Quantum Superposition Distribution Generator

Developed by:

• Muhammad Jawwad Javeed Iqbal [Linkedin]

📚 Table of Contents

• Project Purpose
• About
• Required Environment Installations
• File Navigation
  • Juypter Notebook Files
  • Python Files
  • Excel Files
    • Juypter Notebook
    • Python
• Notes
  • Juypter Notebook
  • Python
  • Excel

📘 Project Purpose

The ability to specify Quantum Superposition Distributions (P(|0>) and P(|1>)) of a Qubit is effective for representing multiple complex states, an important attribute of Quantum computing that allows it to perform certain calculations more efficiently than a classical computer.

Currently however, it is difficult to specify a given probability distribution; for example, if the set distribution of P(|0>) and P(|1>) is selected to be 74%-26%,it would require trial and error in order to achieve the specific controlled rotation that would result in this Quantum Superposition Distribution(A demonstration of why simply entering a controlled rotation of a given percentage about a non-eigenstate axis would not work is available at Juypter_Notebook_Quantum_Superposition_Distribution_Generator_Demo.ipynb)

This project aims to resolve this problem by using different Polynomial equations in order to predict the controlled rotations required for the specified Quantum Superposition Distribution.

📄 About

Qiskit Program that can generate a specified Quantum Superposition distribution (P(|0>) and P(|1>)) by utilizing Polynomial equations.

For this project it is recommended to use one of IBM's Quantum computers instead of a simulator in order to generate truly random numbers, however for testing purposes the QASM Simulator is the most accurate and similar to a real-life Quantum Simulator and is used as a proof of concept.

💻 Required Environment Installations

$ pip install Qiskit

🗃 File Navigation

• Juypter Notebook Files

  • Juypter_Notebook_Quantum_Superposition_Distribution_Generator_Demo.ipynb is a demonstration on why a given percentage controlled rotation about the y axis would result in significant errors for values that are not located on any of the bases |0>,|+>,or |1>

  • Juypter_Notebook_Quantum_Superposition_Distribution_Generator_Polynomial.ipynb utilizes a polynomial function in order to scale the controlled rotations by a given percentage. However, because the values are predicted by a polynomial equation, they are highly inaccurate and are therefore left as a proof of concept (+/-95% error rate on both very low and very high numbers; average +/-35% error rate) and not recommended for any project utilization.

  • Juypter_Notebook_Quantum_Superposition_Distribution_Generator_Cubic.ipynb utilizes a Cubic function in order to scale the controlled rotations by a given percentage. However, because the values are predicted by a Cubic equation, they are highly inaccurate and are therefore left as a proof of concept (+/-80% error rate on both very low and very high numbers; average +/-30% error rate) and not recommended for any project utilization.

  • Juypter_Notebook_Quantum_Superposition_Distribution_Generator_Quadratic.ipynb utilizes a Quadratic function in order to scale the controlled rotations by a given percentage. However, because the values are predicted by a Quadratic equation, they are highly inaccurate and are therefore left as a proof of concept (+/-80% error rate on both very low and very high numbers; average +/-20% error rate) and not recommended for any project utilization

  • Juypter_Notebook_Quantum_Superposition_Distribution_Generator_Quintic.ipynb utilizes a Quintic function in order to scale the controlled rotations by a given percentage (+/-2% error rate on both very low and very high numbers; average +/-.5% error rate).

• Python Files

  • Python_Quantum_Superposition_Distribution_Generator_Demo.py is a demonstration on why a given percentage controlled rotation about the y axis would result in significant errors for values that are not located on any of the bases |0>,|+>,or |1>;the function Quantum_Superposition_Distribution_Demo(Prob_Value) can be utilized to provide a histogram of all possible measurement values based on specified Quantum Superposition Distribution.

  • Python_Quantum_Superposition_Distribution_Generator_Polynomial.py utilizes a polynomial function in order to scale the controlled rotations by a given percentage. However, because the values are predicted by a polynomial equation, they are highly inaccurate and are therefore left as a proof of concept (+/-95% error rate on both very low and very high numbers; average +/-35% error rate) and not recommended for any project utilization; the function Quantum_Superposition_Distribution_Polynomial(Prob_Value) can be utilized to provide a histogram of all possible measurement values based on specified Quantum Superposition Distribution.

  • Python_Quantum_Superposition_Distribution_Generator_Cubic.py utilizes a Cubic function in order to scale the controlled rotations by a given percentage. However, because the values are predicted by a Cubic equation, they are highly inaccurate and are therefore left as a proof of concept (+/-80% error rate on both very low and very high numbers; average +/-30% error rate) and not recommended for any project utilization;;the function Quantum_Superposition_Distribution_Cubic(Prob_Value) can be utilized to provide a histogram of all possible measurement values based on specified Quantum Superposition Distribution.

  • Python_Quantum_Superposition_Distribution_Generator_Quadratic.py utilizes a Quadratic function in order to scale the controlled rotations by a given percentage. However, because the values are predicted by a Quadratic equation, they are highly inaccurate and are therefore left as a proof of concept (+/-80% error rate on both very low and very high numbers; average +/-20% error rate) and not recommended for any project utilization;the function Quantum_Superposition_Distribution_Quadratic(Prob_Value) can be utilized to provide a histogram of all possible measurement values based on specified Quantum Superposition Distribution.

  • Python_Quantum_Superposition_Distribution_Generator_Quintic.py utilizes a Quintic function in order to scale the controlled rotations by a given percentage (+/-2% error rate on both very low and very high numbers; average +/-.5% error rate);;the function Quantum_Superposition_Distribution_Quintic(Prob_Value) can be utilized to provide a histogram of all possible measurement values based on specified Quantum Superposition Distribution.

• Excel Files

  • Excel_Quantum_Superposition_Distribution_Generator_Calculation.xslx utilizes Excel's Trendline function in order to generate an Polynomial equation to predict the controlled rotations.

  • Juypter Notebook

    • Excel_Juypter_Notebook_Polynomial.ipynb utilizes a polynomial function generated by Excel's Trendline function in order to scale the controlled rotations by a given percentage(+/-2% error rate on both very low and very high numbers; average +/-1% error rate)

    • Excel_Juypter_Notebook_Cubic.ipynb utilizes a Cubic function generated by Excel's Trendline function in order to scale the controlled rotations by a given percentage(+/-1% error rate on both very low and very high numbers; average +/-.3% error rate)

    • Excel_Juypter_Notebook_Quadratic.ipynb utilizes a Quadratic function generated by Excel's Trendline function in order to scale the controlled rotations by a given percentage(+/-80% error rate on very high numbers; average +/-6% error rate)

    • Excel_Juypter_Notebook_Quintic.ipynb utilizes a Quintic function generated by Excel's Trendline function in order to scale the controlled rotations by a given percentage(+/-4% error rate on both very low and very high numbers; average +/-3% error rate)

  • Python

    • Excel_Python_Polynomial.py utilizes a polynomial function generated by Excel's Trendline function in order to scale the controlled rotations by a given percentage(+/-2% error rate on both very low and very high numbers; average +/-1% error rate);the function Excel_Quantum_Superposition_Distribution_Polynomial(Prob_Value) can be utilized to provide a histogram of all possible measurement values based on specified Quantum Superposition Distribution.

    • Excel_Python_Cubic.py utilizes a Cubic function generated by Excel's Trendline function in order to scale the controlled rotations by a given percentage(+/-1% error rate on both very low and very high numbers; average +/-.3% error rate);the function Excel_Quantum_Superposition_Distribution_Cubic(Prob_Value) can be utilized to provide a histogram of all possible measurement values based on specified Quantum Superposition Distribution.

    • Excel_Python_Quadratic.py utilizes a Quadratic function generated by Excel's Trendline function in order to scale the controlled rotations by a given percentage(+/-80% error rate on very high numbers; average +/-6% error rate);the function Excel_Quantum_Superposition_Distribution_Quadratic(Prob_Value) can be utilized to provide a histogram of all possible measurement values based on specified Quantum Superposition Distribution.

    • Excel_Python_Quintic.py utilizes a Quintic function generated by Excel's Trendline function in order to scale the controlled rotations by a given percentage(+/-4% error rate on both very low and very high numbers; average +/-3% error rate);the function Excel_Quantum_Superposition_Distribution_Quintic(Prob_Value) can be utilized to provide a histogram of all possible measurement values based on specified Quantum Superposition Distribution.

🗒 Notes

• Juypter Notebook

  • Activate following code in Juypter notebook files in order to graph Qubit Bloch spheres:

qc.save_statevector()
qobj=assemble(qc)
result=sim.run(qobj).result().get_statevector()
plot_bloch_multivector(result)

• Python

  • Import either Quantum_Superposition_Distribution_Demo(Prob_Value) , Quantum_Superposition_Distribution_Polynomial(Prob_Value), Quantum_Superposition_Distribution_Cubic(Prob_Value),Quantum_Superposition_Distribution_Quadratic(Prob_Value), or Quantum_Superposition_Distribution_Quintic(Prob_Value) from Python_Quantum_Superposition_Distribution_Generator_Demo.ipynb, Python_Quantum_Superposition_Distribution_Generator_Polynomial.ipynb,Python_Quantum_Superposition_Distribution_Generator_Cubic.ipynb, Python_Quantum_Superposition_Distribution_Generator_Quadratic.ipynb,or Python_Quantum_Superposition_Distribution_Generator_Quintic.ipynb respectively.

• Excel

  • Import either Excel_Quantum_Superposition_Distribution_Polynomial(Prob_Value) , Excel_Quantum_Superposition_Distribution_Cubic(Prob_Value),
    Excel_Quantum_Superposition_Distribution_Quadratic(Prob_Value), or Excel_Quantum_Superposition_Distribution_Quintic(Prob_Value) from Excel_Juypter_Notebook_Polynomial.ipynb, Excel_Python_Cubic.ipynb,Excel_Python_Quadratic.ipynb or Excel_Python_Quintic.ipynb respectively.