Classical and Quantum Computation
Classical and Quantum Computation
Classical complexity and quantum entanglement
Journal of Computer and System Sciences - Special issue: STOC 2003
Efficient algorithms using the multiplicative weights update method
Efficient algorithms using the multiplicative weights update method
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
Parallel Approximation of Non-interactive Zero-sum Quantum Games
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
SIAM Journal on Optimization
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
A quasipolynomial-time algorithm for the quantum separability problem
Proceedings of the forty-third annual ACM symposium on Theory of computing
Strong NP-hardness of the quantum separability problem
Quantum Information & Computation
Quantum Information & Computation
Computational complexity of the quantum separability problem
Quantum Information & Computation
Parallel Approximation of Min-max Problems with Applications to Classical and Quantum Zero-Sum Games
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
Testing Product States, Quantum Merlin-Arthur Games and Tensor Optimization
Journal of the ACM (JACM)
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We give algorithms for the optimization problem: $\max_\rho \left\langle Q , \rho\right\rangle $, where Q is a Hermitian matrix, and the variable ρ is a bipartite separable quantum state. This problem lies at the heart of several problems in quantum computation and information, such as the complexity of QMA(2). While the problem is NP-hard, our algorithms are better than brute force for several instances of interest. In particular, they give PSPACE upper bounds on promise problems admitting a QMA(2) protocol in which the verifier performs only logarithmic number of elementary gate on both proofs, as well as the promise problem of deciding if a bipartite local Hamiltonian has large or small ground energy. For Q≥0, our algorithm runs in time exponential in ||Q||F. While the existence of such an algorithm was first proved recently by Brandão, Christandl and Yard [Proceedings of the 43rd annual ACM Symposium on Theory of Computation , 343---352, 2011], our algorithm is conceptually simpler.