Secure delegation of quantum computation
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Quantum computing is just now hitting a critical threshold. It is expected that a quantum computer with full control of upwards of 50 qubits will soon be available, and 50 is the magic number of qubits at which classical simulation of quantum systems becomes infeasible.
However, it is difficult to imagine that a consumer could have a quantum computer of their own. More likely, they would delegate their quantum computation to some machine in the cloud, similar to IBM's 16-qubit quantum experience . However, how can we maintain the security of our data while outsourcing it to these quantum machines?
In the classical setting, fully homomorphic encryption offers an elegant solution by which a user can delegate computation to a second party without revealing their data. Extending this primitive to the quantum setting has enjoyed major progress in the last five years, culminating in a quantum fully-homomorphic encryption scheme . However, this scheme requires a user to have sufficient quantum capability to prepare many entangled states. Furthermore, it is intrinsically a leveled scheme, wherein the number of entangled states to be prepared must scale with the circuit to be evaluated homomorphically.
Practically speaking, it would be best if a purely classical user could securely delegate a computation to a quantum machine by exchanging only classical information with that machine. In this talk, I will present a new paper  which claims a scheme for quantum fully-homomorphic encryption that can be performed by a purely classical client.
 IBM quantum experience. http://www.research.ibm.com/quantum
 Yfke Dulek, Christian Schaffner, and Florian Speelman. Quantum homomorphic encryption for polynomial-sized circuits, August 2016. CRYPTO 2016: Advances in Cryptology – CRYPTO 2016, pp 3-32.
 Urmila Mahadev, Classical Homomorphic Encryption for Quantum Circuits, Arxiv:1708.02130.