A Quantum counting algorithm is for efficiently counting the number of solutions for a given search problem. The algorithm is based on the quantum phase estimation algorithm and on Grover’s search algorithm.
Counting problems are common in diverse fields such as statistical estimation, statistical physics, networking, etc. As for quantum computing, the ability to perform quantum counting efficiently is needed in order to use Grover’s search algorithm (because running Grover’s search algorithm requires knowing how many solutions exist). Moreover, this algorithm solves the quantum existence problem (namely, deciding whether any solution exists) as a special case.
This algorithm is a precursor to a VisualSim Virtual_Machine Quantum Q-bit Computer implementation, where an array of imaginary Q-bits are generated:
VM Q_Bit_State array:
N = 0
while (N < Quantum_Bit_Number) {
Q_Bit_State (N) = {Q_Bit.random(1.0), Q_Bit.random(1.0)}
++N
}
where Q_Bit=-1.
Quantum_Bit_Number=number of q-bits
Q_Bit_State=array of imaginary states, based on Quantum_Bit_Number
Two registers maintain the current q-bit array and prior q-bit array, while above generates three dimensional location.
Web Reference: https://en.wikipedia.org/wiki/Quantum_counting_algorithm