Interactive Proofs for Quantum Computation

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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 believed, MA is not entirely contained in BQP (problems that can be solved by a quantum computer) (1)(2), 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).

Assumptions[edit]

  • It is assumed that the company and consumer share a classical key drawn from a probability distribution.

Outline[edit]

Notations[edit]

  • :classical key
  • :Probability distribution from which the classical key has been drawn
  • : State to be authenticated
  • : Test state for successful authentication
  • : Encoding procedure
  • : Encoded state sent over insecure channel by the sender
  • : Encoded state tampered by eavesdropper through insecure channel, received by the receiver
  • : Decoding procedure
  • : Decoded state obtained by the receiver

Requirements[edit]

Protocol Description[edit]

Further Information[edit]

References[edit]

  1. Bernstein and Vazirani (1997)
  2. Watrous (2000)
contributed by Shraddha Singh