1. Show how to construct a SWAP gate out of three CNOT gates.

Computer Networking: A Top-Down Approach (7th Edition)
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1. Show how to construct a SWAP gate out of three CNOT gates.
2. Show that SWAP gates and single qubit unitary operators do not form a universal set.
Concretely, show that there exists a unitary operator that cannot be constructed out of
SWAP gates and single qubit unitary operators.
3. Build a "triple-controlled NOT" gate out of Toffoli gates, using one or more work qubits.
Transcribed Image Text:1. Show how to construct a SWAP gate out of three CNOT gates. 2. Show that SWAP gates and single qubit unitary operators do not form a universal set. Concretely, show that there exists a unitary operator that cannot be constructed out of SWAP gates and single qubit unitary operators. 3. Build a "triple-controlled NOT" gate out of Toffoli gates, using one or more work qubits.
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