Experimental Resuls
The set of benchmarks circuits that were analyzed are:
full adder is the quantum full adder it accepts the two addition parameters and the carry.
Shor's algorithm is the Shor's integer foctorization of number 15,
it produces the two primes factors of 15 which are 5 and 3.
gf23mult is to find the product of two elements of a field GF(2^{3}),
a=a_{0}+a_{1}x+a_{2}x^{2} and b=b_{0}+b_{1}x+b_{2}x^{2} with the output,
ab=c=c_{0}+c_{1}x+c_{2}x^{2} written on the last 3 qubits.
2-to-4 decoder
that has 3 inputs and 4 outputs. If the enable qubit is low, all output qubits will be zero.
If the enable qubit is high, one of the four output qubits will become high selected by the remaining two input qubits.
hwb4 is the hidden weighted bit function with four inputs/outputs.
Its output equals its input shifted left by the number of positions equal to the number of ones in the input pattern.
ham3 is the size 3 Hamming optimal coding function.
mod5 is the Grover's oracle, which has 4 inputs and 1 output. Its output is 1
if and only if the binary number represented by its input is divisible by 5.
6sym has 6 inputs and 1 output. Its output is 1 if and only if the number of ones in the input pattern is 2, 3 or 4.
nth\_prime3\_inc is used to find primes with up to 3 binary digits.
Formalized Quantum Circuits
| Circuit Name |
Qubits |
Gates without SWAP |
Total Gates |
Success Probability |
| nth\_prime3\_inc |
3 |
4 |
6 |
5.9 * 10^{-8} |
| ham3 |
3 |
5 |
6 |
9.5 * 10^{-7} |
| hwb4 |
4 |
12 |
22 |
1.2 * 10^{-29} |
| Shor's algorithm |
4 |
8 |
8 |
3.1 * 10^{-2} |
| full adder |
4 |
4 |
6 |
3.7 * 10^{-9} |
| Grover's oracle |
5 |
8 |
18 |
2 * 10^{-28} |
| 2-4 dec |
6 |
3 |
8 |
8.6 * 10^{-19} |
| gf23mult |
9 |
11 |
61 |
1.7 * 10^{-108} |
| 6sym |
10 |
20 |
61 |
1.7 * 10^{-102} |
