About this course
Explore quantum and quantum-inspired approaches to hard optimization problems and the algorithms that exploit them.
Course format. Thirteen weeks, four contact hours each: a two-hour lecture (concepts and theory) and a two-hour practice session. The course is project-based; teams carry one running project end to end and present it three times, in weeks 5, 8, and 13.
What you will build
Built an end-to-end quantum optimization pipeline in Python with Qiskit, PennyLane, and the D-Wave Ocean SDK that maps a real combinatorial problem to QUBO and Ising forms and benchmarks QAOA, quantum annealing, and quantum-inspired solvers head to head.
Expected outcomes
- Explain the postulates of quantum mechanics using qubits, state vectors, and unitary operators
- Derive single and multi-qubit gate algebra from linear algebra over complex Hilbert spaces
- Formulate combinatorial problems as QUBO and Ising Hamiltonians
- Analyze the adiabatic theorem and the theory underlying quantum annealing
- Construct and parameterize QAOA circuits and reason about their cost and mixer Hamiltonians
- Optimize variational parameters using classical optimizers in a hybrid loop
- Implement quantum-inspired heuristics such as simulated and tensor-network annealing on classical hardware
- Benchmark quantum, hybrid, and classical solvers on shared optimization instances
- Evaluate noise, sampling overhead, and embedding limits on near-term devices
- Build an end-to-end pipeline mapping a real problem to a quantum solver and back
Key topics
- Quantum computing basics
- QAOA & quantum annealing
- Combinatorial optimization
- Quantum-inspired methods
Theoretical foundations
The concepts and results this course rests on.
- complex Hilbert spaces, unitary operators, and the postulates of quantum mechanics
- qubits, tensor products, and multi-qubit state spaces
- the adiabatic theorem and time-dependent Hamiltonian evolution
- QUBO and Ising formulations of combinatorial problems
- the variational principle and parameterized quantum circuits
- computational complexity and NP-hard optimization
- statistical mechanics, energy landscapes, and Metropolis sampling
Prerequisites
This is a Year-3 course. It assumes the mandatory CS core: data structures and algorithms, operating systems, computer networks, databases, software engineering, and the core mathematics (linear algebra, probability and statistics, calculus, discrete mathematics). It additionally requires the specific prior courses listed below.
Course-specific prerequisites:
- Basic Quantum Algorithms
- Linear algebra
- Algorithms and optimization basics
Weekly schedule 13 weeks · lecture + practice
Foundations
Wk 1
Linear algebra and quantum states
LectureReview of complex vector spaces, inner products, Dirac notation, and the qubit as a unit vector in a two-dimensional Hilbert space. Tensor products build multi-qubit state spaces.
PracticeSet up the Python and Qiskit environment and represent qubit states and amplitudes numerically with NumPy.
ProjectInitialize the project repository and encode a small toy problem instance as a state vector.
Wk 2
Quantum gates, measurement, and circuits
LectureUnitary operators, the Pauli and Hadamard gates, entanglement, and the Born rule for measurement probabilities. Circuit model semantics and reversibility.
PracticeBuild and simulate basic circuits in Qiskit, inspecting statevectors and measurement histograms.
ProjectImplement a circuit that prepares and measures the equal superposition over candidate solutions.
Optimization theory
Wk 3
Combinatorial optimization and complexity
LectureNP-hard problems, MaxCut, graph coloring, and the QUBO formulation. Reductions and the role of penalty terms in constrained problems.
PracticeTranslate sample problems into QUBO matrices and verify objective values by brute force on small instances.
ProjectChoose the project optimization problem and express it as a QUBO with documented constraints.
Wk 4
Ising models and energy landscapes
LectureMapping QUBO to the Ising Hamiltonian, spin variables, ground states, and the geometry of energy landscapes. Connection between minima and optimal solutions.
PracticeConvert the project QUBO to an Ising Hamiltonian and visualize the energy landscape of a reduced instance.
ProjectProduce a verified Ising formulation of the project problem with a small validation instance.
Quantum annealing
Wk 5
Adiabatic theorem and quantum annealingPresentation
LectureThe adiabatic theorem, time-dependent Hamiltonians, spectral gaps, and annealing schedules. Theory of how slow evolution tracks the ground state.
PracticeTeam presentation of the project specification: problem, Ising formulation, target solvers, and evaluation plan.
ProjectDeliver the written and oral project specification milestone.
Wk 6
D-Wave hardware and minor embedding
LecturePhysical annealers, qubit connectivity, chimera and pegasus topologies, minor embedding, and chain strength. Practical limits of current devices.
PracticeUse the D-Wave Ocean SDK to embed and sample the project Ising model on a simulated or cloud sampler.
ProjectObtain first annealing samples for the project problem and record solution quality.
Gate-based optimization
Wk 7
QAOA theory
LectureThe variational principle, cost and mixer Hamiltonians, the QAOA ansatz at depth p, and the p to infinity limit recovering adiabatic evolution. Performance bounds on MaxCut.
PracticeConstruct a depth one QAOA circuit for a small project instance and evaluate the expectation value.
ProjectImplement a working QAOA cost function for the project problem.
Wk 8
Variational optimization and parameter trainingPresentation
LectureClassical optimizers, gradient and gradient-free methods, parameter landscapes, barren plateaus, and warm starting. The hybrid quantum-classical loop.
PracticeTeam interim presentation: progress, annealing versus QAOA results so far, and obstacles.
ProjectDeliver the interim presentation milestone and a tuned QAOA parameter set.
Quantum-inspired methods
Wk 9
Simulated annealing and parallel tempering
LectureClassical Metropolis sampling, temperature schedules, parallel tempering, and why these are strong baselines for quantum methods.
PracticeRun simulated annealing and parallel tempering on the project instance and compare against quantum samples.
ProjectAdd classical baselines to the project benchmark suite.
Wk 10
Tensor networks and digital annealers
LectureQuantum-inspired tensor-network optimizers, mean-field methods, and commercial digital annealers. Where quantum inspiration helps without quantum hardware.
PracticeApply a tensor-network or specialized quantum-inspired solver to the project instance.
ProjectIntegrate a quantum-inspired solver and log its results in the benchmark.
Practical near-term computing
Wk 11
Noise, error, and mitigation
LectureDecoherence, gate and readout error, sampling overhead, and error mitigation strategies for noisy intermediate-scale devices.
PracticeRun QAOA under a noise model and apply a mitigation technique, measuring the effect on solution quality.
ProjectQuantify noise impact on the project QAOA results and apply mitigation.
Wk 12
Benchmarking and scaling
LectureFair benchmarking methodology, time to solution, approximation ratios, and scaling behavior across solver families. Reporting pitfalls.
PracticeAssemble a unified benchmark comparing all solvers on shared metrics and instance sizes.
ProjectFinalize the benchmark table and figures for the project.
Capstone
Wk 13
Final project defensePresentation
LectureCourse synthesis: when quantum, hybrid, and quantum-inspired methods are justified, and the outlook for fault-tolerant optimization.
PracticeTeam final presentation with oral defense of methodology, results, and design choices.
ProjectDeliver the final report, code, and benchmark with oral defense.
AI tools in this course.
Students lean on AI coding assistants to vibe-code the quantum optimization pipeline: scaffolding Qiskit and PennyLane circuits, refactoring QUBO and Ising mappings, and wiring up the D-Wave Ocean SDK from natural language descriptions of the problem. They drive the assistant to call tools and MCP servers that query quantum simulators and cloud backends, generate small validation instances and unit tests for QUBO objective values, and synthesize parameter sweeps for QAOA and annealing schedules. AI is also used to read back, plot, and interpret benchmark results, sanity checking approximation ratios and flagging suspicious solver behavior before it reaches the report.
Student project
Teams take one real combinatorial optimization problem and carry it through the full quantum optimization pipeline. They formulate it as QUBO and Ising, then solve it with quantum annealing, QAOA, and quantum-inspired baselines, producing a rigorous head-to-head benchmark and a final defended report.
Requirements
- Build a working system, not a set of disconnected exercises.
- Be original: a new system that solves a real problem, not a re-implementation of a tutorial or course demo.
- Show real depth: real data, real users or realistic load, and engineering trade-offs that are measured rather than assumed.
- Carry one running project from specification to a deployed, defensible result across the whole term.
- Work in a team of three or four and defend the design at each of the three presentations (weeks 5, 8, and 13).
Example projects
Portfolio asset selectionVehicle routingJob shop schedulingMax-cut on social graphsTraffic flow optimizationProtein folding lattice modelSensor placementWireless channel assignment
Assessment & grading
Grading is project-based, with no written exam. Teams of three or four present one running project three times.
| Component | What it covers | Weight |
|---|---|---|
| Project · Specification | Presentation 1 (week 5): problem, objectives, and architecture | 20% |
| Project · Interim | Presentation 2 (week 8): the working system demonstrated live | 30% |
| Project · Final | Presentation 3 (week 13): end-to-end demo with oral defense | 50% |
Tools & platforms
- Qiskit: build, simulate, and run gate-based circuits and QAOA
- Qiskit Optimization: high-level QUBO and converter workflows
- PennyLane: differentiable variational quantum optimization
- D-Wave Ocean SDK: QUBO and Ising sampling on annealers
- dimod: shared QUBO and Ising data structures and samplers
- minorminer: minor embedding onto annealer topologies
- NumPy: linear algebra and statevector manipulation
- SciPy: classical optimizers for the variational loop
- NetworkX: graph problem construction and visualization
- Matplotlib: energy landscapes and benchmark plots
- IBM Quantum Platform: cloud access to real quantum hardware
- Jupyter: interactive notebooks for the running project
Free online courses
Existing free, video-based courses this course can build on, for self-study or as a teaching basis.
In Hebrew · בעברית
- Technion (YouTube)טכנולוגיות קוונטיות - הרצאה
- Technion (YouTube)טכנולוגיות קוונטיות - תרגול
Primary literature
Seminal works to read for graduate-level depth.
References
Books and resources link to an online or publisher page.
- TextbookQuantum Computation and Quantum Information
- TextbookQuantum Computing: An Applied Approach
- PaperA Quantum Approximate Optimization Algorithm
- DocumentationQiskit Documentation
- DocumentationD-Wave Ocean SDK Documentation
- DocumentationPennyLane Documentation
- PaperIsing formulations of many NP problems
Role in each concentration
| Concentration | Role |
|---|---|
| Intelligent Software Systems | Elective |
| Networking & Cyber Security | Elective |
| AI & Robotics | Elective |
| AI and Quantum Computing for Finance | Core · Semester 2 |
| Immersive Systems & Game Development | Elective |
| Defense Technologies & Autonomous Systems | Elective |