The first outcome of this project is the examination of secure delegation of multiparty quantum computation to a powerful Server. In the proposed protocol, the quantum operations required from the clients are limited to a simple quantum encryption process, in order to ensure input privacy. More interestingly, the quantum communication from the clients to the Server can be done in single-qubit rounds, not necessitating any quantum memory from the clients. Furthermore, all quantum communication takes place in the preparation (offline) phase, which makes the computation phase more efficient, since only classical communication is required. In order to provide any type of security in the multiparty setting, we need two assumptions about the dishonest parties; we will assume that the clients have secure access to classical multiparty functionalities, which we will treat as oracles, and we also assume that a set of malicious clients cannot corrupt the Server, and the other way around. This means that we only prove security against two adversarial models, against a dishonest Server, and against a coalition of dishonest clients. Security in the more general scenario where a Server and some clients collaborate to cheat, remains as an open question, as well as exploration of verification of the computation performed. This is the first such examination of multiparty delegation of quantum computation and paves the way for further study of the remaining open questions.
The second exploration of this project was to explore a restricted quantum server, and exploit verification of computation by a limited client. I have proposed a protocol that can be used to delegate the construction of so-called IQP circuits to a powerful quantum Server. By giving the client of the computation limited quantum abilities (i.e. manipulation of single qubits), we have managed to remove the computational restriction of the Server required in previous works, and therefore have proven information-theoretical security against a malicious Server. The protocol is also proven to be composable and therefore can be used to verify an IQP machine as part of a larger delegated computation. IQP circuits are also important because they are relatively easy to implement in an experimental setup in comparison to fully fledged quantum computers needed for universal computations. Our protocol requires two layers of measurements, in order to do the appropriate corrections resulting from the blind creation of the state at the Server’s side, and for a small number of qubits, it can be implemented even with present technology. A future avenue of research would therefore be the study of this protocol under realistic experimental errors in view of a potential implementation.
I have then examined the case of classical computation and how quantum information can boost the capabilities of participants. The two resulting papers studied the setting where by the use of a single qubit, we can achieve non-linear computation, both deterministically and probabilistically, without having access to a non-linear classical process. Our method harnesses quantum resources to increase the computational power of the individual parties. Furthermore, in collaboration with the University of Oxford, we experimentally demonstrated how a set of clients with access to only classical XOR gates and singlequbit gates on quantum states can compute a specific example of a multiparty function, the pairwise AND, in a proof-of-concept implementation using photonic qubits.
A further study on quantum networks is underway, concerning quantum network routing. Quantum communication between distant parties is based on suitable instances of shared entanglement. For efficiency reasons, in an anticipated quantum network beyond point-to-point communication, it is preferable that many parties can communicate simultaneously over the underlying infrastructure; however, bottlenecks in the network may cause delays. Sharing of multi-partite entangled states between parties offers a solution, allowing for parallel quantum communication. In this ongoing work, I am examining how graph theoretic tools, and specifically local complementation, help decrease the number of required measurements compared to usual methods applied in repeater schemes. I am interested in different types of network architectures, where deploying local complementation techniques provides an advantage.
Finally, I am in the process of finalising a survey on quantum electronic voting, that identifies the problems in present proposals in the literature, and aims to propose solutions in order to achieve security in this setting. All proposals up to this point have been found to be faulty, and I am working towards solving the identified problems and finally achieving a quantum electronic protocol that is correct, secure, and also easy to implement.
