[Verse 1] In the quantum realm where qubits dance and play We seek the hidden rhythms in a function's way Take f of x, it hides a secret beat A period r that makes the pattern repeat When f of x equals f of x plus r The quantum oracle holds the key so far Superposition lets us query all at once Finding cycles classical computers can't [Chorus] Period finding, period finding Secret cycles we're dividing Quantum Fourier Transform reveals The hidden frequency that's real Period finding, period finding Mathematical key we're binding Powers the strength of Shor's attack Breaking codes we can't take back [Verse 2] Start with qubits in equal superposition state Query the oracle, let quantum mechanics create Entanglement between our input and result Now measurement gives us patterns difficult The magic happens in the frequency domain Quantum Fourier Transform breaks the chain Peaks appear at multiples of one over r Probability amplitudes show us where we are [Chorus] Period finding, period finding Secret cycles we're dividing Quantum Fourier Transform reveals The hidden frequency that's real Period finding, period finding Mathematical key we're binding Powers the strength of Shor's attack Breaking codes we can't take back [Bridge] Classical brute force takes exponential time But quantum interference makes the answer shine Continued fractions help us approximate The period from the frequencies we locate Greatest common divisor finds the final prize Factoring large numbers before our very eyes RSA encryption falls to quantum might When period finding brings the factors to light [Chorus] Period finding, period finding Secret cycles we're dividing Quantum Fourier Transform reveals The hidden frequency that's real Period finding, period finding Mathematical key we're binding Powers the strength of Shor's attack Breaking codes we can't take back [Outro] In quantum computing's revolutionary song Period finding proves that quantum is strong The mathematical foundation standing tall That threatens cryptography once and for all
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