The quantum search algorithm Grovers Algorithm in 1996

The circuit of Grover’s algorithm n n qubits oracle workspace The Algorithm Begins with

The circuit of the Grover iteration (G) n qubits oracle workspace Phase : 2

What does the Grover iteration do? (1) n We define the new basis:

What does the Grover iteration G : ( 2 | y ñáy | -

Performance n n How many times must the Grover iteration be repeated? What’s the

How many times(R) must the Grover iteration be repeated? n The times R

The probability of get a solution? n n By observation: The probability at least

Conclusion n Difference with classic : Grover’s Algorithm have high probability when M<<N Advantage:

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The quantum search algorithm Grover’s Algorithm in 1996 報告人: 莊額碩

The circuit of Grover’s algorithm n n qubits oracle workspace The Algorithm Begins with the equal superposition state. measure

The circuit of the Grover iteration (G) n qubits oracle workspace Phase : 2 | 0ñá 0 | - I G : ( 2 | y ñáy | - I ) O

What does the Grover iteration do? (1) n We define the new basis:

What does the Grover iteration G : ( 2 | y ñáy | - I ) O do? (2)

Performance n n How many times must the Grover iteration be repeated? What’s the probability of getting a solution?

How many times(R) must the Grover iteration be repeated? n The times R

The probability of get a solution? n n By observation: The probability at least ½ For example when M<<N:

Conclusion n Difference with classic : Grover’s Algorithm have high probability when M<<N Advantage: faster than classic Disadvantage: M need to be known in advance