Homomorphic encryption of the k=2 Bernstein–Vazirani algorithm

We introduce a class of circuits that solve a particular case of the Bernstein–Vazirani recursive problem for second-level recursion. This class of circuits allows for the implementation of the oracle using a number of T-gates that grows linearly with the number of qubits in the problem. We find an application of this scheme to quantum homomorphic encryption (QHE), which is an important cryptographic technology useful for delegated quantum computing, allowing a remote server to perform quantum computations on encrypted quantum data, so that the server cannot know anything about the client’s data. Liang’s QHE schemes are suitable for circuits with a polynomial number of gates T/T†. Thus, the simplified circuits we have constructed can be evaluated homomorphically in an efficient manner.