The universal set for quantum computation comprises CNOT gates and single-qubit unitary operations, which together can decompose any arbitrary $n$-qubit unitary transformation via the Solovay-Kitaev theorem context of universality. This theoretical framework establishes that a valid Quantum Circuit model consists of initializing qubits in a computational basis state, applying sequences of these universal gates to implement functions, and concluding with projective measurements in the computational basis to extract probability amplitudes squared as results. The concept bridges classical logic gate universality (e.g., NAND or AND-NOT sets) with quantum mechanical linearity, demonstrating that efficient factorization protocols like Shor's algorithm can leverage this superposition-based model for exponential speedups over deterministic classical circuits while maintaining mathematical equivalence across alternative theoretical models such as measurement-only approaches.
The universal set for quantum computation comprises CNOT gates and single-qubit unitary operations, which together can decompose any arbitrary $n$-qubit unitary transformation via the Solovay-Kitaev …