https://github.com/xanaduai/cfqmagnus

Numerical analysis of the Magnus Hamiltonian simulation technique
https://github.com/xanaduai/cfqmagnus

hamiltonian-simulation quantum-computing time-dependent

Last synced: about 2 months ago
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Numerical analysis of the Magnus Hamiltonian simulation technique

• Host: GitHub
• URL: https://github.com/xanaduai/cfqmagnus
• Owner: XanaduAI
• Created: 2023-11-01T18:00:48.000Z (about 1 year ago)
• Default Branch: main
• Last Pushed: 2024-03-26T13:58:27.000Z (9 months ago)
• Last Synced: 2024-03-26T14:54:28.490Z (9 months ago)
• Topics: hamiltonian-simulation, quantum-computing, time-dependent
• Language: Python
• Homepage:
• Size: 8.75 MB
• Stars: 1
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Commutator-free quasi-Magnus operators

This repository contains the code to compute the cost of implementing quantum simulation using Commutator-free quasi-Magnus (CFQM) operators, originally introduced in [Fourth- and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems](https://www.sciencedirect.com/science/article/abs/pii/S0168927405002163) (see pdf [here](https://personales.upv.es/~serblaza/2006APNUM.pdf)) such as:

$$

\exp(\Omega^{[4]}(h)) = \exp(-i \alpha_1 h H(t_1) - i \alpha_2 h H(t_2))\exp(-i\alpha_2 h H(t_1) -i \alpha_1 h H(t_2)),

$$

with $\alpha_1 = \frac{3-2\sqrt{3}}{12}$, $\alpha_2 = \frac{3+2\sqrt{3}}{12}$, $H(t)$ the time-dependent Hamiltonian, and $t_1$ and $t_2$ defined as the roots of the Legendre polynomial of order 2 of the time segment of length $h$.

## Navigating the repository

This repository has the following structure

- The cost estimation cost is found in folder `CFQMagnus/`,

- while `coefficients/` contains the coefficients of the CFQMs (see `CFQMagnus/compute_coefficients.py` for their preparation),

- and `results/` saves the error-per-step incurred simulating the CFQM when using time step `h`.

The main files can are `magnus_errors.py` , containing the primitives that we need to compute their cost; and `main.py`, where we compute the error-per-step of each CFQM, which are saved to `results/`.

The cost minimizaton and associated paper figure generation can be implemented using the figure generation files in `CFQMagnus/figure_generation/`.

We additionally included a file `CFQMagnus/pennylane_simulation.py` providing an example of how to implement time simulation of a CFQM in [Pennylane](https://pennylane.ai/), using a Heisenberg model for the sake of an example.

## Installation

Navigate to the root directory of this repository and run

```shell

pip install -e .

```

You may also create a new conda environment before this, though the packages we use are standard ones and can be found in the `requirements.txt`.

## How to cite

Find the article in [Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators](https://arxiv.org/abs/2403.13889)

```

@misc{casares2024quantum,

      title={Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators},

      author={Pablo Antonio Moreno Casares and Modjtaba Shokrian Zini and Juan Miguel Arrazola},

      year={2024},

      eprint={2403.13889},

      archivePrefix={arXiv},

      primaryClass={quant-ph}

}

```