Mathematics of Operations Research
Introduction to the Theory of Computation: Preliminary Edition
Introduction to the Theory of Computation: Preliminary Edition
Quantum computation and quantum information
Quantum computation and quantum information
Succinct quantum proofs for properties of finite groups
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Classical and Quantum Computation
Classical and Quantum Computation
Classical complexity and quantum entanglement
Journal of Computer and System Sciences - Special issue: STOC 2003
Computational Complexity
All Languages in NP Have Very Short Quantum Proofs
ICQNM '09 Proceedings of the 2009 Third International Conference on Quantum, Nano and Micro Technologies
A quasipolynomial-time algorithm for the quantum separability problem
Proceedings of the forty-third annual ACM symposium on Theory of computing
On QMA protocols with two short quantum proofs
Quantum Information & Computation
Epsilon-net method for optimizations over separable states
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Although it is believed unlikely that NP-hard problems admit efficient quantum algo-rithms, it has been shown that a quantum verifier can solve NP-complete problemsgiven a "short" quantum proof; more precisely, NP ⊆ QMAlog(2) where QMAlog(2) de-notes the class of quantum Merlin-Arthur games in which there are two unentangledprovers who send two logarithmic size quantum witnesses to the verifier. The inclusionNP ⊆ QMAlog(2) has been proved by Blier and Tapp by stating a quantum Merlin-Arthurprotocol for 3-coloring with perfect completeness and gap 1/24n6. Moreover, Aaronson etal. have shown the above inclusion with a constant gap by considering Õ(√n) witnessesof logarithmic size. However, we still do not know if QMAlog(2) with a constant gapcontains NP. In this paper, we show that 3-SAT admits a QMAlog(2) protocol with thegap 1/n3+ε for every constant ε 0.