Post hoc verification with a single prover

  title={Post hoc verification with a single prover},
  author={Tomoyuki Morimae and Joseph Fitzsimons},
We propose a simple protocol for the verification of quantum computation after the computation has been performed. Our construction can be seen as an improvement on previous results in that it requires only a single prover, who is restricted to measuring qubits in the X or Z basis, while requiring only one way communication, from the prover to the verifier. We also show similar constant round protocols with purely classical verifiers are not possible, unless BQP is contained in the third level… 
Classical Verification of Quantum Computations
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Reducing resources for verification of quantum computations
Two verification protocols where the correctness of a “target” computation is checked by means of “trap” computations that can be efficiently simulated on a classical computer and are the least demanding techniques able to achieve linear overhead.
A simple protocol for fault tolerant verification of quantum computation
This paper presents a simple protocol for verifying quantum computations, in the presence of noisy devices, with no extra assumptions, based on post hoc techniques for verification, which allow for the prover to know the desired quantum computation and its input.
Verifier-on-a-Leash: new schemes for verifiable delegated quantum computation, with quasilinear resources
This work presents two protocols for a classical verifier to verifiably delegate a quantum computation to two non-communicating but entangled quantum provers, and achieves near-optimal complexity in terms of the total resources employed by the verifier and the honest provers.
On Information-Theoretic Classical Verification of Quantum Computers
A family of protocols which seem natural for verifying quantum computations and generalizes such known protocols, namely those of [AAV13,AG17], showing that any protocol from this family is bound to require an extremely powerful prover, much like the classical protocols of [LFKN92] and [Sha92].
Robust verification of quantum computation
This work considers a single-prover verification protocol developed by Fitzsimons and Kashefi and shows that this protocol is indeed robust with respect to deviations on the quantum state prepared by the verifier, and proves a rigidity result for a type of quantum correlations known as steering correlations.
Efficient classical verification of quantum computations
An efficient scheme for verifying quantum computations in the ‘high complexity’ regime i.e. beyond the remit of classical computers, based on the fact that adaptive Clifford circuits on general product state inputs provide universal quantum computation, while the same processes without adaptation are always classically efficiently simulatable.
J un 2 01 9 Verifier-ona-Leash : new schemes for verifiable delegated quantum computation , with quasilinear resources
The main technical innovation is an efficient rigidity theorem that allows a verifier to test that two entangled provers perform measurements specified by an arbitrary m-qubit tensor product of singlequbit Clifford observables on their respective halves of m shared EPR pairs, with a robustness that is independent of m.
Relativistic verifiable delegation of quantum computation
This work presents the first verifiable delegation scheme where a classical client delegates her quantum computation to two entangled servers that are allowed to communicate, but respecting the plausible assumption that information cannot be propagated faster than speed of light.
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This work constructs a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device's state and measurements.


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