Quantum-Simulation

Description:

The project focuses on simulating the interactions of three atoms using the Heisenberg model on three qubits. It explores quantum simulation on NISQ (Noisy Intermediate-Scale Quantum) devices, specifically IBM’s quantum processor 'ibmq_jakarta'. The simulation begins with a classical approach, followed by transitioning to a quantum method. This is done by representing the quantum states of a 3-qubit system, which has 8 possible states, using an 8x8 matrix. This system can be simulated classically for smaller qubit numbers, but for a larger system with 50 particles, classical simulation becomes impractical. In contrast, quantum computers can handle such simulations efficiently, requiring only 15 qubits for a simulation of that scale.

Features:

• Quantum Simulation: Simulates a 3-atom Heisenberg model interaction using 3 qubits on IBM’s quantum processor, 'ibmq_jakarta'.
• Classical vs. Quantum Approach: Initially implements the simulation using classical methods, then transitions to a quantum approach for the same.
• State Representation: The quantum state of the system is represented by an 8x8 matrix, highlighting the power of quantum systems in representing multiple quantum states.
• Scalability: Demonstrates the limitations of classical computing and the scalability of quantum computing, showing that for larger systems (e.g., N=50), classical simulation is not feasible, while a quantum computer can handle it with just 15 qubits.
• NISQ Device Integration: Uses a real-world noisy intermediate-scale quantum device ('ibmq_jakarta') for performing the quantum simulations.

Requirements:

• Python 3.x: The code is likely implemented in Python.
• Qiskit: A quantum computing framework by IBM for working with quantum computers and simulators.
  • Install using pip install qiskit
• IBM Q Experience Account: Access to the quantum processor via IBM's quantum computing service.
  • Create an IBM Q account here and get an API key.
• Other Dependencies:
  • NumPy: For numerical computations.
  • Matplotlib: For visualizations (if applicable).
  • SciPy: For additional scientific computations.
  • Pandas: For data manipulation (if applicable).

To install the required dependencies, you can use:

bash

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pip install qiskit numpy matplotlib scipy pandas

Instructions:

• Clone the Repository: First, clone the repository from GitHub to your local machine:

  bash

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  git clone https://github.com/your-repo-name/Quantum-Simulation.git cd Quantum-Simulation

• Set up IBM Q Account:

  • Sign up for an IBM Q Experience account.

  • Generate an API token from your IBM Q dashboard.

  • Set up your IBM Q account in your Python script using the following command:

    python

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    from qiskit import IBMQ IBMQ.save_account('YOUR_API_TOKEN')

• Install Dependencies: Ensure all required libraries (such as Qiskit, NumPy, etc.) are installed. You can install them by running:

  bash

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  pip install -r requirements.txt

• Run Classical Simulation:

  • Before running the quantum simulation, execute the classical simulation to understand the baseline of the problem.
  • The classical simulation could involve calculating the interactions using standard computational methods (e.g., matrix multiplication).

• Run Quantum Simulation:

  • Use the ibmq_jakarta backend (or any available IBM quantum device) for simulating the Heisenberg model.

  • To run the quantum simulation on IBM’s quantum computer, execute the following:

    python

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    from qiskit import Aer, execute from qiskit.providers.ibmq import least_busy from qiskit import IBMQ # Load IBMQ account provider = IBMQ.load_account() # Choose the least busy device or a specific device like 'ibmq_jakarta' backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 3 and not x.configuration().simulator)) # Run the quantum simulation result = execute(circuit, backend).result() print(result.get_counts())

• Analyze Results: Once the quantum computation is done, use Qiskit’s plot_histogram or other visualization tools to visualize the output states of the quantum system.

  python

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  from qiskit.visualization import plot_histogram plot_histogram(result.get_counts())

• Expand to Larger Systems: The repository may provide guidelines for expanding the simulation to larger systems and investigating more complex quantum models using additional qubits.