bernstein_vazirani

An implementation of the Bernstein-Vazirani quantum algorithm.

• The 1st section uses for n=4 qubits with the secret string 1011
• The 2nd section is applicable to any secret string of any length

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The Bernstein-Vazirani algorithm is an example of a quantum algorithm that outperforms classical methods.

• Say you have a secret string of 1's and 0's. Then put the secret string in a box (function).
• Now the computer wants to determine what's inside the box by guessing the secret number.

Classically,

• the comp can apply AND operations by guessing n attempts
• or exponentially: for n-bit secretNum, tries from 0 to 2^n-1

Using Bernstein-Vazirani's alg

• finds secretNum in 1 attempt (regardless of secretNum size)

reference: https://github.com/qiskit-community/qiskit-community-tutorials/blob/master/Coding_With_Qiskit/ep6_Bernstein-Vazirani_Algorithm.ipynb

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Algorithm

1. initialize 1st n qubits in |0> state, & last qubit in |1> state
2. apply Hadamard gates to all qubits
3. build oracle (box containing secret number)
4. measure the 1st n qubits in the Bell basis (applying h gates before measurements)

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Section 1

n=4 qubits, secret string: 1011

output: {'1011': 1}

Section 2

n=11 qubits, secret string: 10111100101

The histogram shows how 100% of the results contain the secret number (this example uses 1 shot).

output: {'10111100101': 1}