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Conference Papers Year : 2020

Non-interactive classical verification of quantum computation


In a recent breakthrough, Mahadev constructed an interactive protocol that enables a purely classical party to delegate any quantum computation to an untrusted quantum prover. In this work, we show that this same task can in fact be performed non-interactively and in zero-knowledge. Our protocols result from a sequence of significant improvements to the original four-message protocol of Mahadev. We begin by making the first message instance-independent and moving it to an offline setup phase. We then establish a parallel repetition theorem for the resulting three-message protocol, with an asymptotically optimal rate. This, in turn, enables an application of the Fiat-Shamir heuristic, eliminating the second message and giving a non-interactive protocol. Finally, we employ classical non-interactive zero-knowledge (NIZK) arguments and classical fully homomorphic encryption (FHE) to give a zero-knowledge variant of this construction. This yields the first purely classical NIZK argument system for QMA, a quantum analogue of NP. We establish the security of our protocols under standard assumptions in quantum-secure cryptography. Specifically, our protocols are secure in the Quantum Random Oracle Model, under the assumption that Learning with Errors is quantumly hard. The NIZK construction also requires circuit-private FHE.

Dates and versions

hal-03043284 , version 1 (07-12-2020)



Gorjan Alagic, Andrew M. Childs, Alex Grilo, Shih-Han Hung. Non-interactive classical verification of quantum computation. Theory of Cryptography - 18th International Conference, TCC 2020, Nov 2020, Durham, United States. pp.153--180, ⟨10.1007/978-3-030-64381-2_6⟩. ⟨hal-03043284⟩
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