# Homomorphic encryption of linear optics quantum computation on almost arbitrary states of light with asymptotically perfect security

## TL;DR

This paper introduces a homomorphic encryption scheme for linear optics quantum computation on light states with fixed photon numbers, ensuring asymptotically perfect security and practical implementation using current technology.

## Contribution

It presents a novel encryption protocol for quantum states of light that maintains data secrecy during computation, applicable to universal linear optics quantum computing.

## Key findings

- Achieves asymptotically perfect information-theoretic secrecy.
- Uses random coherent displacements for data obfuscation.
- Experimental implementation is feasible with current technology.

## Abstract

Future quantum computers are likely to be expensive and affordable outright by few, motivating client/server models for outsourced computation. However, the applications for quantum computing will often involve sensitive data, and the client would like to keep her data secret, both from eavesdroppers and the server itself. Homomorphic encryption is an approach for encrypted, outsourced quantum computation, where the client's data remains secret, even during execution of the computation. We present a scheme for the homomorphic encryption of arbitrary quantum states of light with no more than a fixed number of photons, under the evolution of both passive and adaptive linear optics, the latter of which is universal for quantum computation. The scheme uses random coherent displacements in phase-space to obfuscate client data. In the limit of large coherent displacements, the protocol exhibits asymptotically perfect information-theoretic secrecy. The experimental requirements are modest, and easily implementable using present-day technology.