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## Smart answer:

After reading 1648 websites, we found 9 different results for *"What is the first quantum algorithm to show exponential speedup"*

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

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The Bernstein–Vazirani algorithm

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

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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.

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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).

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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.

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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.

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in part from the use of the quantum fast fourier transform which achieves interference among frequencies that are not related to the period (period-finding

The exponential speedup comes in part from the use of the quantum fast fourier transform which achieves interference among frequencies that are not related to the period (period-finding

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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 ...

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from Shor's algorithm, which can find the factors of numbers (e.g. 5 and 3 are factors of 15) almost exponentially faster than the best classical algorithms

Perhaps the most famous quantum speedup comes from Shor's algorithm, which can find the factors of numbers (e.g. 5 and 3 are factors of 15) almost exponentially faster than the best classical algorithms.

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