Verifier-on-a-Leash: new schemes for verifiable delegated quantum computation, with quasilinear resources

@article{Coladangelo2019VerifieronaLeashNS,
  title={Verifier-on-a-Leash: new schemes for verifiable delegated quantum computation, with quasilinear resources},
  author={Andrea Coladangelo and Alex Bredariol Grilo and Stacey Jeffery and Thomas Vidick},
  journal={IACR Cryptol. ePrint Arch.},
  year={2019},
  volume={2019},
  pages={247}
}
The problem of reliably certifying the outcome of a computation performed by a quantum device is rapidly gaining relevance. We present two protocols for a classical verifier to verifiably delegate a quantum computation to two non-communicating but entangled quantum provers. Our protocols have near-optimal complexity in terms of the total resources employed by the verifier and the honest provers, with the total number of operations of each party, including the number of entangled pairs of qubits… 
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References

SHOWING 1-10 OF 55 REFERENCES
How to Verify a Quantum Computation
TLDR
This work gives a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity, using a reduction to an entanglement-based protocol and showing that verification could be achieved at minimal cost compared to performing the computation.
Computationally-Secure and Composable Remote State Preparation
  • A. Gheorghiu, Thomas Vidick
  • Mathematics, Computer Science
    2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2019
TLDR
The implementation of "random remote state preparation with verification", a functionality first defined in (Dunjko and Kashefi 2014), is expected to be useful for removing the need for quantum communication in such protocols while keeping functionality.
Post hoc verification of quantum computation
TLDR
It is demonstrated that the verification can be achieved independently from the blindness, and it is shown that a constant round protocol with a single prover and a completely classical verifier is not possible, unless bounded error quantum polynomial time (BQP) is contained in the third level of thePolynomial hierarchy.
A Multiprover Interactive Proof System for the Local Hamiltonian Problem
TLDR
This work gives a quantum interactive proof system for the local Hamiltonian problem on n qubits in which the verifier has a single round of interaction with five entangled provers and completeness and soundness are separated by an inverse polynomial in $n.
Unconditionally verifiable blind quantum computation
TLDR
It is rigorously proved that the probability of failing to detect an incorrect output is exponentially small in a security parameter, while resource overhead remains polynomial in this parameter, which allows entangling gates to be performed between arbitrary pairs of logical qubits with only constant overhead.
Relativistic verifiable delegation of quantum computation
TLDR
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.
Low-Degree Testing for Quantum States, and a Quantum Entangled Games PCP for QMA
We show that given an explicit description of a multiplayer game, with a classical verifier and a constant number of players, it is QMA-hard, under randomized reductions, to distinguish between the
Device-Independent Verifiable Blind Quantum Computation
TLDR
This work presents a novel approach based on a combination of verified blind quantum computation and Bell state self-testing that has dramatically reduced overhead, with resources scaling as only O(m4lnm) in the number of gates.
Robustness and device independence of verifiable blind quantum computing
TLDR
The robustness of the single server verifiable universal blind quantum computing protocol of Fitzsimons and Kashefi is proved in the most general scenario and the composition of this protocol with a device-independent state tomography protocol that is based on the rigidity of CHSH games as proposed by Reichardt et al.
A quantum linearity test for robustly verifying entanglement
TLDR
A simple two-player test which certifies that the players apply tensor products of Pauli σX and σZ observables on the tensor product of n EPR pairs is introduced, which is the first robust self-test for n E PR pairs.
...
...