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Computational Complexity of Quantum Hamiltonian Systems |
The computational complexity of quantum
simulations is an active area of research which is of interest to workers in
quantum information theory, theoretical computer science, mathematical physics
and many-body physics. The intent of the workshop is bring
together these different communities, to exchange ideas and discuss the latest results
in this area. Quantum computers hold the promise of being
able to simulate quantum systems more efficiently than classical
machines. But exactly what problems can be solved efficiently on a quantum computer?
Recent work has exhibited a class of problems, the estimation of the smallest eigenvalue of a Hamiltonian, which are even hard for quantum
computers. On the other hand physicists have developed
methods such as DMRG, matrix product state techniques, and quantum During the workshop we expect to discuss
topics such as 1. Complexity-theoretic classification of quantum
Hamiltonian problems. The containment of these problems in complexity classes
such as QMA, (Q)AM, BQP, NP, BPP etc. 2. Classical simulation methods for quantum
systems. The dependence on spectral gaps, correlation
lengths, bounded-entanglement properties of ground-states. The applications of Lieb-Robinson bounds.
The use of matrix product states and other efficient classical representations of
quantum states. The use and efficiency of DMRG
(density-matrix renormalization group) methods. 3. Relations between classical Markov chains,
Hamiltonian problems and quantum adiabatic computation. 4. Entanglement scaling theory in critical and
non-critical quantum systems and area laws. This workshop
cosponsored by EUs 6^{th} Framework; the Marie Curie Action
SCF (Conferences and Training Courses). [Back] |