Simulating quantum field theories on gate-based quantum computers

[NadavClassiq]

Simulating quantum field theories on gate-based quantum computers

Abstract

Simulation of Quantum Field Theories (QFTs) enables researchers to model quantum particle interactions governed by principles of quantum mechanics and special relativity. QFT simulations are essential in modern physics for exploring phenomena like particle collisions, confinement in quantum chromodynamics, and cosmological phase transitions. The paper Simulating Quantum Field Theories on Gate-Based Quantum Computers by Gayathree M. Vinod et al. presents a method to map QFTs onto qubits, enabling their dynamics to be simulated using Hamiltonian Simulation methods on quantum computers. This project challenges you to implement the approach for QFT simulation as outlined in the paper and reproduce specific results for comparison with exact simulations.

Project Overview

Challenge: Implement the QFT simulation method from the referenced paper, applying the technique to simulate the Quantum Field Theory described in Section IV.1. The task is to reproduce the paper’s FIG. 2 by performing both an exact simulation and a Hamiltonian simulation on a quantum computer. You may select the Hamiltonian simulation method that best fits your setup and compare its results to the exact simulation.

Objective

1. Reproduce the Quantum Field Theory simulation as described in the paper's Section IV.1.
2. Implement a parametrized quantum program that evolves over time.
3. Run the program and compare population states for the state $|f_1\rangle = |100-000-01-00-00\rangle$ between exact and Hamiltonian simulations.

Deliverables

• Jupyter Notebook containing:
  • Quantum programs for simulating the QFT using both exact and Hamiltonian methods.
  • A graph comparing the populations of the state $|f_1\rangle = |100-000-01-00-00\rangle$ over time between the exact simulation and Hamiltonian simulation.

Follow the Contribution Guidelines in CONTRIBUTING.md. For any questions, you can reach out via GitHub or join our Slack Community.

Getting Started

1. Review Paper: Study the method proposed in Simulating Quantum Field Theories on Gate-Based Quantum Computers by Gayathree M. Vinod et al., focusing on Section IV.1 for the QFT example.
2. Set Up Environment: Create a new Jupyter Notebook and install the Classiq SDK; refer to the setup guide.
3. Guiding Materials:
   • Classiq 101 - Introduction to platform concepts.
   • Classiq Fundamentals Workshop - Hands-on Classiq basics.
   • Platform walkthrough on home page.

Implementation Steps

1. Algorithm Coding:

   • Implement the QFT simulation technique outlined in the paper using the Classiq SDK.
   • Define the Hamiltonian for the QFT example in Section IV.1 and parameterize the time evolution. This is probably the complex point in this project
   • Document steps in markdown, following the Glued Trees Example.
   • For support, reach out via GitHub or Slack.

2. Mathematical Explanation:

   • Use markdown and LaTeX to provide theoretical explanations, key equations, and algorithm insights.

3. Generate .qmod File:

   • Use write_qmod(model, "filename.qmod") to save your models.
   • Confirm successful notebook execution and .qmod file generation.

4. Quality Check:

   • Proofread for accuracy and ensure code correctness.
   • Use clear markdown formatting and a professional presentation.

5. Submit Contribution:

   • Follow Contribution Guidelines.
   • Open a Pull Request in classiq-library/research/qft_simulation.
   • Include a summary of insights and results.

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Resources

• Reference Paper: Simulating Quantum Field Theories on Gate-Based Quantum Computers by Gayathree M. Vinod et al.
• Classiq Documentation: Classiq Library
• Glued Trees Example: Link
• Contribution Guidelines: CONTRIBUTING.md

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Note: No strict deadline. Confirm with us if you start this task so we can assign it to you.

Good Luck!