational past and present knowledge.
• IMPACT POTENTIAL: Build skills around developing and refining products which contribute to impacting and creating the future.

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• 1. Identify, breakdown, and define open-ended problems.
• 2. Research the context and background of problems and solutions, including user needs and technical requirements, through scholarly and authoritative sources, and stakeholder input.
• 3. Design solutions through a cycle of testing, refining, iterating, and feedback.
• 4. Equitably contribute to team efforts from start to end on a collaborative project, and participate in learning activities and coaching activities in the team.
• 5. Apply common workplace practices, tools and software in a semester-long team project, including project planning tools, team management tools, tools to generate solution alternatives, decision analysis methods, risk analysis methods, and value proposition analysis/baseline comparison.
• 6. Present technical ideas and solutions graphically, orally, written, and through prototype demonstrations
• 7. Visually depict ideas to teammates, supervisors, and stakeholders through the use of field sketching for the purposes of communication as well as idea development and development through iteration.
• 8. Model and communicate formalized design ideas through the use of standardized engineering graphics conventions as applied to engineering sketching and computer-aided design/solid modeling software

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• Graph functions of two variables in three-dimensions by using formulaic function knowledge, traces, and contour maps and extend this understanding to functions of three variables.
• Calculate partial derivatives and use them to solve applied problems.
• Construct and evaluate multiple integrals in appropriate coordinate systems such as rectangular, polar, cylindrical and spherical coordinates and apply them to solve problems involving volume, surface area, flux, density, and/or center of mass.
• Identify and use key theorems from vector calculus such as the Fundamental Theorem for Line Integrals, Green's Theorem, Stokes' Theorem, and/or the Divergence Theorem as appropriate to solve applied problems.

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• Investigate the models of physical systems such as exponential and logistic growth, Newton's Law of Heating/Cooling, Mixing (Tank) problems, spring mass systems, LRC circuits, and predator/prey models using first and second order differential equations.
• Apply classical techniques such as Separation of Variables, Integrating Factors, the Method of Undetermined Coefficients, Bernoulli substitutions, and Laplace Transforms to solve first and second order ordinary differential equations.
• Use eigenvalues and eigenvectors to solve 2x2 linear, constant-coefficient, homogeneous systems of differential equations; interpret the corresponding phase portraits for linear systems; use linearization to analyze the stability of critical points for nonlinear two dimensional systems.
• Apply the concepts of linearity, superposition, existence, and uniqueness of solutions to solve linear differential equations.

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• Develop two- and three-dimensional particle free body diagrams and use scalar approaches in two-dimensions and vector approaches in three-dimensions to solve for unknown forces for systems with pulleys and springs.
• Calculate the moment of a force in two-dimensional scalar and three-dimensional vector notation and correlate force couples to couple moments.
• Resolve forces, distributed loads, and couple moments into an equivalent resultant system as either a concentrated force at a calculated location or as a concentrated force and a couple moment at a specified location.
• Identify translational and rotational support reactions and construct free body diagrams for two- and three-dimensional statically determinant rigid body systems and use equations of equilibrium to solve associated support reactions.
• Use the equations of force and moment equilibrium to solve for unknowns in statically determinate beams, trusses, frames, machines, sliding friction, friction on flat belts, discrete loaded cables, cables subject to distributed loads, and systems with hydrostatic fluid pressure on flat, vertical, sloping, and curving surfaces.
• Solve for the internal shear force, normal force, and bending moment in a structural or mechanical member; express these concepts in the form of an equation; and graphically construct shear and moment diagrams.
• Determine centroids with the composite area method and the integration method and determine moments of inertia via the parallel axis theorem to develop Mohr’s circle and interpret values for the principle moments of inertia and moments of inertia for any inclined axes.

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• Perform basic matrix and vector operations, including row reducing matrices, adding/multiplying matrices, calculating determinants, determining eigenvalues/eigenvectors, computing orthogonal projections, and computing matrix decompositions.
• Recall/restate basic definitions and theorems of linear algebra to determine properties of matrices and sets of vectors.
• Communicate linear algebra concepts using proper terminology and notation.
• Utilize matrix and vector operations to solve applied problems including least squares approximation and orthogonal projection.
• Compute a singular value decomposition and use the result to solve an applied problem and determine properties of a matrix.

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• 1. Identify, select, and apply appropriate Linux commands for file, process, and network management.
• 2. Utilize the command line by designing and creating shell scripts; compiling and linking programs; redirecting input and output of processes; and executing commands for controlling jobs/processes.
• 3. Explain the purpose of and apply advanced SSH functions such as port forwarding, dynamic proxying, effectively.
• 4. Administer a Linux system applying knowledge of the file system hierarchy, package management, kernel compilation, and network management.
• 5. Design and write C programs composed of dynamic memory management, function pointers, c-style polymorphism, recursive functions, and data structures.
• 6. Examine the capabilities of a code repository maintenance tool, such as git, through command line version control.
• 7. Select and implement appropriate security, privacy, and encryption protocols at the operating system level.
• 8. Design and implement programs with client-server architecture using inter-process communication.
• 9. Discuss and apply appropriate time and project management strategies through the development of multiple substantial programming projects throughout the semester.

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• Identify the boundary of a system by drawing a control surface and label the transfer of mass and energy across the control surface for a given process.
• Apply balance equations (mass, energy, and entropy) to analyze steady and unsteady processes, relating a system’s inputs and outputs (heat, work, and mass transfer) and material properties (temperature, pressure, etc.) with one another.
• Determine the properties of pure substances using equations of state, property tables, software tools, or thermodynamic surfaces, choosing an appropriate method.
• Use the 1st and 2nd law of thermodynamics to identify possible and impossible processes.
• Apply the concept of isentropic efficiency to compare actual and ideal devices.
• Use the concepts of thermal efficiency and coefficient of performance to analyze the performance of power cycles (power plants and internal combustion engines), and assess the performance by comparing to other cycles, to theoretical limits, and to practical material and economic limitations.
• Represent thermodynamic processes in multiple formats, by drawing process schematics, drawing thermodynamic property (P-v and T-s) diagrams, applying balance equations, and writing for diverse audiences (science and non-science).
• Design and analyze thermodynamic systems (cycles and other devices) to meet heating, cooling, and/or power needs for a specified application.

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• 1. to give students a working knowledge of the practical aspects of materials, instrumentation and phenomena associated with laboratory practice
• 2. to train students in the use of important experimental and data analysis devices and tools
• 3. to show students how working physicists operate and to help them achieve professional standards in work practice and communication

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• Program in RISC-V assembly language
• Translate between C programs and RISC-V assembly code
• Translate between RISC-V assembly code and RISC-V machine code
• Represent a number using IEEE 754 floating point standard
• Describe how a CPU performs addition, subtraction, multiplication, and division
• Evaluate CPU performance
• Design a single-cycle processor and its control
• Design pipelining techniques to speed up a single-cycle processor
• Elaborate how memory hierarchy works

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• Convert between numbering representations.
• Design a combinational logic circuit from a word statement to a circuit diagram.
• Manipulate a logic function in any of its representations; word statement, truth table, symbolic, and circuit diagram.
• Determine SOPmin and POSmin realizations of logic function with or without don't cares.
• Build and operate adders, comparators, multiplexers and decoders.
• Determine output behavior of D,T,SR,JK; latches, clock latches and flip flops.
• Build and operate registers, shift registers, counters, tri-state logic and RAMs.
• Design Finite State Machines using a dense or Ones Hot encoding.
• Implement complex digital systems using the datapath and control design approach.

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• Develop mathematical models for linear dynamic systems (mechanical, electrical, fluid, and/or thermal).
• Analyze and predict the behavior of linear systems using both time domain and frequency domain tools.
• Design feedback compensators to achieve a specified performance criterion using both time domain and frequency domain techniques.
• Analyze and design feedback control systems using Matlab.

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• Describe social and technical interconnections of real-world design practice by exploring organizational contexts and stakeholder perspectives.
• Apply sociotechnical, environmental and economic reasoning to consider values in the context of design systems thinking.
• Identify and interpret ethical implications of designs.
• Practice empathy and listening to better understand stakeholder needs and concerns.

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• Write C-code to manipulate pins of the PIC.
• Write code to communicate using serial protocols. I can write a program with one or more interrupt sources.
• Write a program with shared variables between main and an ISR.
• Design an anti-alias filter for an ADC.
• Write code to interface to the PIC ADC subsystem.
• Write code to interface to the PIC timer subsystems.
• Build a system to generate analog output from the PIC.
• Write code on the PIC to communicate to a PC.
• Write code to manipulate fixed-point format numbers.
• Design a direct digital synthesis system using a PIC.
• Can search technical documents to find needed information.

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• Understand the phenomena in semiconductor devices that lead to their terminal characteristics (I-V and C-V curves) relevant for circuit applications.
• Analyze the transport of charge carriers in semiconductor devices when subjected to electromagnetic fields and predict their behavior.
• Design models for semiconductor devices that correlate terminal characteristics with device geometry, material parameters such as doping, mobility, and carrier lifetime, and ambient conditions including temperature.
• Simulate device characteristics using TCAD tools like Silvaco Victory to validate and the developed models.

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• 1. Construct Hilbert spaces, operators, wavefunctions and predict the outcome of measurements
• 2. Identify the key ways in which quantum mechanics differs from classical mechanics: entanglement and superposition
• 3. Simulate time evolution in quantum systems
• 4. Diagonalize simple quantum Hamiltonians and predict their spectra
• 5. Simulate oscillating fields in quantum systems
• 6. Implement simple calculations using the gate model of quantum computing. They will also learn how to use ancilla qubits, and how to construct arbitrary operations from one- and two-qubit gates
• 7. Identify mechanisms for a quantum speedup in quantum algorithms, learned through a survey of some of the most famous ones

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• Building on the education received in Fundamentals of Quantum Information, students will learn:
• 1. How to write and implement simple quantum algorithms,
• 2. Understand mechanisms by which a quantum speedup can be obtained
• 3. Use and execute code on an API of publicly available quantum hardware (e.g. IBM’s qiskit, Rigetti’s Forest, Google’s forthcoming Cirq, and many more)
• 4. “Debug” their code to improve its performance given the realities of noise and gate error