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Simulating Arbitrary Pair-Interactions by a Given Hamiltonian: Graph-Theoretical Bounds on the Time Complexity

P. Wocjan·D. Janzing·Th. Beth
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Abstract

We use an n-spin system with permutation symmetric zz-interaction for simulating arbitrary pair-interaction Hamiltonians. The calculation of the required time overhead is mathematically equivalent to a separability problem of n-qubit density matrices. We derive lower and upper bounds in terms of chromatic index and the spectrum of the interaction graph. The complexity measure defined by such a computational model is related to gate complexity and a continuous complexity measure introduced in a former paper. We use majorization of graph spectra for classifying Hamiltonians with respect to their computational power.

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P. Wocjan, D. Janzing, Th. Beth. 2001-06-13. Simulating Arbitrary Pair-Interactions by a Given Hamiltonian: Graph-Theoretical Bounds on the Time Complexity. https://arxiv.org/abs/quant-ph/0106077

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