# Interactive Proofs for Quantum Computation

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

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

## Notations

• ${\displaystyle k}$:classical key
• ${\displaystyle p(k)}$:Probability distribution from which the classical key has been drawn
• ${\displaystyle |\psi \rangle }$: State to be authenticated
• ${\displaystyle |flag\rangle }$: Test state for successful authentication
• ${\displaystyle Enc_{k}}$: Encoding procedure
• ${\displaystyle \rho }$: Encoded state sent over insecure channel by the sender
• ${\displaystyle \rho '}$: Encoded state tampered by eavesdropper through insecure channel, received by the receiver
• ${\displaystyle Dec_{k}}$: Decoding procedure
• ${\displaystyle Dec_{k}(\rho ')}$: Decoded state obtained by the receiver