An Introduction to Quantum Computing
An Introduction to Quantum Computing ____________________________________________________________________________________
Figure 2. Classical bit versus qubit: discrete logic states compared with a coherent quantum state.
Like the classical digital computer bits introduced earlier in this text, a qubit also has only two optimal reference states. Their standard written form is |0 ⟩ and |1 ⟩ , which are pronounced "ket zero" and "ket one" in speech. This set of symbols originates from Dirac notation, which is universally used across all subfields of quantum mechanics which is the mathematical notation for linear algebra and linear operators on complex vector spaces together with their dual spaces both in the finite- and infinite-dimensional. The core difference between classical information and quantum information is that a qubit can exist in a coherent quantum superposition of these two basis states. |ψ ⟩ = α|0 ⟩ + β|1 ⟩ In the simple equation above, there exist two mathematically complex probability amplitudes, α and β. The coefficients α and β are complex probability amplitudes. Their squared magnitudes determine the probabilities of measuring the computational basis states 0 and 1, while their relative phase influences how the quantum state evolves and interferes under subsequent quantum operations.
|α|² + |β|² = 1
This strict condition, known as the normalisation condition, is derived entirely from the probabilistic interpretation of quantum bits. Measurement on this fragile quantum bit that is in the computational basis, the sum of the total probabilities of measuring 0 or 1 must equal 100%. Specifically, the mathematical expression for the probability of measuring logical 0 is | α|², and the probability of measuring logical 1 is strictly defined as | β|². The quantum properties of a quantum bit disappear the moment it interacts with an external measurement device. Its coherent quantum state will inevitably collapse into a single digital discrete outcome of either 0 or 1. The unique computing power of quantum bits does not come from the final measured reading at all. Its core potential arises entirely from the fact that before that irreversible measurement takes place, a systematically performed series of complex, interconnected transformation operations on its probability amplitudes and its fragile relative phases, can be conducted with precision.
Superposition: More Than an Unknown Bit
_______________________________________________________________________________________________ SCTE Technical Committee : Dave Hodges and Dr Anthony Basham. © 2026 Society for Broadband Professionals. All rights reserved Page 5 To explain the quantum superposition, a widely familiar analogy of a spinning coin in the macroscopic world. When a coin spins rapidly in the air, no one can predict in advance whether it will land heads or tails. This simplified analogy does help to grasp the core probabilistic uncertainty of quantum superposition. However, this analogy cannot accurately describe real quantum mechanical phenomena. Under the framework of classical physics, the spinning coin has a fixed position and orientation at every moment of its movement. Humans only lack sufficiently precise
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