microsoft/qdk

# Resource Estimation for Double-factorized Chemistry

In this sample we evaluate the physical resource estimates of using the so-called double-factorized qubitization algorithm described in [[Phys. Rev. Research 3, 033055 (2021)](https://doi.org/10.1103/PhysRevResearch.3.033055)] to calculate the energy of a user provided Hamiltonian to chemical accuracy of 1 mHa.

The Hamiltonian is provided as an FCIDUMP file that is available on your machine or can be downloaded via an HTTPS URL.

```text
usage: chemistry.py [-h] [-f FCIDUMPFILE]

Double-factorized chemistry sample

options:
  -h, --help            show this help message and exit
  -f FCIDUMPFILE, --fcidumpfile FCIDUMPFILE
                        Path to the FCIDUMP file describing the Hamiltonian
  -p [PARAMSFILE ...], --paramsfile [PARAMSFILE ...]
                        Optional parameter files to use for estimation
```

For example, the following command will download the FCIDUMP file `n2-10e-8o` to the working folder and run resource estimation for it:

```shell
chemistry.py -f https://aka.ms/fcidump/n2-10e-8o
```

After that, you can pass the path to the downloaded file to the script instead:

```shell
chemistry.py -f n2-10e-8o
```

By default, physical resources are estimates for a Majorana based qubit with 10⁻⁶ error rates (`qubit_maj_ns_e6`), a Floquet code QEC scheme.  The error budget is set to 0.01 to reach the required chemical accuracy of 1 mHa.  The `-p` program argument can be used to load other resource estimation parameters, specified in JSON files.  The JSON files can either contain a JSON object for one configuration, or an array of JSON objects for multiple configurations.  Make sure to set the error budget to 0.01 to guarantee the correct chemical accuracy.

You can choose some of the following URLs to download example files:

| URL  | Instance name  | Description  |
|------|----------------|--------------|
| https://aka.ms/fcidump/n2-10e-8o             | n2-10e-8o             | 10 electron, 8 orbital active space of he dissociated nitrogen at 3 Angstrom distance (the default file used in the example) |
| https://aka.ms/fcidump/XVIII-cas4-fb-64e-56o | XVIII-cas4-fb-64e-56o | 64 electron, 56 orbital active space of one of the stable intermediates in the [ruthenium-catalyzed carbon fixation cycle](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.033055) |
| https://aka.ms/fcidump/nitrogenase-54e-54o   | nitrogenase-54e-54o   | 54 electron, 54 orbital active space of the active core of the nitrogenase that is used in [this paper](https://www.pnas.org/doi/10.1073/pnas.1619152114) |
| https://aka.ms/fcidump/fe2s2-10e-40o         | fe2s2-10e-40o         | 10 electron, 40 orbital active space of [2Fe, 2S] cluster that is shown in [this paper](https://www.nature.com/articles/nchem.2041) |
| https://aka.ms/fcidump/polyyne-24e-24o       | polyyne-24e-24o       | 24 electron, 24 orbital active space of the polyyne molecule |

The numbers for the XVIII-cas4-fb-64e-56o instance roughly match the numbers in the paper [Assessing requirements for scaling quantum computers to real-world impact](https://aka.ms/AQ/RE/Paper), as we incorporated a few improvements in the implementation of the double-factorized chemistry algorithm as compared to the version used when the paper was published.