Comments about the article in Nature: Evidence for the utility of quantum computing before fault tolerance

Following is a discussion about this article in Nature Vol 618 15 June 2023, by Youngseok Kim e.a.
To study the full text select this link: https://www.nature.com/articles/s41586-023-06096-3 In the last paragraph I explain my own opinion.

Reflection

It is a challenge to try to understand the most difficult documents.

Introduction

It is almost universally accepted that advanced quantum algorithms such as factoring or phase estimation will require quantum error correction.
See: Shor's Algorithm Describes a simulation of "Shor's Algorithm" (factoring) on a Digital Computer using Parallel Processing.
However, it is acutely debated whether processors available at present can be made sufficiently reliable to run other, shorter-depth quantum circuits at a scale that could provide an advantage for practical problems.
Honest description
At this point, the conventional expectation is that the implementation of even simple quantum circuits with the potential to exceed classical capabilities will have to wait until more advanced, fault-tolerant processors arrive.
It is important to understand the type of problems the authors have in mind.
Quantum advantage can be approached in two steps: first, by demonstrating the ability of existing devices to perform accurate computations at a scale that lies beyond brute-force classical simulation, and second by finding problems with associated quantum circuits that derive an advantage from these devices.
What is meant with: "brute-force classical simulation" ?
https://pubs.aip.org/aip/jcp/article/159/8/086101/2908319/Brute-force-nucleation-rates-of-hard-spheres
General quantum circuits of this size lie beyond what is feasible with brute-force classical methods.
Okay.
We thus first focus on specific test cases of the circuits permitting exact classical verification of the measured expectation values.
This is the normal first step when you want to replace a certain mathematical methodology by a different methodology.
When this steps shows: that repeating the same test shows the same result, you can be satisfied.
We then turn to circuit regimes and observables in which classical simulation becomes challenging and compare with results from state-of-the-art approximate classical methods.
That is the logical next step: make small modifications.
Our benchmark circuit is the Trotterized time evolution of a 2D transverse-field Ising model, sharing the topology of the qubit processor.
All relevant physical problems are 3D.
The Ising model appears extensively across several areas in physics and has found creative extensions in recent simulations exploring quantum many-body phenomena, such as time crystals quantum scars and Majorana edge modes

Reflection 1 - Ising model

The Ising model is considered one area to study, which problems can be 'solved' by using a quantum computer.
For more detail select this link: https://farside.ph.utexas.edu/teaching/329/lectures/node110.html
And this link: https://en.wikipedia.org/wiki/Ising_model And: https://en.wikipedia.org/wiki/Ising_model#Applications

The question raised is: to what extend a Quantum Computer can be used to solve the Ising model.
IMO the real problem is how the parameters of the Ising model are measured and or calculated in an actual example i.e. experiment.
The second issue is how the solution is validated.

Reflection 2

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Created: 6 September 2023

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