Quantum Homomorphic Encryption for Circuits of Low T-gate Complexity

Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic encryption, which is the encryption of quantum information such that quantum computations can be performed given the ciphertext only. Our schemes allow for arbitrary Clifford group gates, but become inefficient for circuits with large complexity, measured in terms of the non-Clifford portion of the circuit (we use the “\(\pi /8\)” non-Clifford group gate, also known as the \(\mathsf{T}\)-gate).

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