let's say I'd Multiply 2*2, first this 2 in Binary will be 1 0; hence, the multiplication of 1 0 * 1 0 = 1 0 0 which equals 4.
So for the classical multiplications on a QC: if i have a state |0> and a state |1> multiplied it will reflect |010> |1> and a state |1> multiplied will return: |111> while |1> and |0> = |100> and |0> and |0> = |000>
1-Create 3 register: q0, q1 and q3 (q1 and q2 will contain the multiplier and multiplicand while q3 will return the product) 2- Assign the 3 registers to a Zero State 3- Apply Hadamard gate for q0 and q1; This will let the register iterate between 0 and 1 state. 4- leave the 3rd register q2 at zero state. 5- Apply the Teffoli gate. The Toffoli gate is a CCX controlled-controlled-X gate, which means that it flips the state of the third qubit if the first two qubits are both in the state |1>. The Truth Table of Teffoli or CCX gate will be as follows:
6- The third register q3 will reflect the Multiplication of q0 and q1 as shown in the table above. 7- The circuit will also has one classical bit, which is used to measure the state of the third qubit at the end of the circuit.
1- 3 register q0,q1 and q3
2- assign 0 state for q0,q1 and q3.
3- apply Not gate to q1 to change its state to 1 instead of 0.
4- apply Teffoli gate and a measure tool at q3 to check the result.
** Find the truth table and implementation below: **
