The rapid evolution of quantum technologies is likely to cause major shifts in the
mainstream computing landscape. In order to fully reach their potential in a wide base
accessible to any user, remote access of quantum computers and manipulation of data
with strong privacy and integrity guarantees are essential.
Consider a setting where a client having a fully classical computer wants to determine the result of some quantum computation, but lacks the necessary resources
to perform the computation herself. She has access to a more powerful server which
has quantum resources and can solve the problem and send the outcome back to the
client. However, the client does not trust the powerful server, so she needs to find a
way to hide her data. Therefore, the main question that arises is how can we guarantee the client’s privacy of the input and even the computation itself against the server
possessing quantum computational capabilities.
In the present thesis, we study this problem, denoted here as classical secure delegation of quantum computations (CSDQC) between a fully classical honest client and
a quantum untrusted server. We focus on different models of security, analyzing the
limitations and potential of each of the settings. Concretely, we first study the CSDQC
problem under information-theoretic security. We analyse two categories of quantum
computations, decision and sampling problems and in both cases we provide evidence
indicating the impossibility of achieving information-theoretic security. Subsequently,
we consider relaxing the security framework and specifically, we will analyze this task
in the computational security setting (against quantum polynomial-time adversaries).
As a result, in the second part of the thesis we put forward the remote state preparation as a key component that would allow us to achieve classical secure delegation of
universal quantum computations. We present two protocols realizing the remote state
preparation primitive assuming only a classical channel between client and server. The
first candidate is shown to be secure in the honest-but-curious model, while the second
candidate is proven secure against the server in the malicious setting. The security of
both constructions relies on the hardness of the learning with errors problem. Finally,
given the important role the remote state preparation plays not only in CSDQC, but also
in other quantum communication protocols, we analyze its composable security to determine the privacy loss as a result of using remote state preparation as a sub-module
in different protocols
