Computational Difficulty of Computing the Density of States

Details Computational Difficulty of Computing the Density of States Computational Difficulty of Computing the Density of States

2010-10-15

arxiv.org/abs/1010.3060v2

Phys. Rev. Lett. 107, 040501 (2011)

Physics

Quantum Physics

v2: Accepted version. 9 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.107.040501

We study the computational difficulty of computing the ground state degeneracy and the density of states for local Hamiltonians. We show that the difficulty of both problems is exactly captured by a class which we call #BQP, which is the counting version of the quantum complexity class QMA. We show that #BQP is not harder than its classical counting counterpart #P, which in turn implies that computing the ground state degeneracy or the density of states for classical Hamiltonians is just as hard as it is for quantum Hamiltonians.

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