Well, we made it to Innsbruck, Austria!

It was a huge journey to get here, and I have to tell you, Austria in general, and Innsbruck in particular, is absolutely beautiful.

On the train ride from Vienna to Salzburg, we spent most of the time looking out of the window taking photos. The weather is amazing; it’s perfectly warm and sunny, and it’s amazing to walk around the town and just see mountains everywhere.

But, I’m here, of course, on business, and in particular, primarily to attend the QML+ — *Quantum Machine Learning … Plus* — conference.

It’s the night of Day 1, so here’s a review of what happened:

### Opening Talk: Why QML+?

*by Hans Briegel*

Hans Briegel, famous partly for his involvement measurement-based quantum computation (and of particular relevance to me, because this was part of what my Masters work was about) gave an overview talk about why we might care to think about how quantum computing could play a role in machine learning.

I quite enjoyed one of his ideas, which is thinking about how “Embodied AI” relates to the ideas of “information is physical” insofaras both imply that in order to think about the primary subject, we need to involve physics. This has been particularly fruitful in physics and information theory, and relates to some very far-reaching ideas, such as black holes.

He used this as motivation to study a “Artificial Agent” (or in standard lingo, *Reinforcement learning*) in the quantum setting:

His observation is: What is quantum? There are four options:

*CC*: Classical Agent, Classical Environment*CQ*: Classical Agent, Quantum Environment*QC*: Quantum Agent, Classical Environment*QQ*: Quantum Agent, Quantum Environment

He noted that in the Quantum-Quantum setting, there are some foundational open problems:

- How do you measure that you’re learning?
- What does it mean to “act” in a fully quantum setting?
- What role does decoherence play?

I don’t think even these questions are quite clear to me, let alone the answers; but still interesting to think about.

One idea/question I had is: What is the simplest truly quantum reinforcement learning problem?

### Quantum algorithms for the Hopfield network, quantum gradient descent, and Monte Carlo

*by Patrick Rebentrost*

Next up was Patrick, who gave a far-reaching talk on a variety of topics that he and his colleagues have been researching over the last few years.

He started off by reminding us of a bunch of challenges that he posed in a prior paper:

- The “input” challenge – How to get data in to a quantum network? It turns out this is very subtle.
- The “costing” challenge – Just how many qubits are required to implement these algorithms? How practical is it to build?
- The “output” challenge – Even if we build an efficient quantum machine learning algorithm that produces a final state that encodes the answer; how do we read out the answer efficiently? It takes many measurements to extract the known state, so is it efficient to do so?
- The “benchmarking” challenge –
*even if*we solve all the above, how does it compare to classical algorithms? It can be very hard to prove that the quantum algorithm is better than any possible classical one.

Next, he talked about a quantum algorithm for training a so-called “Hopfield” neural network via the Hebbian learning procedure.

The Hopfield network is simply one in each every node is connected to every other node; and there is only one layer, and every node is both input and output (there are no layers, essentially). This may seem odd, and you should rightly wonder how you could train such a thing. One way to train it turns out to be the so-called “Hebbian” learning, which is inspired by the Human brain. The idea is captured by the phrase: “Neurons that fire together wire together”. With this idea in hand, it’s possible to develop a scheme to encode all this into a quantum computer, and perform all the updates and training. You can find more here.

For the everyday deep learning person, these ideas may sound a bit odd. Rightly so, because it’s not standard practice. Essentially the only reason to focus on these for in the quantum machine learning setting is that this is a network for which we *can* come up with a scheme to implement it on a quantum computer. A natural question is: Can we adapt the Hopefield-network techniques to work with multiple layers? I tentatively feel like the answer could be “yes”, but I haven’t thought a lot about it.

The next paper he talked about is this one: Quantum gradient descent and Newton’s method for constrained polynomial optimization.

I happened to read this one when it came out, because it was quite a big step. Previously, we had no idea how to even compute a quantum gradient, so this contribution was huge.

Unfortunately, the main problem of this paper is that the algorithm gets exponentially slower as the number of training steps increases. This is, at least naively, incredibly problematic for typical machine learning, where the number of steps is in the hundreds of thousands. In the paper they make the argument that oftentimes good results can be achieved after a very small number of steps, but it’s not clear to me how practical this is.

His final topic was Quantum computational finance; he was basically out of time, so didn’t go in to much detail, but the main idea is that again, using a standard technique in quantum computing called “amplitude amplification”, one can achieve a quadratic speedup in a certain kind of derivative-pricing. It turns out that banks and genuinely interested in these techniques, because being able to price something in say ~2 days, instead of 7 days, is a significant advantage market-wise.

Partick ended with a funny remark along these lines, which is that, the beauty of working in the finance world is that you don’t need to *prove* anything, you just simply build it, and let it go around making trades in the market; if it doesn’t work, you simply lose money!

## Lunch

Over lunch, I had a really nice chat with Pooya Ronagh from 1Qbit and Ronald de Wolf. We chatted largely about how the practical every-day machine learning could be aided by quantum techniques. Ronald pushed hard to understand what areas quantum researchers should focus on, and Pooya and I were trying to come up with ideas. Pooya had an interesting comment that, in many ways, faster machine learning isn’t super useful, because for the physical cost of a quantum computer, you can already buy significant hardware and get great results. So bad results faster doesn’t really help, in a foundational way.

Some thoughts we had is that maybe just flat-out alternatives to gradient descent would be interesting; i.e. we know there are areas where gradient-descent style optimisation is not great: translation, program synthesis, neural architecture search, etc.

In any case, it was a very inspiring chat, and I was really glad to have met them!

## Programmable Superpositions with Hebbian (un)-Learning

*by Wolfgang Lechner*

This, I must say, was quite technical, and I didn’t quite follow most of it. But I did get the general idea.

The main tool of quantum machine learning is the so-called HHL algorithm (see also: Quantum linear systems: a primer). One thing it requires is efficient loading of the training data. It turns out that typically, if you want to load the training data into a quantum algorithm, in general you’ll need to do an exponential amount of work in the number of training samples. Which is hugely problematic. I think I need to understand this a bit more, but at least the basic idea was clear: the data-loading needs to be sped up.

The main contribution of this work is that, through a rather elaborate procedure, partially described here: Programmable superpositions of Ising configurations (but more in upcoming publications), it’s possible to prepare the required state by encoding it into a Hamiltonian, and then letting the Hamiltonian evolve via adiabatic evolution. How? Hebbian Learning, evidently! I admit that I didn’t follow most of this talk, but I do think this kind of thing is quite interesting, and there’s definitely a need to solve this general, and reasonably embarrassing problem.

## That’s it!

That’s all the talks I attended today. Hope you found this helpful!

See also: