SIAM Journal on Computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Parallelization, amplification, and exponential time simulation of quantum interactive proof systems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
imits on the Power of Quantum Statistical Zero-Knowledge
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Classical and Quantum Computation
Classical and Quantum Computation
The Complexity of the Local Hamiltonian Problem
SIAM Journal on Computing
QMA/qpoly \subseteq PSPACE/poly: De-Merlinizing Quantum Protocols
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Perfect Parallel Repetition Theorem for Quantum Xor Proof Systems
Computational Complexity
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
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
An Efficient Test for Product States with Applications to Quantum Merlin-Arthur Games
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Testing non-isometry is QMA-complete
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
Unique Games with Entangled Provers Are Easy
SIAM Journal on Computing
3-local Hamitonian is QMA-complete
Quantum Information & Computation
The Jones polynomial: quantum algorithms and applications in quantum complexity theory
Quantum Information & Computation
The complexity of quantum spin systems on a two-dimensional square lattice
Quantum Information & Computation
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
On QMA protocols with two short quantum proofs
Quantum Information & Computation
Achieving perfect completeness in classical-witness quantum merlin-arthur proof systems
Quantum Information & Computation
Testing Product States, Quantum Merlin-Arthur Games and Tensor Optimization
Journal of the ACM (JACM)
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We study three variants of multi-prover quantum Merlin-Arthur proof systems. We first show that the class of problems that can be efficiently verified using polynomially many quantum proofs, each of logarithmic-size, is exactly MQA (also known as QCMA), the class of problems which can be efficiently verified via a classical proof and a quantum verifier. We then study the class BellQMA(poly), characterized by a verifier who first applies unentangled, nonadaptive measurements to each of the polynomially many proofs, followed by an arbitrary but efficient quantum verification circuit on the resulting measurement outcomes. We show that if the number of outcomes per nonadaptive measurement is a polynomially-bounded function, then the expressive power of the proof system is exactly QMA. Finally, we study a class equivalent to QMA(m), denoted SepQMA(m), where the verifier's measurement operator corresponding to outcome accept is a fully separable operator across the m quantum proofs. Using cone programming duality, we give an alternate proof of a result of Harrow and Montanaro [FOCS, pp. 633-642 (2010)] that shows a perfect parallel repetition theorem for SepQMA(m) for any m.