Classical verification of quantum circuits containing few basis changes

@article{Demarie2016ClassicalVO,
  title={Classical verification of quantum circuits containing few basis changes},
  author={Tommaso F. Demarie and Yingkai Ouyang and Joseph Fitzsimons},
  journal={ArXiv},
  year={2016},
  volume={abs/1612.04914}
}
We consider the task of verifying the correctness of quantum computation for a restricted class of circuits which contain at most two basis changes. This contains circuits giving rise to the second level of the Fourier Hierarchy, the lowest level for which there is an established quantum advantage. We show that, when the circuit has an outcome with probability at least the inverse of some polynomial in the circuit size, the outcome can be checked in polynomial time with bounded error by a… 
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References

SHOWING 1-10 OF 63 REFERENCES
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.
Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
  • M. Bremner, R. Jozsa, D. Shepherd
  • Computer Science, Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2010
TLDR
The class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection is introduced, and it is proved first that post- IQP equals the classical class PP, and that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, then the infinite tower of classical complexity classes known as the polynomial hierarchy would collapse to its third level.
Quantum and classical tradeoffs
  • Yaoyun Shi
  • Computer Science
    Theor. Comput. Sci.
  • 2004
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.
Simulating quantum computers with probabilistic methods
TLDR
It is shown that the exponential speed-ups of Simon's and Shor's algorithms crucially depend on the very last stage in these algorithms, dealing with the classical postprocessing of the measurement outcomes, and it is proved that both algorithms would be classically simulatable if the function classically computed in this step had a sufficiently peaked Fourier spectrum.
Interactive Proofs for BQP via Self-Tested Graph States
  • M. Mckague
  • Computer Science, Mathematics
    Theory Comput.
  • 2016
TLDR
Using the measurement-based quantum computation model, this work constructs interactive proofs with non-communicating quantum provers and a classical verifier and extends the self-testing error bounds on measurements to a very general set which includes the adaptive measurements used for measurement- based quantum computation as a special case.
Measurement-based quantum computation on cluster states
We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster
Verification for measurement-only blind quantum computing
TLDR
This paper proposes a protocol of verification for the measurement-only blind quantum computing, a new secure quantum computing protocol where a client who does not have any sophisticated quantum technlogy can delegate her quantum computing to a server without leaking any privacy.
Classical command of quantum systems
TLDR
A scheme is described that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics, and makes it possible to test whether a claimed quantum computer is truly quantum.
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.
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3
4
5
...