An Introduction to Quantum Computing
An Introduction to Quantum Computing ____________________________________________________________________________________
Current Status of technology
Quantum technology
Typical operating environment
Cryogenic
Superconducting qubits
~10–20 millikelvin
Yes — extremely cold
Ultra-high vacuum, often room- temperature apparatus
Trapped-ion qubits
No, generally
Neutral-atom qubits
Ultra-high vacuum; laser cooled atoms
No, generally
Optical systems, often near room temperature
Photonic qubits
No
Silicon spin qubits
Typically, millikelvin temperatures
Yes, usually
Diamond NV-centre qubits
Can operate at room temperature
No
Generally, requires very low temperatures in current experimental implementations
Topological qubits
Yes
Another view on the mathematics What is a matrix?
_______________________________________________________________________________________________ SCTE Technical Committee : Dave Hodges and Dr Anthony Basham. © 2026 Society for Broadband Professionals. All rights reserved Page 24 A matrix is a rectangular arrangement of numbers. In quantum computing, matrices are used to describe operations that transform quantum states. A state is often written as a column vector, and a gate acts by matrix multiplication. A simple 2 × 2 matrix has two rows and two columns: A = [ a b ; c d ] The notation “2 × 2” means two rows by two columns. A matrix can multiply a two-entry column vector: A [ x ; y ] = [ ax + by ; cx + dy ] The key idea is: matrix × state vector = new state vector . The numbers in the matrix determine how the input amplitudes are combined to produce the output amplitudes. In quantum computing, the entries may be real or complex numbers. Complex numbers matter because quantum states can have both magnitude and phase. A qubit has two basis states, written |0) and |1). In column-vector form: |0) = [1 ; 0] |1) = [0 ; 1] A general pure qubit state is:
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