A quantum operation transforms the state of one or more qubits. In gate-based computation, it changes amplitudes and therefore the probabilities of possible measurement outcomes. section 1.4.3 section 4.3
A quantum operation works by applying a gate to selected qubits:
- The target qubit determines which amplitude pairs are recombined; paired indices differ in the target qubit's binary position. section 1.4.3 section 4.3
- The same gate equations update every selected pair in parallel while preserving the total probability within each pair. section 1.4.3
- Control qubits can condition the transformation, while quantum circuits combine operations to create useful states and probability distributions. section 4.6
Three-qubit operation
A three-qubit state has eight amplitudes. Applying a gate to target qubit 1 pairs amplitudes whose binary indices differ in the middle position, then recombines all such pairs according to the gate formula. Measurement returns one binary-string outcome according to the resulting probabilities.
