Lecture 8: Cluster Model of QC 1) Models of QC 2) 1-bit teleportation 3) Cluster states 4) Cluster QC model 5) Fault tolerance 1) Models of QC * Quantum circuit model = Universal QC ≈ Universal QC Classical Classical Program Controller Data In → | Quantum variable | → Data Out • Different model: Quantum Program Data In → Fixed Qgate array → Data Out • Teleportation model: |Ψ⟩ → |B⟩ → |Fix⟩ → |Ψ⟩ • Cluster Model 1) Create state (perhaps complex) 2) Measure qubits in various bases 3) Feedback on measurement results Pauli Frame Can do comp if replace qubit → 2 qubits Ex: [Diagram: A quantum circuit with two qubits, with H gates applied to both qubits.] Claim: Inputs: a, b Outputs: CNOT a, b Use a |1X⟩ b |1⟩ a |1X⟩ → H → |+⟩ b |1⟩ → H → |+⟩ d |1⟩ → H → |+⟩ |1X⟩ |1⟩ |1⟩ → X^M1 |1⟩ |1X⟩ |1⟩ |1⟩ → X^M2 |1⟩ |1⟩ Altogether, eq'n to: |1X⟩ |1⟩ |1⟩ → H X^M1 H X^M2 |1⟩ |1⟩ = |1X⟩ |1⟩ |1⟩ → H X^M1 X^M2 |1⟩ |1⟩ = |1X⟩ |1⟩ |1⟩ → H X^(M1+M2) |1⟩ |1⟩ = |1X⟩ |1⟩ |1⟩ → X^(M1+M2) H |1⟩ |1⟩ = |1X⟩ |1⟩ |1⟩ → X^(M1+M2) |1⟩ |1⟩

Lecture 8: Cluster Model of QC

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