I am interested how quantum computing can contribute to the development of artificial intelligence, I did some searching, but could not find much. Does somebody have an idea (or speculations)?
In my view, if artificial general intelligence (AGI) is ever 'solved', it likely won't be because of the development of a quantum AI algorithm. Rather, it will be because of a breakthrough in the training of existing classical algorithms.
That said, much like in the classical case (i.e. classical machine learning), research on quantum algorithms with plausible applications to some future AGI largely center on quantum machine learning (QML). QML research is still in its infancy relative to classical machine learning research and its practical benefits are only beginning to be understood. Here’s a broad overview of some general themes that appear to be emerging:
We know that QML can provide algorithmic speedups. Much of the work in QML has been based on the quantum linear systems algorithm (QLSA, also known as HHL). This algorithm can be used to invert a covariance matrix, which is useful for the training of (for example) support vector machines and Gaussian process models. While somewhat controversial, the speedups of QML algorithms based on the HHL algorithm were originally thought to be superpolynomial (given some caveats, see this paper by Aaronson and another by Childs). Now, however, the speedups are generally believed to be polynomial (in many cases) due to the assumptions made in developing many QML algorithms and dequantization arguments (see here and here). For a nice overview, see this Quanta article. Also note that some of the caveats discussed in the links above have been addressed by refinements to the HHL algorithm. Also, it's notable that these specific algorithms often require quantum data as their input, which means they can't simply be added into a classical ML pipeline.
It's unclear to what extent quantum information enhances or limits model representations. When developing a machine learning model, one of the central goals is to learn a representation (e.g. the parameters of a neural network model) that enables us to make accurate predictions on unseen data drawn from a distribution we assume to be i.i.d. with the training data. An interesting question in this respect is whether using qubits to generate a learned representation offers any advantage over the standard (classical) representations currently being generated. Intuitively, quantum representations may have advantages for certain problems that inherently involve quantum effects, such as molecular simulation. Some recent work in this area indicates that certain QML algorithms may have improved trainability (i.e. fewer barren plateaus and narrow gorges), lower generalization error, and reduced sample complexity.
How should we be performing regularization in the QML context. It's been argued that some existing QML algorithms would massively overfit the data, severely limiting generalizability (for example, Peter Wittek notes the issue here while discussing quantum support vector machines). In classical machine learning, to ensure the ability of a model to generalize, we usually make use of some kind of regularization technique. I haven't yet seen any research around a QML approach to regularization (although variational quantum algorithms, discussed below, represent a glaring exception); perhaps someone else can comment on whether such approaches have been proposed for algorithms processing quantum data. A linking concept here may be the recent development of quantum kernel methods.
Limited complexity guarantees. Typically, we like our algorithms to offer some kind of guarantee around the worst-case behavior in terms of resource usage given some input size. Variational quantum algorithms, which are now central to the pursuit of practical quantum advantages in the near term, rarely provide these guarantees. While a lack of these guarantees doesn't preclude the possibility of a practical application in any way, it does mean that evidence that a classical approach couldn't do better is heterogenous, often informal, and highly problem specific.
I/O Another aspect is the input and output of the QML algorithm – are we inputting and outputting classical data like a traditional ML algorithm but doing quantum processing in the middle? Or rather is our input or output quantum? Or maybe they're both quantum? These details are hugely important to the realization of quantum advantages and, in particular, how to best input classical data into a QML algorithm is an area of great interest (and the input problem, in general, is not new).
There's certainly more that could be discussed relating to this question and, to be transparent, I am still very much learning this area. I hope more answers roll in but, until then, perhaps the information above can provide some context around what I would suggest the answer to your question is: We don't really know, yet.