[Verse 1] Not every gate can build what quantum minds conceive Some combinations leave you trapped, unable to achieve But certain sets unlock the power, break computational walls When gates combine in perfect ways, the quantum curtain falls [Chorus] CNOT and Hadamard, T gates in their hand Universal trio, any circuit they command Toffoli alone can simulate the classical domain But add just one more quantum twist, infinite power you obtain [Verse 2] Deutsch showed us long ago that some gates can't complete The quantum algorithms that make our systems beat But universality means every unitary door Can be approximated close, within epsilon's shore [Chorus] CNOT and Hadamard, T gates in their hand Universal trio, any circuit they command Toffoli alone can simulate the classical domain But add just one more quantum twist, infinite power you obtain [Bridge] Solovay-Kitaev theorem proves the magic true Finite gate sets can approximate what infinite sets do Polynomial overhead, logarithmic in precision Universal computation through strategic gate division [Verse 3] Fault-tolerant requires gates that error-correct with ease Surface codes and magic states bring T gates to their knees But clifford gates are native, they preserve the stabilizer Universal sets must balance cost with quantum analyzer [Chorus] CNOT and Hadamard, T gates in their hand Universal trio, any circuit they command Toffoli alone can simulate the classical domain But add just one more quantum twist, infinite power you obtain [Outro] From discrete to continuous, the universal bridge Any computation possible on quantum's cutting edge
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