Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing

Details Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing

2008-08-13

arxiv.org/abs/0808.1768v1

Physics

Quantum Physics

14 pages

Scientific paper

Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but useful for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians. We then prove that adiabatic quantum computing can realize the ground states of Hamiltonians with certain random interactions, as well as the ground states of one, two, and three-dimensional fermionic interaction lattices, in polynomial time. Finally, we use the Jordan-Wigner transformation and a related transformation for spin-3/2 particles to show that our results can be restated using spin operators in a surprisingly simple manner. A direct consequence is that the one-dimensional cluster state can be found in polynomial time using adiabatic quantum computing.

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