Shor's algorithm

Peter Williston Shor is known for Peter Williston Shor's work on quantum computation, in particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical computer.

Bernstein–Vazirani algorithm

The Bernstein–Vazirani algorithm is the first quantum algorithm that is exponentially more efficient than classical algorithms.

Simon's algorithm for identifying a hidden exclusive-or mask

The first quantum algorithm to offer an exponential speedup (in the query complexity setting) over classical algorithms was Simon's algorithm for identifying a hidden exclusive-or mask.

Simon's algorithm

Simon's algorithm is the first example of a quantum algorithm exponentially faster than any classical algorithm, and has many applications in cryptanalysis.

the least-square quantum support vector machine ( LS-QSVM)5

One of the first quantum algorithms exhibiting an exponential speed-up capability is the least-square quantum support vector machine (LS-QSVM)5.

Deutsch–Jozsa algorithm

1992 – David Deutsch and Richard Jozsa develop the Deutsch–Jozsa algorithm, one of the first examples of a quantum algorithm that is exponentially faster than any possible deterministic classical algorithm.

Shor Algorithm , the most complex quantum algorithm known to date,

For example, Shor Algorithm, the most complex quantum algorithm known to date, has ‘exponential’ speed-up over classical algorithms.

Shor’s algorithm

Shor’s algorithm, for example, is a famous quantum algorithm that we know will yield exponential speedups on a scaled quantum computer.

The Quantum Fourier Transform (QFT) subroutine

The Quantum Fourier Transform (QFT) subroutine seems ubiquitous in most quantum algorithms that are conjectured to give an exponential (or at least superpolynomial) speedup over the best classical ...

Repeated application of ‘Q’ controlled on ancilla qubits

Repeated application of ‘Q’ controlled on ancilla qubits provide the quantum speedup (From reference [3]).

Breaking cryptography

Breaking cryptography is one example where quantum computers appear to give exponential speed ups.

ABSTRACT Quantum algorithms for optimisation and cryptography

ABSTRACT Quantum algorithms for optimisation and cryptography offer exponential speedups over classical algorithms and can solve difficult computing problems.

in performing an unsorted database search, using the famous Grover’s quantum algorithm (Grover 1996)

A quantum computer delivers an exponential speed-up in performing an unsorted database search, using the famous Grover’s quantum algorithm (Grover 1996).

Boson Sampling

The main motivation behind such complexity is due to the presence of genuine multiphoton interference Given its computational hardness and current technological state-of-the-art for the-art's implementation on quantum hardware, Boson Sampling represents one of the most promising approaches to provide a first demonstration of quantum speedup.

the Fourier transform

Apparently, the Fourier transform is the source of the exponential speed up in all known quantum algorithms.

large number factorization

Indeed quantum information science was highly accelerated by the discovery by Peter Shor of quantum algorithm for large number factorization which provides an exponential speedup of computation compared to any conventional (classical) algorithm.

For example over classical algorithms

For example, Shor Algorithm, the most complex quantum algorithm known to date, has ‘exponential’ speed-up over classical algorithms.

polynomial-time algorithm for factoring integers

Interest in quantum computing surged with the introduction by Shor of a polynomial-time algorithm for factoring integers , giving an exponential speedup over the best known classical algorithm and threatening to break most modern encryption systems.

by effectively suppressing errors in a bitstring guessing game,

Scientists achieved a quantum speedup by effectively suppressing errors in a bitstring guessing game, managing strings up to 26 bits long.

amplitude amplification and the Bernstein-Vazirani algorithm

The core techniques behind the quantum speedup are amplitude amplification and the Bernstein-Vazirani algorithm.