Classical zero-knowledge arguments for quantum computations

Vidick, Thomas; Gilroy, Simon

doi:10.22331/q-2020-05-14-266

Cited by 14 publications

(7 citation statements)

References 19 publications

(80 reference statements)

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“…However, for general QMA relations, and some applications, the idea of safeguarding the state against the verifier becomes more relevant. In prior work [VZ19], we showed that the protocol introduced in [Mah18b] can be made zero-knowledge. Since we show in the current work that [Mah18b] is an argument of quantum knowledge for any QMA relation, we believe zero-knowledge classical arguments of quantum knowledge can also be constructed for any QMA relation.…”

Section: A|mentioning

confidence: 99%

Classical Proofs of Quantum Knowledge

Vidick

Gilroy

2021

Lecture Notes in Computer Science

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We define the notion of a proof of knowledge in the setting where the verifier is classical, but the prover is quantum, and where the witness that the prover holds is in general a quantum state. We establish simple properties of our definition, including that nondestructive classical proofs of quantum knowledge are impossible for nontrivial states, and that, under certain conditions on the parameters in our definition, a proof of knowledge protocol for a hard-to-clone state can be used as a (destructive) quantum money verification protocol. In addition, we provide two examples of protocols (both inspired by private-key classical verification protocols for quantum money schemes) which we can show to be proofs of quantum knowledge under our definition. In so doing, we introduce new techniques for the analysis of such protocols which build on results from the literature on nonlocal games. Finally, we show that, under our definition, the verification protocol introduced by Mahadev (FOCS 2018) is a classical argument of quantum knowledge for QMA relations.

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Section: A|mentioning

confidence: 99%

Classical Proofs of Quantum Knowledge

Vidick

Gilroy

2021

Lecture Notes in Computer Science

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“…The notion and techniques developed in [35,82] have recently been utilized to put forward protocols with e.g. zero-knowledge polynomial-time verifiers [83] and non-interactive classical verification [84].…”

Section: Verification Of the Output Of An Untrusted Quantum Devicementioning

confidence: 99%

Theoretical and Experimental Perspectives of Quantum Verification

Carrasco,

Elben,

Kokail

et al. 2021

Preprint

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In this perspective we discuss verification of quantum devices in the context of specific examples, formulated as proposed experiments. Our first example is verification of analog quantum simulators as Hamiltonian learning, where the input Hamiltonian as design goal is compared with the parent Hamiltonian for the quantum states prepared on the device. The second example discusses crossdevice verification on the quantum level, i.e. by comparing quantum states prepared on different quantum devices. We focus in particular on protocols using randomized measurements, and we propose establishing a central data repository, where existing experimental devices and platforms can be compared. In our final example, we address verification of the output of a quantum device from a computer science perspective, addressing the question of how a user of a quantum processor can be certain about the correctness of its output, and propose minimal demonstrations on present day devices.

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“…Therefore, the remaining task is to prove Eq. (39). In so doing, we use the algorithm D to construct an algorithm A for the injective invariance of F.…”

Section: E Computational Indistinguishability Of Post-measurement Statesmentioning

confidence: 99%

“…Recently, by exploiting the ENTCF families, various protocols have been invented for the proof of quantumness [16,[28][29][30][31], verification of quantum computations [17,[32][33][34], remote state preparation [35,36], and zero-knowledge proofs for quantum computations [37][38][39]. We show that our self-testing protocol for the entangled magic state is applicable to another type of proof of quantumness where the classical verifier can certify whether the device generates a state having nonzero magic.…”

mentioning

confidence: 99%

Computational self-testing for entangled magic states

Mizutani,

Takeuchi,

Hiromasa

et al. 2021

Preprint

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Classical zero-knowledge arguments for quantum computations

Cited by 14 publications

References 19 publications

Classical Proofs of Quantum Knowledge

Classical Proofs of Quantum Knowledge

Theoretical and Experimental Perspectives of Quantum Verification

Computational self-testing for entangled magic states

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