Quantum Algorithms

QFT - Quantum Field Theory

Quantum Field Theory provides the mathematical framework for a description of contemporary elementary particle physics without the classical systems of gravity. Combines fields of systems with emerging quantum mechanical understanding.

QFT - Quantum Fourier Transform

A critical element of many quantum algorithms including Shor's algorithm that becomes a quite powerful operator when combined with qubit functionality. it is a linear transformation of a quantum bit. Requires only O n log n gates to achieve efficient appproximations.

BHT algorithm

A quantum algorithm that uses Grover's algorithm to solve "the collision problem". Has many applications across industries especially in biotech, chemistry, & medicine on a molecular level.

Grover's Algorithm

Lov Grover's pioneering quantum database search algorithm that finds with high probability the unique input to a black-box function that produces a particular output value (Using just O sqrtN time) In theory could brute-force a 128bit symm cryptographic key in 2^64 iterations, & break a 256bit key in 2^128 Invented in 1996. Typically oracle used to not represent database explicitly.

Shor's Algorithm

Peter Shor's pioneering quantum factorization algorithm that is able to find prime factors given an integer N in polynomial-time. Theoretically breaks RSA encryption with large enough quantum computer. Invented 1994. Another quantum algorithm (GEECM) is said to possibly run often much faster (2017)

HoloQUADS algorithm

simulates the time-evolution of correlated initial states expressed as matrix product states (MPS)