Rational proofs for quantum computing
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It is an open problem whether a classical client (verifier) can delegate quantum computing to a remote quantum server (prover) in such a way that the correctness of quantum computing is somehow guaranteed. We show that such a delegation is possible if the prover is rational. More precisely, we introduce the following protocol. The BQP prover first sends the BPP verifier a single bit allegedly equal to the solution of the BQP decision problem that the verifier wants to solve. The verifier then gives the prover a reward whose amount is determined by the bit sent from the prover and some random numbers the verifier samples from certain probability distributions. The reward function is constructed in such a way that the rational prover, who wants to maximize the expected profit, has to send the correct bit to the verifier.
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