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3.8. Quantum Information and Computing (QIC)

This area covers the mathematical theory of quantum information and computation, including the linear algebraic formalism of quantum mechanics, quantum algorithms, entanglement theory, error correction, and tensor network methods. This frontier knowledge area is increasingly essential for Computing students engaged with quantum software and post-quantum security.

Knowledge Area (KA)	CS Core	KA Core
3.8.1 Quantum Mechanics Foundations for Computing	Elective
3.8.2 Quantum Circuits and Gates	Elective
3.8.3 Quantum Algorithms	Elective
3.8.4 Entanglement and Bell Inequalities	Elective

3.8.1. QIC/Quantum Mechanics Foundations for Computing ↑ Back to top

Postulates of quantum mechanics formulated for computation: state spaces, observables, measurement, and unitary evolution.
Topics:
Core

• Hilbert space formalism: state vectors, Dirac notation, and inner products
• Observables as Hermitian operators: eigenvalues, eigenstates, and the spectral theorem
• Measurement postulate: Born rule, projective measurements, and collapse of the state
• Unitary evolution: the Schrödinger equation and the time evolution operator
• Density matrices: mixed states, partial trace, and the Bloch sphere representation

Learning Outcomes:
Core:

1. State the postulates of quantum mechanics and represent single-qubit states on the Bloch sphere [Familiarity]
2. Compute measurement probabilities and post-measurement states using the Born rule and projection operators [Usage]
3. Distinguish pure from mixed states using density matrices and the partial trace over a subsystem [Assessment]

3.8.2. QIC/Quantum Circuits and Gates ↑ Back to top

Qubits, quantum gates, quantum circuits, universality, and the circuit model of quantum computation.
Topics:
Core

• Single-qubit gates: Pauli, Hadamard, phase, and rotation gates
• Multi-qubit gates: CNOT, Toffoli, and controlled-U gates
• Quantum circuits: circuit diagrams, depth, and reversibility
• Universality: the Solovay-Kitaev theorem and universal gate sets
• Quantum parallelism, interference, and the role of superposition in computation

Learning Outcomes:
Core:

1. Construct quantum circuits using standard gate sets and represent their action on basis states [Familiarity]
2. Analyze the action of a quantum circuit on an input state using matrix multiplication and Dirac notation [Usage]
3. Justify the universality of a gate set using the Solovay-Kitaev theorem and approximate a target unitary [Assessment]

3.8.3. QIC/Quantum Algorithms ↑ Back to top

Quantum Fourier transform, phase estimation, Shor's factoring algorithm, Grover's search, and HHL for linear systems.
Topics:
Core

• Quantum Fourier transform: circuit construction and complexity analysis
• Quantum phase estimation algorithm and its role as a subroutine
• Shor's factoring algorithm: period finding and reduction to factoring
• Grover's search algorithm: quadratic speedup and amplitude amplification

Non Core

• HHL algorithm for linear systems and quantum speedup for machine learning

Learning Outcomes:
Core:

1. Describe the quantum Fourier transform and explain how phase estimation extracts eigenvalue information [Familiarity]
2. Trace through Shor's and Grover's algorithms step by step and identify the source of quantum speedup [Usage]

NonCore:

1. Analyze the resource requirements of the HHL algorithm and identify the conditions under which it achieves exponential speedup [Assessment]

3.8.4. QIC/Entanglement and Bell Inequalities ↑ Back to top

Quantum entanglement: Bell states, Bell inequalities, CHSH inequality, no-cloning, and entanglement measures.
Topics:
Core

• Bell states, entangled versus separable states, and the Schmidt decomposition
• Bell inequalities and the CHSH inequality: local hidden variable theories vs. quantum mechanics
• No-cloning theorem and no-communication theorem
• Entanglement measures: entanglement entropy, concurrence, and negativity
• Quantum teleportation and superdense coding protocols

Learning Outcomes:
Core:

1. Explain what entanglement is and why Bell inequality violations rule out local hidden variable theories [Familiarity]
2. Construct Bell state circuits and verify entanglement using the CHSH inequality [Usage]
3. Analyze the quantum teleportation protocol and verify that no information travels faster than light [Assessment]