starts with the input ,

Simon's algorithm starts with the input , where is the quantum state with zeros.

quantum algorithm

Simon exhibited a quantum algorithm, usually called Simon's algorithm, that solves the problem exponentially faster than any deterministic or probabilistic classical algorithm, requiring exponentially less computation time (or more precisely, queries) than the best classical probabilistic algorithm.

an iterative algorithm

Simon's algorithm can be thought of as an iterative algorithm (which makes use of a quantum circuit) followed by a (possibly) "classical" algorithm to find the solution to a linear system of equations.

the problem of period-finding

Simon's algorithm solves the problem of period-finding, i.e. calculating the period \(T\) of a function \(f\) that satisfies \(f(x) = f(x+T)\) for all \(x\).

requires queries to the black box

Simon's algorithm requires queries to the black box, whereas a classical algorithm would need at least queries.

to discover periodicity in functions

Simon's algorithm helps to discover periodicity in functions and does so exponentially faster than any classic algorithm.

with the input , where is the quantum state with zeros

Simon's algorithm starts with the input , where is the quantum state with zeros.

by changing the odds of binary trading

The idea is that Simon’s system works by changing the odds of binary trading so that you can win 96.3% of the time.

on a control register and target register

Simon's Algorithm operates on a control register and target register, changing state like: $|\textbf{x}\rangle|\textbf{y}\rangle->|\textbf{x}\rangle|\textbf{y}\oplus f(...

the first example of a quantum algorithm exponentially faster than any classical algorithm

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

a very large order

One of Jim Simons's algorithms determines whether a very large order is executed and front runs a very large order .

the properties ) of a “black-box” function f(x

Simon’s algorithm determines the properties of a “black-box” function f(x), figuring out if a function is

simply works when you need SIMON to

SIMON simply works when you need SIMON to and SIMON saves time.

multiple measurements

The actual implementation of Simon's algorithm involves multiple measurements in order to determine the secret string.

by decomposing problems into smaller more manageable sub-problems

Simon worked by decomposing problems into smaller more manageable sub-problems, solving each sub-problem and assembling the partial answers into one final answer.

enabling them to better understand

Simon and Simon's team implement their proprietary algorithmic solution that consistently delivers millions of pounds in savings to major corporations by enabling them to better understand what they do and, more importantly, how they do what .

an efficient method for finding the relationship between the pairs: ) \(f(x

Simon's algorithm is an efficient method for finding the relationship between the pairs: \(f(x) =

Simon's problem quantumly using only a polynomial number of Hadamard gates and $O(n)$ oracle queries

Simon's algorithm solves Simon's problem quantumly using only a polynomial number of Hadamard gates and $O(n)$ oracle queries.

of a commonly used example oracle for f, as well as a detailed explanation of how and why a commonly used example oracle works

The Simon’s Algorithm notebook provides an implementation of a commonly used example oracle for f, as well as a detailed explanation of how and why a commonly used example oracle works.

an oracle separation between BQP and BPP

For instance Simon’s algorithm gives you an oracle separation between BQP and BPP.