QC1 Quantum Computing Principles

This skill group introduces learners to the practical and mathematical foundations of quantum computing. Starting with the representation of quantum information, learners explore how a single qubit is described mathematically and visualised using the Bloch sphere. They then study how single qubits are manipulated with quantum gates and represented in basic single-qubit circuits, together with measurement and the no-cloning theorem. Finally, learners extend these concepts to multi-qubit systems, learning how qubits combine through tensor products, how multi-qubit gates operate, and how entanglement arises and influences computation, culminating in an understanding of the gate model and universal gate sets. They also examine quantum state preparation and measurement, including expectation values, fidelity, and quantum state tomography.

External: Basic linear algebra
External: Introductory quantum mechanics (helpful but not required)

• Examine mathematical and geometric representations of single-qubit states and superpositions.
• Analyse how single-qubit gates transform quantum states and how reversibility and unitarity distinguish quantum gates from classical logic.
• Examine how measurement and the no-cloning theorem constrain the manipulation and extraction of quantum information.
• Analyse how multi-qubit states, gates, and entanglement extend the principles of single-qubit computation.
• Examine how the gate model and universal gate sets provide a general framework for quantum computation.
• Analyse how state-preparation choices and complexity affect the structure of quantum circuits.
• Analyse how measurement bases and repeated measurements determine the information that can be extracted from quantum states.
• Analyse how expectation values, fidelity, and quantum state tomography are used to characterise quantum states and the limitations of full state reconstruction.

• QC1.1 Foundations of Quantum Computing and Qubits
• QC1.2 Single-Qubit Systems
• QC1.3 Multi-Qubit Systems and the Gate Model of Quantum Computation
• QC1.4 State Preparation in Quantum Circuits
• QC1.5 Quantum Measurement