The Computational Power of Symmetric Hamiltonians

Details The Computational Power of Symmetric Hamiltonians The Computational Power of Symmetric Hamiltonians

2008-01-21

arxiv.org/abs/0801.3228v3

Phys. Rev. A 78, 012346 (2008)

Physics

Quantum Physics

8 pages, 4 figures v3: much clearer presentation of main construction. Results extended to rotationally invariant Hamiltonians

Scientific paper

10.1103/PhysRevA.78.012346

The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the computational complexity of simulating Hamiltonian dynamics; the problem is still BQP complete, and is believed to be hard on a classical computer. This is achieved by designing a system to implement a Universal Quantum Interface, a device which enables control of an entire computation through the control of a fixed number of spins, and using it as a building-block to entirely remove the need for control, except in the system initialisation. Finally, it is shown that cooling such Hamiltonians to their ground states in the presence of random magnetic fields solves a QMA-complete problem.

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