Quantum Simulation of Geometrically Frustrated Magnets - Paper Implementation

[AbiralShakya]

In this issue, we will create an implementation of the Quantum Simulation of Geometrically Frustrated Magnets, following this research paper: https://arxiv.org/pdf/1911.03446.

A quantum simulation of geometrically frustrated magnets leverages quantum computing to explore exotic quantum phenomena, such as topological obstructions and order-by-disorder effects. Classical methods, like Path-Integral Monte Carlo (PIMC), struggle with slow relaxation and poor scaling at low temperatures. Quantum annealing offers a promising alternative by efficiently exploring low-energy states through quantum tunneling.
The key advantages of quantum simulation for frustrated magnets include:
• Faster Relaxation – Quantum annealing can achieve quicker convergence compared to classical Monte Carlo methods, especially in highly frustrated systems.
• Scalability – Quantum approaches may offer a significant advantage for large system sizes and low temperatures, where classical simulations become intractable.
• Insights into Quantum Materials – Understanding frustrated magnets can aid in the design of novel quantum materials and inform quantum computing applications.
This project will implement a quantum annealing protocol for the transverse field Ising model on a square-octagonal lattice, comparing results against classical PIMC simulations. The study will provide insights into quantum phase transitions, order-by-disorder effects, and potential quantum advantages in simulating complex magnetic systems.

[NadavClassiq]

It sounds like an interesting application @AbiralShakya .!

We will be glad to have such a contribution in our repository!

Since this project involves quantum annealing, how do you plan to implement it within the Classiq framework? Given that Classiq primarily focuses on high-level quantum circuit design and supports gate-based quantum computing,

Please note that we accept high-quality implementations in our repository and will gladly accept a contribution that meets our standards.

Feel free to reach out to the community if you have any questions.

Looking forward to hearing from you!

[AbiralShakya]

Hi @NadavClassiq , thank you for the feedback and considering our project idea, we really appreciate it.

We believe that approaching these problems on Classiq's gate based logic is of interest because, although the original paper approached it with annealing, we can work approach it with a gate based equivalent (which may be of interest to the greater community as well). For the actual physics simulation aspect, there are instances of approaching similar problems via VQE such as this paper https://arxiv.org/pdf/2306.00467 .

Moreover, we could also empirically explore the cost of emulating the annealing process on a gate-based hardware/ software stack like this paper does https://arxiv.org/html/2402.17667v1. Overall, we believe that exploring such a problem on gate based computing is valuable because it allows us to explore the effectiveness of simulated annealing and possible comparisons to results from the original research paper which used annealing.
Please let me know of any other questions and concerns.

Best,
Abiral