Journal of the ACM (JACM)
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Limits on the Hardness of Lattice Problems in lp Norms
Computational Complexity
An application of quantum finite automata to interactive proof systems
Journal of Computer and System Sciences
Quantum multiparty communication complexity and circuit lower bounds
Mathematical Structures in Computer Science
A full characterization of quantum advice
Proceedings of the forty-second ACM symposium on Theory of computing
A note on quantum algorithms and the minimal degree of ε-error polynomials for symmetric functions
Quantum Information & Computation
Lower bounds on matrix rigidity via a quantum argument
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Consistency of local density matrices is QMA-Complete
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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We consider coGapSVP_{\sqrt n } a gap version of the shortest vector in a lattice problem. This problem is known to be in AM \cap coNP but is not known to be in NP or in MA. We prove that it lies inside QMA, the quantum analogue of NP. This is the first non-trivial upper bound on the quantum complexity of a lattice problem.The proof relies on two novel ideas. First, we give a new characterization of QMA, called QMA+ formulation allows us to circumvent a problem which arises commonly in the context of QMA: the prover might use entanglement between different copies of the same state in order to cheat. The second idea involves using estimations of autocorrelation functions for verification. We make the important observation that autocorrelation functions are positive definite functions and using properties of such functions we severely restrict the prover's possibility to cheat. We hope that these ideas will lead to further developments in the field.