Symmetry Enhanced Variational Quantum Spin Eigensolver

[NadavClassiq]

Symmetry Enhanced Variational Quantum Spin Eigensolver

Abstract

Variational Quantum Algorithms (VQAs) have emerged as powerful methods for achieving quantum advantage on Noise Intermediate-Scale Quantum (NISQ) devices. Their adaptability to current quantum technology, without the need for error correction, makes them ideal for a range of applications. A key component in building effective VQAs is tailoring the variational ansatz to include symmetries or conserved quantities, which can improve performance and accuracy. This project focuses on implementing the Symmetry Enhanced Variational Quantum Spin Eigensolver by Chufan Lyu et al., specifically designed for spin systems with a conserved total spin number using the Variational Quantum Eigensolver (VQE).

Project Overview

Challenge: Implement the VQE algorithm using a symmetry-enhanced ansatz on the Classiq platform to estimate ground state energies for a spin system. Compare the Sz-conserving ansatz with hardware-efficient ansatzes between 5 and 15 layers. Reference the Glued Trees example structure for notebook organization.

Objective

Estimate the ground state energy for a spin system with $N = 4$ qubits:

1. Implement and compare:
   • Sz-conserving ansatz
   • Hardware-efficient ansatzes (5 to 15 layers)
2. Analyze the algorithm’s performance with different initial parameters.

Deliverables

• Jupyter Notebook containing:
  • Quantum programs implementing the VQE with both ansatz types.
  • Graphical comparison of the ground state energy estimates for each ansatz.
  • Analysis of algorithm behavior with varying initial parameters.

Follow the Contribution Guidelines in CONTRIBUTING.md. Reach out on GitHub or in our Slack Community if you have any questions.

Getting Started

1. Review Paper: Study the theory and methods from the paper Symmetry Enhanced Variational Quantum Spin Eigensolver by Chufan Lyu et al.
2. Set Up Environment: Create a new Jupyter Notebook and install the Classiq SDK. Follow 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 algorithm using the Classiq SDK.
   • Document steps in markdown, following the Glued Trees Example.
   • For assistance, reach out on GitHub or Slack.

2. Mathematical Explanation:

   • Use markdown and LaTeX for theoretical background, key equations, and algorithm insights.

3. Generate .qmod File:

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

4. Quality Check:

   • Proofread and ensure code accuracy.
   • Format markdown for clarity and professional presentation.

5. Submit Contribution:

   • Follow Contribution Guidelines.
   • Open a Pull Request in classiq-library/research/symmetry_enhanced_variational_spin_eigensolver.
   • Include a summary and key insights from your implementation.

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Resources

• Reference Paper: Symmetry Enhanced Variational Quantum Spin Eigensolver by Chufan Lyu et al.
• 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!