Rational proofs for quantum computing

TL;DR

This paper introduces a protocol where a completely classical client can verify quantum computations by incentivizing a rational quantum server with monetary rewards, ensuring correctness without quantum capabilities on the client side.

Contribution

It demonstrates that rational proofs can enable classical clients to verify quantum computations, removing the need for quantum technology on the client's part.

Findings

Client can verify quantum solutions using monetary incentives

Rational server is motivated to provide correct solutions

Protocol guarantees correctness through economic incentives

Abstract

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.