Representing Multi-Qubit States

• single bit -> 2 possible states(0 1)
• two bits -> 4 possible states(00 01 10 11)
• ...
• n qubits -> 2^n possible states

Entangled States

• Bell state
• spooky action at a distance

Proving Universality

• Matrices as outer products
• Unitary and Hermitian matrices(UU†=U†U=1)
• Pauli decomposition

Basic Gate Sets

• Clifford gates
• • conjugation by that unitary
• • transforms eigenstates of the matrix, but leaves eigenvalues unchanged
• Non-Clifford Gates
• • Rx(θ)、Ry(θ)、Rz(θ)
• • transform it to the same rotation around another axis