1. 1 hardware of quantum computer 1. quantum registers 2. quantum gates

2. 2 quantum registers one qubit length 1 two qubits length 2 L qubits length L

3. 3 quantum gates one qubitHadamard 2 qubits CNOT or XOR H CNOT Hadamard and CNOT is a universal set of gates

4. 4 Hadamard gate Hadamard one qubit gate is quantum mechanical! H H Hadamard gate gives superposition!

5. 5 CNOT or XOR two qubit gate 2 input bits2 output bits control bit target bit CNOT  if control bit is 0 the target bit is the same  if control bit is 1 the target bit is reversed 0101 CNOT 0000 CNOT CNOT CNOT 0000 0101 1111 1010 1111 1010

6. 6 CNOT or XOR the spin notation

7. 7 superposition in input control bit target bit CNOT CNOT CNOT or XOR gives entanglement! control bit target bit

8. 8problems 2. Show the swap two qubit gate (swaps the two input qubits) 1.Show that the circuit below does nothing by trying & HH 3. The stabilizer two qubit gate if |0> in the lower input always goes in the upper output

9. 9 quantum hardware circuits made of Hadamard (1 qubit) and CNOT (2 qubit) gates registers of length L qubits (spins) Hadamard gives superposition when inputs are bits CNOT gives entanglement when input is superposition ‘ quantum systems can be effectively simulated by a quantum computer only” R. Feynman