[0] https://pubs.aip.org/aip/cha/article/27/2/023107/135054/Poly... [1] https://scottaaronson.blog/?p=2212

Looks like market speech to me.

I take issue with this line, however.

> Both MemComputing and quantum computers are physics-based approaches to computation. That is, they set aside many of the foundations of traditional computer science and rethink computation from the ground up. For example, they don’t follow the von Neumann architecture, the computing framework that separates the processing unit from the memory unit, which is employed by all of today’s computers.

From what I recall of Von Neumann, his titular architecture was the 'first draft' of what he was going for, and we've been stuck with it before he could figure out version two. He based his design on the notion of cellular automaton, where of course the processing units are not separated from the memory units.

Rather, from what I recall, the Architecture we've been stuck with was just his best attempt at emulating what's here called memcomputing, but with the limited engineering resources at his disposal. If he hadn't died, I think he would have been trying to do proper memcomputing in the second draft. Only took us the better part of a century to catch up!

```MemComputing is available today and is delivering the performance expected of quantum computers across a wide range of valuable optimization problems in industry. ```

Quantum computers unfortunately are not expected to do well against traditional OR algorithms in most (all?) OR problems (Grover search only helps in brute force search; Shor it not quite an OR application, and relies on quantum effects), so not really a strong selling point in my view

It smells like some BS to anyone who knows about this kind of thing, but I think their marketing is for the ones who don't know.

- the quality of the solutions found (in the best case: optimal solutions)

- the presence or absence of optimality guarantees (for example, some algorithms provide optimal solutions very often, but cannot guarantee it 100%)

- the time (or computational cost) needed to find such solutions

Furthermore, the state-of-the-art (SOTA) is well known for most types of optimization problems. In this article, they present a list of real and practical applications, so let us have a look at them one by one:

1.1 Traffic flow optimization

Simple flow problems can be solved in polynomial time (and quickly in practice), so there is no need for anything fancy. Once you introduce additional constraints or discrete variable, the SOTA is mixed-integer programming for offline problems. For online problems it's more complicated. In both cases, I am not aware of any application in which MemComputing can reach SOTA.

1.2 Vehicle routing & scheduling

Here, depending on your computing time constraints, needs for solution quality and/or optimality guarantees, the SOTA can be constraint programming (gecode, OptaPlanner), local search heuristics (LocalSolver), or mixed-integer programming (CPLEX/XPress/Gurobi) with column generation. MemComputing is nowhere to be seen again.

1.3 Supply chain optimization

This is a very broad field, but in general mixed-integer programming is king here.

2.1 Protein folding

Here there is quite an objective measure: the biennal CASP competition. This is where AlphaFold made a splash in 2022. MemComputing has never participated.

2.2 Genome sequencing

I am not knowledgeable enough to comment here.

2.3 Radiotherapy treatment

I am not very knowledgeable here either, but last I looked mixed-integer programming approaches were favored.

3.1 Portfolio risk optimization

Various types of branch-and-bound solvers. Mixed-integer linear/quadratic/convex programming. No MemComputing.

3.2 Detecting market instabilities

No idea.

3.3 Optimizing trading trajectories

No idea.

4.1 Training neural networks

Many people here know how this is done. Stochastic gradient descent on GPUs or TPUs. No MemComputing involved. How can they even claim to be active in this field?

4.2 Detecting statistical anomalies

Vague.

4.3 Classifying unstructured datasets

No idea.

The problem is that if you invent a new optimization algorithm, it is very easy to find one instance of one problem for which your algorithm works well. They did literally that in a paper [1]: They took a library of mixed-integer programming problem instances containing 270 benchmark problems, and published a whitepaper showing that they beat a SOTA solver on one of them. A single instance out of 270!

The really hard part is the opposite: given a class of problems, find an algorithm that beats the SOTA. MemComputing has never done that. Combined with their propensity for grand claims backed by misleading evidence, MemComputing have accumulated a lot of badwill from the academic community over the years. My suspicion is that, while on the surface this post seems to put their approach in contrast to quantum computing, what they really try to do here is ride on the quantum computing hype wave.

[1] https://arxiv.org/abs/2003.10644