Delegated and distributed quantum computation

This dissertation explores the possibilities and impossibilities of securely delegating and distributing quantum computations. We construct explicit protocols for several quantum-cryptographic primitives (quantum message authentication, multi-party quantum computation, and verifiable quantum homomorphic encryption), but show that one other primitive is impossible to achieve in general (quantum virtual black-box obfuscation).
For the primitives that we do realize, we often need to make assumptions on the computational power of the adversary's quantum computer. Such computational assumptions are necessary because the variants of the primitives that we wish to achieve are impossible information-theoretically. Nonetheless, our protocols are information-theoretic upgrades from their classical variants: the only computational assumptions are those that are already required to achieve the classical primitives. The advantage of this approach is that advances in classical and post-quantum cryptography directly influence our protocols as well.
In all of the cryptographic primitives studied in this dissertation, verification plays a crucial role. Whether a client wants to check the outcome of a computation he delegated to an untrustworthy server, or whether a player in a multi-party protocol wants to monitor the honesty of the other players in the protocol, an honest party always needs some kind of mechanism to ensure that the dishonest parties are not deviating from the protocol without being noticed.