An Introduction to Quantum Computing
An Introduction to Quantum Computing ____________________________________________________________________________________
Quantum Fourier Transform (QFT)
Fourier transform of quantum amplitudes
Exponential in certain settings
Building block for Shor, phase estimation
Quantum Phase Estimation (QPE)
Potential exponential advantage
Estimate eigenvalues
Chemistry, physics, simulation
Amplitude Estimation (QAE)
Estimate probabilities/expectations
Quadratic
Finance, risk, Monte Carlo
Amplitude Amplification
Increase probability of desired answer
Quadratic
Generalised search
Exponential under restrictive assumptions
Linear algebra, ML, differential equations
HHL
Solve linear systems
VQE – Variational Quantum Eigensolver
Find ground-state energies
Hybrid quantum/digital
Chemistry, materials
QAOA – Quantum Approximate Optimization Algorithm
Potential/instance- dependent
Combinatorial optimisation
Routing, scheduling, networks
Logistics, scheduling, portfolio optimisation
Quantum Annealing
Optimisation
Problem dependent
Polynomial to exponential in special cases
Quantum Walk algorithms
Networks, graph analysis
Search/graph problems
Quantum Counting
Estimate number of solutions
Quadratic
Search and optimisation
Exponential query advantage
Simon’s algorithm
Find hidden XOR structure
Cryptography/research
Exponential query separation in idealized setting
Determine function properties
Deutsch–Jozsa
Mostly educational/theoretical
Bernstein–Vazirani
Determine hidden bit string
Query reduction
Mostly theoretical
_______________________________________________________________________________________________ SCTE Technical Committee : Dave Hodges and Dr Anthony Basham. © 2026 Society for Broadband Professionals. All rights reserved Page 21
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