EEE4423: Introduction to Quantum Computers

Course Description

EEE 4423 Introduction to Quantum Computers is an undergraduate introduction to quantum computation taught from an engineering standpoint. The Statewide Course Numbering System description makes the emphasis explicit: the course “provides the foundations of quantum computers and quantum information systems with an emphasis on physical implementations.”

That last phrase distinguishes this course from the computer-science and physics versions of the same subject. A computer science treatment concentrates on algorithms and complexity; a physics treatment concentrates on quantum mechanics. An electrical engineering treatment asks how a qubit is actually built, why it decoheres, what the control electronics look like, and why a machine with a thousand physical qubits may deliver only a handful of useful logical ones.

Three Florida institutions carry it, all at 3 credits, and the titles show a mild and instructive spread:

• Florida International University — Introduction to Quantum Computers, matching the statewide title.
• University of Florida — Introduction to Quantum Computing: “introduces quantum computing concepts and hardware implementations discussing fundamentals of quantum mechanics and quantum computing algorithms.”
• University of South Florida — Quantum Computing and Communications.

⚠ USF’s title adds a subject the others do not. Communications signals coverage of quantum key distribution, quantum teleportation and quantum networking — a related but distinct body of material. A student comparing institutions, or transferring, should expect USF’s version to spend time on secure communication that the others spend on computation. This is an emphasis difference within a shared core rather than two different subjects, and the guide below labels it where it matters.

Learning Outcomes

Required Outcomes

• Represent quantum states using Dirac notation, the Bloch sphere and state vectors, and distinguish pure from mixed states.
• Apply the postulates of quantum mechanics relevant to computation: superposition, unitary evolution, measurement and its probabilistic outcome, and state collapse.
• Compute the action of single-qubit gates (Pauli, Hadamard, phase, rotation) as matrix operations, and construct arbitrary single-qubit unitaries.
• Apply multi-qubit gates (CNOT, controlled-U, SWAP, Toffoli) and compute multi-qubit state evolution using tensor products.
• Explain entanglement, construct and identify Bell states, and explain why entanglement cannot be used for superluminal signalling.
• Construct and analyse quantum circuits, and reason about circuit depth and gate count as resource measures.
• Explain the no-cloning theorem and its consequences for error correction and for quantum communication.
• Analyse foundational algorithms — Deutsch–Jozsa, Bernstein–Vazirani, Grover’s search and the quantum Fourier transform — and state the speedup each provides and over what.
• Explain Shor’s algorithm at the level of its structure and its implication for public-key cryptography.
• Describe the principal physical qubit implementations — superconducting, trapped ion, photonic, spin and topological — and compare them on coherence time, gate fidelity, connectivity and scalability.
• Explain decoherence and the principal noise mechanisms, and define T₁ and T₂ and what they measure.
• Explain the principle of quantum error correction and the distinction between physical and logical qubits.
• Implement and run a simple quantum circuit on a simulator and, where available, on real quantum hardware.

Optional Outcomes

• Analyse quantum key distribution protocols (BB84, E91) and their security arguments.
• Analyse quantum teleportation and superdense coding.
• Analyse the surface code and estimate the physical-qubit overhead for fault tolerance.
• Apply variational algorithms (VQE, QAOA) suited to noisy intermediate-scale devices.
• Analyse the control and readout electronics for a superconducting qubit system, including microwave generation and cryogenic constraints.
• Describe quantum sensing and metrology applications.
• Evaluate benchmarking methods: randomised benchmarking, quantum volume, and claims of quantum advantage.

Major Topics

Required Topics

• Mathematical foundations — complex vector spaces, inner products, Hermitian and unitary operators, eigenvalues and eigenvectors, tensor products, and Dirac notation as an engineering notation.
• Quantum mechanics for computation — the state postulate, unitary evolution, measurement in a basis and the Born rule, collapse, and the density matrix for mixed states.
• Qubits — the two-level system, superposition, global and relative phase, the Bloch sphere representation, and why phase rather than amplitude carries the computational advantage.
• Single-qubit gates — Pauli X, Y and Z, Hadamard, S and T gates, rotation operators, and universal single-qubit control.
• Multi-qubit systems and gates — tensor product states, CNOT and controlled operations, SWAP, Toffoli, and universal gate sets.
• Entanglement — Bell states and their preparation, separability, EPR and Bell inequalities, and the no-signalling constraint.
• Quantum circuits — circuit notation, composition, reversibility, ancilla qubits and uncomputation, and circuit depth as the resource that matters on real hardware.
• The no-cloning theorem — its proof, and its consequences for copying, error correction and eavesdropping detection.
• Foundational algorithms — Deutsch and Deutsch–Jozsa, Bernstein–Vazirani, Simon’s problem; Grover’s search and its quadratic speedup and optimality; amplitude amplification.
• The quantum Fourier transform and phase estimation — construction, and their role as the engine of exponential speedup.
• Shor’s algorithm — period finding, the reduction of factoring to period finding, and the consequence for RSA and elliptic-curve cryptography.
• Physical implementations — superconducting transmon qubits (Josephson junctions, microwave control, dilution refrigeration); trapped ions (laser control, long coherence, slower gates); photonic qubits; spin and quantum-dot qubits; neutral atoms; topological approaches. Comparison on coherence, fidelity, connectivity and scalability.
• Decoherence and noise — relaxation and dephasing, T₁ and T₂, gate and readout error, crosstalk, and the fidelity budget that determines usable circuit depth.
• Quantum error correction — the repetition and Shor codes, stabiliser formalism at introductory level, the threshold theorem, and the distinction between physical and logical qubits.
• Programming and running circuits — expressing algorithms in a quantum SDK, simulating them, transpiling to a hardware topology, and interpreting noisy measured results.

Optional Topics

• Quantum communication: BB84 and E91 key distribution, quantum teleportation, superdense coding, repeaters and networking (emphasised at USF).
• Post-quantum cryptography and the NIST standardisation of quantum-resistant algorithms.
• The surface code, fault-tolerance thresholds and physical-qubit overhead estimates.
• Variational algorithms for noisy devices: VQE, QAOA, and quantum machine learning.
• Control and readout electronics; cryogenic engineering and wiring constraints.
• Quantum sensing and metrology.
• Benchmarking: randomised benchmarking, quantum volume, and the evaluation of quantum-advantage claims.
• Quantum annealing and adiabatic computation.

Resources & Tools

• Quantum Computation and Quantum Information (Nielsen and Chuang) is the field’s standard reference and is universally cited, though its full depth exceeds a one-semester undergraduate course. Quantum Computing for Computer Scientists (Yanofsky and Mannucci) and Quantum Computing: An Applied Approach (Hidary) are more accessible; Quantum Computer Systems (Ding and Chong) is the best match for the engineering and implementation emphasis this course carries.
• Quantum Computing: A Gentle Introduction (Rieffel and Polak) is a good bridge for students uneasy about the mathematics.
• Qiskit (IBM) is the most widely used platform in teaching, and IBM Quantum provides free cloud access to real superconducting hardware — running a circuit on an actual quantum computer and seeing the noise is one of the more valuable exercises available in any undergraduate course. The Qiskit textbook is free and well maintained.
• Cirq (Google), PennyLane (Xanadu, strong on variational and machine-learning applications), Amazon Braket and Microsoft Azure Quantum with Q# are the other common environments.
• Python with NumPy — worth stating explicitly: much of this course can be done with matrix multiplication in NumPy, and building a small state-vector simulator yourself is an excellent way to understand what the SDKs are doing.
• Reference material — the IEEE Quantum Initiative, Quantum Science and Technology, the arXiv quant-ph section, and NIST’s post-quantum cryptography standardisation documents, which are the authoritative source on the cryptographic consequences.

Career Pathways

• Quantum hardware engineer — the destination this course’s implementation emphasis points at most directly: cryogenic systems, microwave control electronics, packaging and qubit fabrication. These roles are more numerous than quantum-algorithm roles and are more accessible to an electrical engineering graduate.
• Quantum control and instrumentation engineer — RF and microwave engineering applied to qubit control, an area where conventional electrical engineering skills transfer directly.
• Quantum software engineer and quantum algorithm researcher (usually requiring graduate study).
• Cryptography and security engineer — the post-quantum transition is a live, funded engineering programme, not a speculative one: NIST has standardised quantum-resistant algorithms and federal systems are migrating. This is currently the largest source of quantum-adjacent employment, and it does not require a quantum computer to exist.
• Quantum sensing engineer — quantum metrology is commercially closer to deployment than quantum computing, in magnetometry, gravimetry and timing.
• Research scientist in national laboratories and industry research groups.
• Employers include IBM, Google Quantum AI, IonQ, Rigetti, Quantinuum, PsiQuantum, Atom Computing, and the defence primes — L3Harris, Lockheed Martin, Northrop Grumman and Raytheon/RTX — all of which have quantum programmes and all of which have substantial Florida operations. Florida research settings include the National High Magnetic Field Laboratory in Tallahassee (whose cryogenic and low-temperature expertise is directly relevant), and quantum research groups at UF, USF and FIU.
• ⚠ An honest note on the market. Quantum computing employment is real and growing but remains small, and most dedicated roles require a PhD. The realistic value of this course for a bachelor’s graduate is as a differentiator within a conventional electrical engineering career — particularly in RF, cryogenic and control electronics, where quantum hardware companies hire people with exactly those skills — and as preparation for graduate study. Take it because the physics and the engineering are genuinely interesting and increasingly relevant, not on the expectation that it leads directly to a quantum job.

Special Information

⚠⚠ The real prerequisite is linear algebra, not quantum physics

This is the most useful thing to know before registering, and it reverses most students’ assumption.

UF requires EEE 3396 (solid-state devices) with a minimum grade of C, and either MAS 3114 (linear algebra) or EEL 3850, also with a C. The statewide record lists EEL 3120 and EEL 3135. Institutional requirements differ — check your own catalog.

The binding requirement is linear algebra over the complex numbers. Quantum computation is linear algebra: states are vectors, gates are unitary matrices, composition is matrix multiplication, multi-qubit systems are tensor products, and measurement probabilities are squared magnitudes of inner products. A student fluent in complex linear algebra can learn the quantum mechanics in this course from scratch. A student who took linear algebra as a real-valued computational course — row reduction and determinants — and never met eigenvectors as a conceptual tool or worked over the complex field will struggle regardless of how interested they are in the physics.

Preparation that pays: review complex arithmetic in polar form, inner products and orthonormal bases, eigenvalues and eigenvectors, unitary and Hermitian matrices, and the tensor (Kronecker) product. That last one is the operation most students have never seen, and it is used constantly from about week three.

No prior quantum mechanics is required at any of the three institutions, and none is assumed. The physics is developed as needed, and only the parts computation requires.

⚠ Institutional variation: computation versus communication

FIU and UF — computation emphasis	USF — computation and communication
Gates, circuits, algorithms	The same core
Physical qubit implementations	Plus quantum key distribution (BB84, E91)
Decoherence and error correction	Plus teleportation, entanglement distribution, networking

A syllabus test: if security proofs and eavesdropping detection appear in the assessed work, you are in the communications-inclusive version. Both are legitimate readings of the subject; the communication material is the more immediately practical, since quantum key distribution is deployed commercially while general-purpose quantum computing is not.

⚠ Course-code variation across Florida

Quantum computing is a young subject in undergraduate curricula and its numbering has not settled:

• EEE 4423 — FIU, UF, USF.
• Comparable material appears under physics (PHY) and computer science (CDA, COT) prefixes at several institutions, with substantially different emphasis — a physics version will spend far longer on quantum mechanics and far less on implementation.
• Graduate treatments appear under various numbers.

⚠ This is a prefix-divergence case. A student who took “quantum computing” under a physics or computer science number has probably covered a genuinely different subset of this material, and a receiving programme naming EEE 4423 will not match it automatically. Read the topic list rather than the title, and carry the syllabus.

Position in the curriculum

EEE 4423 is a senior-level technical elective. At UF it sits downstream of the devices course (EEE 3396) alongside the nanoelectronics electives — EEE 4420 Introduction to Nanodevices and EEE 4414 Modern Memory Device Technologies — which is a coherent grouping, since a superconducting or spin qubit is a nanoscale device. It pairs well with a solid-state devices background and with RF and microwave coursework for students interested in the hardware side.

Difficulty and time commitment

The difficulty is unusual and worth describing accurately. The mathematics is not hard — it is linear algebra on small matrices, and a two-qubit calculation is a 4×4 matrix multiplication. What is hard is that the physical intuition actively misleads. Superposition is not “both at once” in any classical sense, measurement is not observation of a pre-existing value, and entanglement is not correlation. Students who try to build a mental picture first and do the mathematics second generally get stuck; students who trust the mathematics and let the interpretation follow generally do not.

Plan on eight to ten hours a week. The single most effective study method in this course is to compute small examples by hand — apply a Hadamard to a qubit, build a Bell state with a CNOT, work through Deutsch’s algorithm on paper — before running anything in a simulator. The simulator will give the right answer without teaching you why.

Articulation and transfer

SCNS records EEE 4423 as guaranteed to transfer to an institution offering the same course, and three institutions carry it, all at 3 credits — unusually good coverage for a subject this new. The course is upper-division and carries no general-education or Gordon Rule designation.

FE exam relevance

The NCEES Fundamentals of Engineering (Electrical and Computer) exam does not cover quantum computing. This is an elective taken for its own value and for graduate preparation.

AI Integration

Quantum computing and machine learning intersect in several genuine ways and in a great many spurious ones, and distinguishing between them is a skill this course should develop.

Where the intersection is real. Machine learning is used inside quantum computing as an engineering tool: optimal control pulse shaping for higher-fidelity gates, error decoding for the surface code (a fast classical inference problem that neural decoders address well), calibration of large qubit arrays, and noise characterisation. These are unglamorous and important, and they are where an engineer is most likely to touch both fields.

Quantum machine learning — running learning algorithms on quantum hardware — is an active research area, but ⚠ a student should treat claims in this area with particular scepticism. Several proposed exponential speedups have been “dequantised,” meaning classical algorithms were found with comparable performance, and no practical quantum advantage for machine learning has been demonstrated on real hardware. This is a case where the honest engineering answer is that the question is open.

Where a general-purpose assistant helps in coursework. Explaining Dirac notation or the tensor product in different words; checking a small matrix calculation; generating and debugging Qiskit or Cirq code, which has a steep initial learning curve; explaining a transpiler decision or a hardware topology constraint; and summarising a paper before you read it closely.

⚠ Where it fails, and why the failure is precisely this course’s subject. The characteristic error of an AI tool asked about quantum computing is to reproduce the popular-science account: that a quantum computer “tries all possibilities simultaneously,” that superposition means being in two states at once, that entanglement transmits information. Correcting exactly these misconceptions is what the first three weeks of this course are for. A quantum computer does not try all paths and read off the answer — measurement returns one outcome, and the entire art of quantum algorithm design is arranging interference so that wrong answers cancel. A model trained overwhelmingly on popular explanations reproduces the popular explanation fluently and confidently, and it is wrong in the specific way the course exists to fix.

Two further failures matter. Models routinely overstate what current hardware can do, conflating physical qubit counts with logical ones and ignoring the error rates that make deep circuits impossible — when the gap between physical and logical qubits is one of the central engineering facts of the field. And they get sign and phase conventions wrong in gate matrices and circuit calculations; because global phase is unobservable but relative phase is everything, a phase error is both easy to make and fatal to the result.

The engineer’s responsibility. Quantum computing is a field with an unusually wide gap between what is claimed and what has been demonstrated, and engineers are among the few people positioned to tell the difference. The habit worth forming here is to ask of any claim: how many physical qubits, at what gate fidelity, at what circuit depth, and was it run on hardware or simulated? Those four questions dispose of most overstatement, including your own.

Academic integrity. FIU, UF and USF each maintain academic integrity policies covering AI-generated work, and practice varies by instructor. Derivations and circuit analysis are normally expected to be your own even where coding assistance is permitted. Ask before you rely on a tool, and disclose its use where the syllabus requires it.