  We present a new scheme for quantum homomorphic encryption which is compact
and allows for efficient evaluation of arbitrary polynomial-sized quantum
circuits. Building on the framework of Broadbent and Jeffery and recent results
in the area of instantaneous non-local quantum computation, we show how to
construct quantum gadgets that allow perfect correction of the errors which
occur during the homomorphic evaluation of T gates on encrypted quantum data.
Our scheme can be based on any classical (leveled) fully homomorphic encryption
(FHE) scheme and requires no computational assumptions besides those already
used by the classical scheme. The size of our quantum gadget depends on the
space complexity of the classical decryption function -- which aligns well with
the current efforts to minimize the complexity of the decryption function.
  Our scheme (or slight variants of it) offers a number of additional
advantages such as ideal compactness, the ability to supply gadgets "on
demand", circuit privacy for the evaluator against passive adversaries, and a
three-round scheme for blind delegated quantum computation which puts only very
limited demands on the quantum abilities of the client.
