Quantum technologies hold the promise of not only faster algorithmic processing of data, via quantum computation, but also of more secure communications, in the form of quantum cryptography. In recent years, a number of protocols have emerged which seek to marry these concepts for the purpose of securing computation rather than communication. These protocols address the task of securely delegating quantum computation to an untrusted device while maintaining the privacy, and in some instances the integrity, of the computation. We present a review of the progress to date in this emerging area.npj Quantum Information (2017) 3:23 ; doi:10.1038/s41534-017-0025-3
INTRODUCTIONFor almost as long as programmable computers have existed, there has been a strong motivation for users to run calculations on hardware that they do not personally control. Initially, this was due to the high cost of such devices coupled with the need for specialised facilities to house them. Universities, government agencies and large corporations housed computers in central locations where they ran jobs for their users in batches. Over time, computers have become ubiquitous, but demand for centralised resources has not abated. Even today, the use of delegated computation is widespread, in the form of cloud computing.While we do not yet know how the field of quantum computing will develop, it seems reasonable to speculate that it will follow a similar path. Indeed this speculation is somewhat born out by recent efforts to provide access to rudimentary quantum processors over the Internet.1 Today we are in a far better position to enable remote access to quantum computers than was possible with early conventional computers, due to the existence of high speed global communications networks, and the ubiquity of classical processors. Furthermore, the discovery of quantum key distribution protocols 2, 3 has provided the impetus to develop quantum communication over existing optical fibre networks