Physical sciences
10 topics
Physical sciences
Quantum computing
Quantum computing exploits superposition and entanglement to solve certain problems exponentially faster than classical computers. Its mathematics draws on linear algebra, group theory, and information theory.
Topics in this field
Density Matrices
The mathematical framework for describing both pure and mixed quantum states, open systems, and quantum channels.
Grover's Algorithm
A quantum search algorithm achieving quadratic speedup over classical exhaustive search via amplitude amplification.
Quantum Annealing
A metaheuristic for combinatorial optimisation that uses quantum tunnelling to escape local minima in energy landscapes.
Quantum Entanglement
The non-classical correlations between quantum systems that cannot be explained by any local hidden-variable theory.
Quantum Error Correction
Techniques for protecting quantum information from decoherence and gate errors using redundant encoding and syndrome measurements.
Quantum Gates
The fundamental building blocks of quantum circuits, implementing unitary transformations on qubit states.
Quantum Key Distribution
Protocols for distributing cryptographic keys with information-theoretic security guaranteed by the laws of quantum mechanics.
Quantum Phase Estimation
A core quantum subroutine that extracts eigenphases of unitary operators, underpinning Shor's algorithm and quantum chemistry simulations.
Shor's Algorithm
A quantum algorithm for integer factorisation running in polynomial time, breaking RSA encryption.
Variational Quantum Eigensolver
A hybrid quantum-classical algorithm for approximating ground-state energies of quantum systems using parameterised circuits.