[Draft] Adding Subspace Expansion error mitigation technique

[bubakazouba]

Authors: Ammar Jahin (amar.jahin@gmail.com), Dariel Mok (darielmok@caltech.edu), Preksha Naik(pnaik@caltech.edu), Abdulrahman Sahmoud (ahssahmoud@gmail.com)

Closes #818
Request For Comments (RFC) — Error Mitigation by Subspace Expansion

Description

This implementation features the Subspace Expansion error mitigation method. The purpose of this Pull Request is to support the associated RFC during the review process. If approved, we anticipate further modifications to the PR.

Issues with PR

Our code relies on being able to multiply PauliStrings, which doesn't seem to be supported in Mitiq's PauliString class. We couldn't find examples in the code of doing this, so we chose to access the private API to convert Mitiq's PauliStrings into Cirq's PauliStrings to do the multiplication operations. We instead propose to update the PauliString class to support multiplication if the PR/RFC is approved.

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License

• I license this contribution under the terms of the GNU GPL, version 3 and grant Unitary Fund the right to provide additional permissions as described in section 7 of the GNU GPL, version 3.

Before opening the PR, please ensure you have completed the following where appropriate.

• I added unit tests for new code.
• I used type hints in function signatures.
• I used Google-style docstrings for functions.
• I updated the documentation where relevant.
• Added myself / the copyright holder to the AUTHORS file

[github-actions]

👈 Launch a binder notebook on branch bubakazouba/mitiq/bubakazouba/subspace_expansion

[github-actions]

Hello @bubakazouba, thank you for submitting a PR to Mitiq! We will respond as soon as possible, and if you have any questions in the meantime, you can ask us on the Unitary Fund Discord.