On QMA protocols with two short quantum proofs

This paper gives a QMA (Quantum Merlin-Arthur) protocol for 3-SAT with two logarithmic-size quantum proofs (that are not entangled with each other) such that the gap between the completeness and the soundness is Omega(1/n polylog(n)). This improves the best completeness/soundness gaps known for NP-complete problems in this setting.

[1]  Keiji Matsumoto,et al.  Quantum Merlin-Arthur Proof Systems: Are Multiple Merlins More Helpful to Arthur? , 2009, Chic. J. Theor. Comput. Sci..

[2]  John Watrous,et al.  Succinct quantum proofs for properties of finite groups , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[3]  Alain Tapp,et al.  A Quantum Characterization Of NP , 2007, computational complexity.

[4]  E. Knill.  Quantum Randomness and Nondeterminism , 1996 .

[5]  Chris Marriott,et al.  Quantum Arthur–Merlin games , 2004, Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004..

[6]  M. Christandl,et al.  N-representability is QMA-complete , 2006 .

[7]  Michael A. Forbes,et al.  Improved Soundness for QMA with Multiple Provers , 2011, Electron. Colloquium Comput. Complex..

[8]  Bill Fefferman,et al.  The Power of Unentanglement , 2008, 2008 23rd Annual IEEE Conference on Computational Complexity.

[9]  Salman Beigi,et al.  NP vs QMA_log(2) , 2008, Quantum Inf. Comput..

[10]  A. Harrow,et al.  Testing Product States, Quantum Merlin-Arthur Games and Tensor Optimization , 2010, JACM.

[11]  Alain Tapp,et al.  All Languages in NP Have Very Short Quantum Proofs , 2007, 2009 Third International Conference on Quantum, Nano and Micro Technologies.

[12]  Ashley Montanaro,et al.  An Efficient Test for Product States with Applications to Quantum Merlin-Arthur Games , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[13]  Irit Dinur,et al.  The PCP theorem by gap amplification , 2006, STOC.

[14]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[15]  Matthias Christandl,et al.  Quantum computational complexity of the N-representability problem: QMA complete. , 2007, Physical review letters.

[16]  Mikhail N. Vyalyi,et al.  Classical and Quantum Computation , 2002, Graduate studies in mathematics.

[17]  R. Cleve,et al.  Quantum fingerprinting. , 2001, Physical review letters.

[18]  Jing Chen,et al.  Short Multi-Prover Quantum Proofs for SAT without Entangled Measurements , 2010, 1011.0716.