New proposed tutorial on quantum phase transitions

[DamianPope]

Hello,
We’ve been using PennyLane (PL) for four years and love it. This tutorial came about when we realized that many researchers were interested in phase transitions and quantum computers. However, some of them don’t have backgrounds in quantum computing. We’d love for you to consider this as a PL demo.

This is only our second PR for PL. So, we hope that we followed the instructions correctly. Many thanks. Damian Pope & Tirth Shah.

Title: Seeing Quantum Phase Transitions with Quantum Computers

Summary
A phase transition is when some property of a physical system changes abruptly. A quantum phase transition is when this happens due to quantum fluctuations. Quantum phase transitions are widely studied in condensed matter physics and cosmology. Many recent papers and current research are investigating them.

This tutorial introduces the concept of a quantum phase transition and walks through the PennyLane code for simulating three well-known quantum phase transitions with a quantum computer. It uses PennyLane’s qubit.lighting simulator.

Relevant references
M. Heyl, A. Polkovnikov, and S. Kehrein, “Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model”, Phys. Rev. Lett. 110, 135704 (2013)
https://arxiv.org/abs/1206.2505

Hashizume, Tomohiro 2022, “Dynamical phase transitions in the two-dimensional transverse-field Ising model”, Phys. Rev. Research 4, 013250 (2022) https://arxiv.org/abs/1811.09275

Reza Haghshenas et al. “Probing critical states of matter on a digital quantum computer” Phys. Rev. Lett. 133, 266502 (2024) arXiv:2305.01650 [quant-ph]

Possible Drawbacks:
The demo doesn’t directly relate to a recent paper. (But it is indirectly related to many recent papers.)

Related GitHub Issues:
N/A

If you are writing a demonstration, please answer these questions to facilitate the marketing process.
GOALS — Why are we working on this now?

Quantum phase transitions are a widely studied topic in multiple fields of physics. However, there are many cases where both analytic and classical computing techniques struggle to generate solutions. Quantum computers may be able to help where these other techniques fail. Simulating quantum phase transitions on quantum computers is currently a hot topic. Recently, there have been many papers on it including, for example, this Nature paper from February: https://www.nature.com/articles/s41567-024-02765-w

There are many researchers who are interested in quantum phase transitions but don’t have a background in quantum computing. An introductory tutorial on quantum phase transitions could be beneficial to these individuals.

PennyLane is well-suited to efficiently programming quantum computers to simulate quantum phase transitions. Its qml.spin module is especially useful for simulating phase transitions in the Ising model.

AUDIENCE — Who is this for?
Researchers interested in quantum phase transitions.
Quantum computing researchers who’d like to learn about quantum phase transitions.
Educators teaching phase transitions and condensed matter physics.

KEYWORDS — What words should be included in the marketing post?
quantum phase transition, condensed matter physics, many-body physics, Ising model, transverse Ising model

Which of the following types of documentation is most similar to your file?
(more details here note this requires a Xanadu email to view)
Tutorial
Demo -check
How-to

Notes:
The suggested thumbnail is a graphic showing an ice cube (i.e. solid water) melting into liquid water. This is a familiar visual cue for the general idea of a phase transition.

I suggest that the hero image conveys the idea of a group of qubits changing from one state (|0>) to another very different state (0> + |1>). This is a visual representation of a simple quantum phase transition. Below is a rough sketch of it.

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