Physical sciences 10 topics
Physical sciences
Quantum computing
10 topics 12 math concepts connects to 5 fields
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.
linear algebra hilbert spaces information theory
Grover's Algorithm
A quantum search algorithm achieving quadratic speedup over classical exhaustive search via amplitude amplification.
linear algebra hilbert spaces probability theory
Quantum Annealing
A metaheuristic for combinatorial optimisation that uses quantum tunnelling to escape local minima in energy landscapes.
quantum mechanics optimization dynamical systems
Quantum Entanglement
The non-classical correlations between quantum systems that cannot be explained by any local hidden-variable theory.
linear algebra hilbert spaces information theory
Quantum Error Correction
Techniques for protecting quantum information from decoherence and gate errors using redundant encoding and syndrome measurements.
group theory information theory linear algebra
Quantum Gates
The fundamental building blocks of quantum circuits, implementing unitary transformations on qubit states.
linear algebra group theory hilbert spaces
Quantum Key Distribution
Protocols for distributing cryptographic keys with information-theoretic security guaranteed by the laws of quantum mechanics.
information theory quantum mechanics probability theory
Quantum Phase Estimation
A core quantum subroutine that extracts eigenphases of unitary operators, underpinning Shor's algorithm and quantum chemistry simulations.
fourier transform linear algebra eigenvalues
Shor's Algorithm
A quantum algorithm for integer factorisation running in polynomial time, breaking RSA encryption.
number theory fourier transform linear algebra
Variational Quantum Eigensolver
A hybrid quantum-classical algorithm for approximating ground-state energies of quantum systems using parameterised circuits.
optimization linear algebra variational calculus