the quantum factor algorithm for N=91 is carried out.
What is the period k of the periodic superposition set up if it chooses x=8?
Guys please help...its very urgent!!
To determine the period "k" of the quantum period-finding algorithm for N=91 when x=8, we need to follow these steps:
Step 1: Choose an appropriate value for "a" such that it is coprime with N. In this case, N=91, and since 8 is coprime with 91 (as their greatest common divisor is 1), we can choose a=8.
Step 2: Calculate the order "r" of the chosen "a". The order represents the value that satisfies a^r ≡ 1 (mod N). To determine the order, we apply the Quantum Phase Estimation algorithm, which is a subroutine within the quantum period-finding algorithm.
Step 3: Implement the quantum circuit for the Quantum Phase Estimation algorithm. This circuit consists of applying a series of Quantum Fourier Transform (QFT) operations to a set of qubits representing the exponent part of the superposition state, and using controlled operations to propagate the phase information from the period to an ancilla qubit.
Step 4: Measure the ancilla qubit's state and convert the measurement result into a decimal number, which will be the estimated phase "theta" in radians.
Step 5: Calculate the estimated order "r" by dividing "theta" by 2π and rounding to the nearest integer.
Based on these steps, the Quantum Phase Estimation algorithm will provide an estimate for the order "r". The period "k" can be calculated as k = N/r, where N=91 and r is the estimated order.
Please note that running quantum algorithms and obtaining results may not be instantaneous and can vary depending on the hardware and software used. It is essential to have access to a quantum computer or a quantum simulator capable of running such algorithms to obtain the exact results.
If you don't have access to a quantum computer or simulator, you can try using existing quantum programming frameworks such as Qiskit, IBM Quantum Experience, or Microsoft Quantum Development Kit. These frameworks provide tools to simulate the quantum circuits and execute them on available quantum hardware.
Alternatively, you can use classical algorithms to find the period of a function. For example, you can use the classical Extended Euclidean Algorithm or Shor's classical algorithm for finding the period of a function. These algorithms may be slower than their quantum counterparts but can provide the desired results.