3 research outputs found
Sumcheck-based delegation of quantum computing to rational server
Delegated quantum computing enables a client with a weak computational power
to delegate quantum computing to a remote quantum server in such a way that the
integrity of the server is efficiently verified by the client. Recently, a new
model of delegated quantum computing has been proposed, namely, rational
delegated quantum computing. In this model, after the client interacts with the
server, the client pays a reward to the server. The rational server sends
messages that maximize the expected value of the reward. It is known that the
classical client can delegate universal quantum computing to the rational
quantum server in one round. In this paper, we propose novel one-round rational
delegated quantum computing protocols by generalizing the classical rational
sumcheck protocol. The construction of the previous rational protocols depends
on gate sets, while our sumcheck technique can be easily realized with any
local gate set. Furthermore, as with the previous protocols, our reward
function satisfies natural requirements. We also discuss the reward gap. Simply
speaking, the reward gap is a minimum loss on the expected value of the
server's reward incurred by the server's behavior that makes the client accept
an incorrect answer. Although our sumcheck-based protocols have only
exponentially small reward gaps as with the previous protocols, we show that a
constant reward gap can be achieved if two non-communicating but entangled
rational servers are allowed. We also discuss that a single rational server is
sufficient under the (widely-believed) assumption that the learning-with-errors
problem is hard for polynomial-time quantum computing. Apart from these
results, we show, under a certain condition, the equivalence between
and delegated quantum computing protocols. Based on this
equivalence, we give a reward-gap amplification method.Comment: 28 pages, 1 figure, Because of the character limitation, the abstract
was shortened compared with the PDF fil