Foundations of classical and quantum verifiable computing

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Recent years have seen a vast surge in the volume and sensitivity of data that are being generated and collected, e.g., in genetic sequencing, distributed storage services, and graphs of social networks. The ubiquity and sheer size of modern data sets raise an urgent need to develop new techniques and methodologies for scalable computation.At the same time, the rise of blockchain technology, which underlies deployed distributed systems such as Bitcoin and Ethereum, provides ample motivation for developing decentralised protocols that could go beyond challenging centralised financial control, and profoundly impact society by providing a foundation for real-world distributed systems that can be used for public benefit.A key paradigm for meeting the challenges imposed by both of the aforementioned desiderata is that of verifiable computing. Here, the goal is to allow verification of computation that is performed by a third-party, in a scalable, secure, and privacy-preserving way. Moreover, with the advent of quantum computing on the horizon, it is imperative that the verification would also be post-quantum secure.This proposal is focused on pushing the boundaries of classical and quantum verifiable computing and its real-world applications to delegation of computation to the cloud, as well as to blockchain technology. Its primary objective is to develop a wide arsenal of tools that would open new possibilities for meeting the challenges imposed by big data and the need for decentralised peer-to-peer systems.The proposed approach is inherently interdisciplinary, involving fundamental concepts in cryptography, complexity theory, randomised algorithms, and quantum information, as well as relying on techniques from coding theory, combinatorics, and abstract algebra.