Add a tutorial on quantum simulation

[nathanshammah]

Issue Description

According to google scholar, reading among those papers that cite the Mitiq white paper and use Mitiq, it turns out that several of them have used Mitiq's ZNE for quantum simulation toy models and tests on hardware. See a screenshot from a slide, below, for a summarized view. Given this fact, it seems like to me that adding to the documentation, in the examples section, one tutorial (or more) about quantum simulation with Mitiq would prove useful.

Proposed Solution

Add a tutorial about quantum simulation to the documentation. One could even reach out to the authors of such papers if they wish to provide a tutorial.

Some loose ideas for a specific tutorial:

• reproduce a plot from one of the citing papers (snapshot above)
• make a simple example for quantum simulation + ZNE
• make a more elaborate example, with a bigger focus on the physical interpretation, a possible use case could be phase transitions, including (precursors of) dissipative phase transitions or time crystals for a relatively small number of qubits

Additional References

See among papers citing and using Mitiq https://scholar.google.com/scholar?oi=bibs&hl=en&cites=1985661232443186918&as_sdt=5 There is one example about the simulation of a simple Hamiltonian energy (without a VQA approach).

Issue List

• [ ] #1794
• [ ] #1795
• [ ] #1796
• [x] #1797
• [ ] #1798
• [x] #1799

[tinaoberoi]

Hi @nathanshammah I am a new contributor to mitiq. This issue could be a hands-on-learning assignment for me to learn more about mitiq. I would love to work on it.

[purva-thakre]

Reopening this because there are still some tutorials that could be added and the wrong issue was closed previously.

[purva-thakre]

@tinaoberoi This issue has multiple sub-issues. Would you like one of the sub-issues to be assigned to you? Feel free to comment on that particular one.

[purva-thakre]

This paper could also be added as a part of the parent tutorials issue: https://arxiv.org/abs/2404.09132

I quickly glanced through the results. They combine ZNE, DDD with QSE and also tailor the noise by Pauli twirling.

According to the authors, better results are obtained through a variation of PEC with QSE and noise characterization via Pauli noise tomography.