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Deutsch-Jozsa-algorithm

1. Overview

his project shows how the Deutsch–Jozsa algorithm lets quantum computers solve certain problems much faster than classical computers.

The problem:

  • You are given a black-box function ( f:{0,1}^n \to {0,1} ).
  • The function is promised to be either:
    • Constant always outputs 0 or always 1.
    • Balanced half outputs are 1 and half are 0 .

Classically, in the worst case, you need to check more than half of all possible inputs to be sure about the nature of the function . The Deutsch–Jozsa algorithm requires only a single test of the oracle.

In this notebook,to keep things simple, we use n=1 case.

  1. Build quantum circuits for constant and balanced oracles.
  2. Run the algorithm on a simulator using Qiskit.
  3. Visualize the outcomes with histograms and statevectors.

2. Topics Learn

As you go through this notebook, you will learn:

  • The difference between constant and balanced oracles.
  • How to build the Deutsch–Jozsa circuit using the Qiskit module.
  • How quantum interference allows us to distinguish function types in one step.
  • How to simulate and visualize results with Qiskit Aer and Matplotlib.

    3. Requirements

  • Python 3.10+ (I used 3.11)
  • Jupyter Notebook or Jupyter Lab

Python packages:

  • qiskit
  • qiskit-aer (for simulation)
  • matplotlib

Install dependencies:

pip install qiskit qiskit-aer matplotlib

4. Usage

  1. Launch Jupyter Notebook or Lab:
  2. Open Deustch-joza algorithm.ipynb.
  3. Run all the cells.
  4. Observe the following outputs:
  • Circuit diagrams.
  • Histograms showing measurement results.

Expected outcomes:

  • Constant oracle → Always measure 0.
  • Balanced oracle → Always measure 1.

5. Next Steps

  • Extend the algorithm to more qubits ((n > 1)) to see the exponential speedup.
  • Run the algorithm on a real IBM Quantum device instead of a simulator.
  • Compare the quantum solution to a classical method to see the efficiency differences.