The Pursuit For Uniqueness: Extending Valiant-Vazirani Theorem to the Probabilistic and Quantum Settings

@article{Aharonov2022ThePF,
  title={The Pursuit For Uniqueness: Extending Valiant-Vazirani Theorem to the Probabilistic and Quantum Settings},
  author={Dorit Aharonov and Michael Ben-Or and Fernando G. S. L. Brand{\~a}o and Or Sattath},
  journal={ArXiv},
  year={2022},
  volume={abs/0810.4840}
}
Valiant-Vazirani showed in 1985 \cite{VV85} that solving NP with the promise that "yes" instances have only one witness is powerful enough to solve the entire NP class (under randomized reductions).We are interested in extending this result to the quantum setting. We prove extensions to the classes Merlin-Arthur MA and Quantum-Classical-Merlin-Arthur QCMA \cite{AN02}. Our results have implications for the complexity of approximating the ground state energy of a quantum local Hamiltonian with a… 

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