Rational proofs for quantum computing
(pp181-193)
Tomoyuki Morimae and Harumichi Nishimura
doi:
https://doi.org/10.26421/QIC20.3-4-1
Abstracts:
It is an open problem whether a classical client can
delegate quantum computing to an efficient remote quantum server in such
a way that the correctness of quantum computing is somehow guaranteed.
Several protocols for verifiable delegated quantum computing have been
proposed, but the client is not completely free from any quantum
technology: the client has to generate or measure single-qubit states.
In this paper, we show that the client can be completely classical if
the server is rational (i.e., economically motivated), following the
``rational proofs" framework of Azar and Micali.
More precisely, we consider the following protocol. The server first
sends the client a message allegedly equal to the solution of the
problem that the client wants to solve. The client then gives the server
a monetary reward whose amount is calculated in classical probabilistic
polynomial-time by using the server's message as an input. The reward
function is constructed in such a way that the expectation value of the
reward (the expectation over the client's probabilistic computing) is
maximum when the server's message is the correct solution to the
problem. The rational server who wants to maximize his/her profit
therefore has to send the correct solution to the client.
Key words:
rational proofs,
delegated quantum computing, verification of quantum computing |