Cross-platform verification, a critical undertaking in the realm of early-stage quantum computing, endeavors to characterize the similarity of two imperfect quantum devices executing identical algorithms, utilizing minimal measurements. While the random measurement approach has been instrumental in this context, the quasi-exponential computational demand with increasing qubit count hurdles its feasibility in large-qubit scenarios. To bridge this knowledge gap, here we introduce an innovative multimodal learning approach, recognizing that the formalism of data in this task embodies two distinct modalities: measurement outcomes and classical description of compiled circuits on explored quantum devices, both enriched with unique information. Building upon this insight, we devise a multimodal neural network to independently extract knowledge from these modalities, followed by a fusion operation to create a comprehensive data representation. The learned representation can effectively characterize the similarity between the explored quantum devices when executing new quantum algorithms not present in the training data. We evaluate our proposal on platforms featuring diverse noise models, encompassing system sizes up to 50 qubits. The achieved results demonstrate a three-orders-of-magnitude improvement in prediction accuracy compared to the random measurements and offer compelling evidence of the complementary roles played by each modality in cross-platform verification. These findings pave the way for harnessing the power of multimodal learning to overcome challenges in wider quantum system learning tasks.

In such networks, symbiosis leads to socioeconomic and environmental benefits for involved industrial agents and the society (see [14, 39]). One barrier against stable ISN implementations is the lack of frameworks able to secure such networks against unfair and unstable allocation of obtainable benefits among the involved industrial firms. In other words, although in general ISNs result in the reduction of the total cost, a remaining challenge for operationalization of ISNs is to tailor reasonable mechanisms for allocating the total obtainable cost reductions--in a fair and stable manner--among the contributing firms. Otherwise, even if economic benefits are foreseeable, lack of stability and/or fairness may lead to non-cooperative decisions. This will be the main focus of what we call the industrial symbiosis implementation problem. Reviewing recent contributions in the field of industrial symbiosis research, we encounter studies focusing on the necessity to consider interrelations between industrial enterprises [43, 47] and the role of contract settings in the process of ISN implementation [1, 44]. We believe that a missed element for shifting from theoretical ISN design to practical ISN implementation is to model, reason about, and support ISN decision processes in a dynamic way (and not by using snapshotbased modeling frameworks). For such a multiagent setting, the mature field of cooperative game theory provides rigorous methodologies and established solution concepts, e.g. the core of the game and the Shapley allocation [15, 30, 34, 7]. However, for ISNs modeled as a cooperative game, these established solution concepts may be either non-feasible (due to properties of the game, e.g.

We propose a novel representation for coalitional games with externalities, called Partition Decision Trees. This representation is based on rooted directed trees, where non-leaf nodes are labelled with agents' names, leaf nodes are labelled with payoff vectors, and edges indicate membership of agents in coalitions. We show that this representation is fully expressive, and for certain classes of games significantly more concise than an extensive representation. Most importantly, Partition Decision Trees are the first formalism in the literature under which most of the direct extensions of the Shapley value to games with externalities can be computed in polynomial time.