Abstract
In this article, we introduce a new complexity class called PQMA log(2). Informally, this is the class of languages for which membership has a logarithmic-size quantum proof with perfect completeness and soundness, which is polynomially close to 1 in a context where the verifier is provided a proof with two unentangled parts. We then show that PQMA log(2) = NP. For this to be possible, it is important, when defining the class, not to give too much power to the verifier. This result, when compared to the fact that QMA log = BQP, gives us new insight into the power of quantum information and the impact of entanglement.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Aaronson, S. Beigi, A. Drucker, B. Fefferman & P. Shor (2008). The Power of Unentanglement. In Proceedings of the 23rd Annual IEEE Conference on Computational Complexity, 223–236
Alizadeh F. (1995) Interior point methods in semidefinite programming with applications to combinatorial optimization. Proceedings of SIAM Journal on Optimization 5: 13–51
S. Beigi (2008). NP vs QMA log(2). Technical notes arXiv:0810.5109v1 [quant-ph].
H. Blier & A. Tapp (2007). All languages in NP have very short quantum proofs. Technical notes arXiv:0709,0738v1 [quant-ph].
H. Blier & A. Tapp (2008). All languages in NP have very short quantum proofs. In Proceedings of The Third International Conference on Quantum, Nano and Micro Technologies.
Harry Buhrman, Richard Cleve, John Watrous & Ronald de Wolf (2001). Quantum fingerprinting. In Phys. Rev. Lett. 87, 167902 (2001), volume 87.
A. Kitaev & J. Watrous (2000). Parallelization, Amplification, and Exponential Time Simulation of Quantum Interactive Proof Systems. In Proceedings ACM Symposium on Theory of Computing, 608–617.
C. Marriott & J. Watrous (2004). Quantum Arthur-Merlin games. In Proceedings of the IEEE Conference on Computational Complexity, volume 14, 122–152.
Vandenberghe L., Boyd S. (1996) Semidefinite programming. SIAM Review 1: 49–95
J. Watrous (2000). Succinct quantum proofs for properties of finite groups. In Proceedings of Symposium on Foundations of Computer Science, 537–546.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Blier, H., Tapp, A. A Quantum Characterization Of NP. comput. complex. 21, 499–510 (2012). https://doi.org/10.1007/s00037-011-0016-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00037-011-0016-2