An Introduction to Quantum Computing
An Introduction to Quantum Computing ____________________________________________________________________________________
Two independent quantum states of quantum superposition show this concept as an example for illustration: | + ⟩ = |0 ⟩ + |1 ⟩ / √ 2; |− ⟩ = |0 ⟩ − |1 ⟩ / √ 2 If these two states are immediately measured under the standard 0/1 computational basis vectors, both will produce an even 50/50 probability distribution of outcomes, with identical chances of being measured as 0 or 1. However, despite their equivalent statistical performance in immediate measurements, these two quantum states are not identical. They have a significant difference in the relative phase between their components. If an extra quantum logic gate is added to the system before the final measurement, this phase difference will become critical: it will cause the complex probability amplitudes to interact in completely distinct ways, such that one measurement outcome is greatly strengthened, while the probability of the other outcome is systematically suppressed, or even completely eliminated. T he direct effect of quantum interference is the core premise that allows all modern quantum algorithms to be properly constructed and successfully executed. Q uantum algorithms should be a carefully design ed combinations of phases and amplitudes throughout the entire process. This causes the complex probability amplitudes tied to correct outputs to undergo constructive interference and amplify one another, while the amplitudes tied to incorrect outcomes undergo destructive interference and are suppressed to nearly zero. All computational work is completed within the quantum state that evolves internally in the system before the final measurement, and the actual results are only presented at the end of the process.
Figure 4. Constructive interference: relative phase changes the combined result
_______________________________________________________________________________________________ SCTE Technical Committee : Dave Hodges and Dr Anthony Basham. © 2026 Society for Broadband Professionals. All rights reserved Page 7 The Bloch Sphere: A Picture of One Qubit The quantum state of a single isolated qubit can be mapped onto a three - dimensional geometric model called the Bloch sphere (Figure 5). The north pole of this sphere corresponds to the qubit's ground state |0 ⟩ , while the south pole corresponds to the other ground state |1 ⟩ . The surface of the Bloch sphere represents the continuous set of possible
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