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Quantum Computation

Bernstein–Vazirani Algorithm

Construct the Bernstein–Vazirani quantum circuit for a given secret string

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The Bernstein-Vazirani algorithm is a quantum algorithm that solves a specific problem known as the "oracle problem." In this problem, we are given a black-box oracle (a function) that computes a dot product between an unknown binary string "s" and an input binary string "x", modulo 2. The goal is to determine the unknown string "s".

Install and load the QuantumFramework paclet:

In[1]:=

PacletInstall["Wolfram/QuantumFramework"]Needs["Wolfram`QuantumFramework`"]

Generate the Bernstein–Vazirani circuit for the secret string 101:

In[2]:=

bv=QuantumCircuitOperator[{"BernsteinVazirani","101"}]

Out[2]=

QuantumCircuitOperator

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View the circuit diagram:

In[3]:=

bv["Diagram"]

Out[3]=

Show only the oracle part of the circuit:

In[4]:=

QuantumCircuitOperator[{"BernsteinVaziraniOracle","101"}]["Diagram"]

Out[4]=

Evaluate the BV circuit and get the measurement:

In[5]:=

meas=bv[]

Out[5]=

QuantumMeasurement

Target: {1,2,3}

Measurement Outcomes: 8

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Return quantum probabilities:

In[6]:=

meas["Probabilities"]

Out[6]=

|000〉0,|001〉0,|010〉0,|011〉0,|100〉0,|101〉1,|110〉0,|111〉0

The only result corresponds to the secret string:

In[7]:=

meas["ProbabilityPlot"]

Out[7]=

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Contributed by: Wolfram Research, Quantum Computation Framework Team

Feb	MAR	Apr
	04
2023	2024	2025

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Bernstein–Vazirani Algorithm

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