Nine-Month Report

Quantum computing on encrypted data (or QCED for short) is a family of techniques and protocols that allow the evaluation of some quantum function on a quantum input, while hiding that input from the party that performs the evaluation. This is useful in a setting involving two or more parties, some of which cannot be trusted: for example, a client holding some sensitive input may want to outsource a quantum computation to a computationally more powerful, but possibly malicious server. If the server can perform computations on encrypted data, the privacy of the client does not need to be compromised. Different flavors of QCED are relevant for different applications: we can allow interaction between the different parties during the computation, we can consider a setting with two parties (a client-server setting) or one with multiple parties that each want to hide their own input, we can require the authentication of the data (QCAD: quantum computing on authenticated data), et cetera. There are currently still many open questions floating around: for certain requirements or combinations of requirements, no protocol is known yet. They might even be impossible under some circumstances. During my master’s thesis project and the first months of my PhD, I have been learning about this field of research by taking courses in quantum information (both online and traditional) to strengthen my theoretical understanding, attending a winter school and several conferences to extend my network and discuss ideas, and of course by reading and reviewing related papers, both old and new. Especially during reviews and discussions, it became apparent how subtle small differences between different results can be. Questions like “How exactly does this relate to existing work?” and “In what way does this protocol really provide an advantage over what we can already do?” kept coming up. I am now starting to feel comfortable enough with my knowledge of the field to be able to answer these questions, given enough time to dig through the literature and understand the constructions of related protocols. However, since there are so many axes along which to improve QCED schemes, papers that focus on one aspect might not always be clear on how well their proposed algorithm performs with respect to the other axes. For example, minimizing the client-server communication may result in an increased demand on the client in terms of quantum memory. Such a scheme may be very suitable for some applications but not for others. Some survey papers exist [Her12, Fit16] that aim to make a fair comparison between different schemes, but even these tend to focus on one specific dimension of QCED. Moreover, they don’t always allow for a quick look-up, and run the risk of quickly becoming outdated in this fast-moving field.