[Verse 1] In the quantum realm where qubits dance and spin We need to find the periods hidden deep within Classical computers struggle with the math so vast But quantum circuits make the analysis fast The QFT takes our quantum states And transforms them to frequency gates From time domain to spectral view Revealing patterns we never knew [Chorus] Quantum Fourier Transform, Q-F-T Finds the frequencies we cannot see Hadamard gates and phase rotations Build the bridge to new computations Inverse transform brings us back With the period we need to crack Q-F-T, the quantum key Unlocking cryptography [Verse 2] Start with Hadamard on every qubit line Creates superposition, looks so fine Then controlled rotations, phase by phase Two to the power k divides the ways Each qubit talks to all the rest Entanglement puts us to the test The circuit grows with n squared gates But quantum speedup compensates [Chorus] Quantum Fourier Transform, Q-F-T Finds the frequencies we cannot see Hadamard gates and phase rotations Build the bridge to new computations Inverse transform brings us back With the period we need to crack Q-F-T, the quantum key Unlocking cryptography [Bridge] In Shor's algorithm it plays its part Period finding is the beating heart RSA encryption meets its match When quantum circuits flip the latch The exponential becomes polynomial time Making large number factoring shine What took forever now takes minutes The cryptographic world has limits [Final Chorus] Quantum Fourier Transform, Q-F-T Spectral analysis quantumly Phase kickback and interference too Show us periods crystal clear and true The future's here, the change is vast Classical crypto's time has passed Q-F-T, the quantum key Rewrites our digital destiny [Outro] From time to frequency and back again The quantum transform breaks the chain Remember well the Q-F-T It holds tomorrow's mystery
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