Estimating Energies with the Rodeo Algorithm

[NadavClassiq]

Quantum Algorithms: Estimating Energies with the Rodeo Algorithm

Abstract

Quantum simulations on noisy intermediate-scale quantum (NISQ) devices are valuable tools for advancing research in fields such as quantum chemistry and materials science. The Rodeo Algorithm for Quantum Computing by Kenneth Choi et al. offers a quantum algorithm tailored for estimating the energy spectrum of a quantum system, with efficient eigenstate preparation and exponential speedup over traditional methods like Quantum Phase Estimation.

Project Overview

Challenge: Implement the Rodeo Algorithm on the Classiq platform to estimate eigenenergies of a Hamiltonian using three distinct evolution methods: exponential_with_depth_constraint(), first-order Suzuki-Trotter, and unitary evolution functions. Follow the Glued Trees example structure as a reference for organizing the notebook.

Objective

Estimate eigenenergies of the Hamiltonian:

$$H_{obj} = J \sum_{\langle j,k \rangle} \vec{\sigma}_j \cdot \vec{\sigma}_k + h \sum_j \sigma_z^j$$

with $J=1.0$ and $h=3.0$, where $\langle j,k \rangle$ represents nearest neighbors and $\sigma$ are the Pauli matrices. The energy search interval is $E \in [-13, -9]$ a.u., using an initial alternating tensor product state. For more info, please refer to the article.

1. Set $N = 5$ qubits.
2. Apply three evolution methods:
   • exponential_with_depth_constraint()
   • First-order suzuki_trotter expansion
   • Unitary evolution functions
3. Quantitatively analyze the CX-gate counts for each method and compare results graphically.

Deliverables

• Jupyter Notebook with:
  • Quantum programs implementing the Rodeo Algorithm for each evolution method.
  • Estimated eigenenergies of the Hamiltonian for each approach.
  • Graphical analysis of CX-gate counts.

Follow the Contribution Guidelines in CONTRIBUTING.md. For any questions, contact us on GitHub or in our Slack Community.

Getting Started

1. Review Paper: Study the theory and methodology of the Rodeo Algorithm. Link to paper.
2. Set Up Environment: Create a new Jupyter Notebook and install Classiq SDK; refer to the setup guide.
3. Guiding Materials:
   • Classiq 101 - Introduction to platform concepts.
   • Classiq Fundamentals Workshop - Hands-on basics of Classiq.
   • Platform walkthrough on the home page.

Implementation Steps

1. Algorithm Coding:

   • Implement the Rodeo Algorithm with each evolution method using Classiq SDK.
   • Document your steps in markdown, referencing the Glued Trees Example.
   • Reach out on GitHub or Slack for support.

2. Mathematical Explanation:

   • Provide theoretical background, key equations, and algorithm insights using markdown and LaTeX.

3. Generate .qmod File:

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

4. Quality Check:

   • Proofread and verify code functionality.
   • Ensure clear markdown formatting and professional presentation.

5. Submit Contribution:

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

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Resources

• Reference Paper: Rodeo Algorithm for Quantum Computing by Kenneth Choi et al.
• Glued Trees Example: Link
• Hamiltonian Simulation: 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!