Interactive Proofs for Quantum Computation: Difference between revisions
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Providing solution to the functionality [[Verification of Universal Quantum Computation|Verification of Quantum Computation]], is a class [https://complexityzoo.uwaterloo.ca/Complexity_Zoo:M#ma MA] (Merlin-Arthur) that consists of all the problems whose solution can be verified by a BPP machine (verifier that has a classical computer) when given a proof by a 'witness' (prover). As MA is not entirely contained in BQP [[Interactive Proofs for Quantum Computation#References|(1)(2)]], as believed (problems that can be solved by a quantum computer), the functionality of verification asks 'Does every problem in BQP admit an interactive-proof system in which the prover is restricted to BQP computations?' The [https://arxiv.org/pdf/1704.04487.pdf example protocol] answers this question by defining quantum prover interactive proofs and state 'Any language in BQP has a QPIP (quantum prover interactive proofs) which hides the computation from the prover'. [https://complexityzoo.uwaterloo.ca/Complexity_Zoo:I#ip IP] (interactive proof systems) is a generalisation of class MA, which involves multiple interaction between the prover (untrusted company) and the verifier (consumer). | Providing solution to the functionality [[Verification of Universal Quantum Computation|Verification of Quantum Computation]], is a class [https://complexityzoo.uwaterloo.ca/Complexity_Zoo:M#ma MA] (Merlin-Arthur) that consists of all the problems whose solution can be verified by a BPP machine (verifier that has a classical computer) when given a proof by a 'witness' (prover). As MA is not entirely contained in BQP [[Interactive Proofs for Quantum Computation#References|(1)(2)]], as believed (problems that can be solved by a quantum computer), the functionality of verification asks 'Does every problem in BQP admit an interactive-proof system in which the prover is restricted to BQP computations?' The [https://arxiv.org/pdf/1704.04487.pdf example protocol] answers this question by defining quantum prover interactive proofs and state 'Any language in BQP has a QPIP (quantum prover interactive proofs) which hides the computation from the prover'. [https://complexityzoo.uwaterloo.ca/Complexity_Zoo:I#ip IP] (interactive proof systems) is a generalisation of class MA, which involves multiple interaction between the prover (untrusted company) and the verifier (consumer). | ||
==Further Information== | |||
==References== | |||
#[https://epubs.siam.org/doi/10.1137/S0097539796300921 Bernstein and Vazirani (1997)] | |||
#[https://dl.acm.org/citation.cfm?id=796590 Watrous (2000)] | |||
<div style='text-align: right;'>''contributed by Shraddha Singh''</div> | |||
Revision as of 20:48, 17 June 2019
Providing solution to the functionality Verification of Quantum Computation, is a class MA (Merlin-Arthur) that consists of all the problems whose solution can be verified by a BPP machine (verifier that has a classical computer) when given a proof by a 'witness' (prover). As MA is not entirely contained in BQP (1)(2), as believed (problems that can be solved by a quantum computer), the functionality of verification asks 'Does every problem in BQP admit an interactive-proof system in which the prover is restricted to BQP computations?' The example protocol answers this question by defining quantum prover interactive proofs and state 'Any language in BQP has a QPIP (quantum prover interactive proofs) which hides the computation from the prover'. IP (interactive proof systems) is a generalisation of class MA, which involves multiple interaction between the prover (untrusted company) and the verifier (consumer).