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arXiv:quant-ph/0109115

On simulation of Hamiltonians using local unitary transformations

Hao Chen

Published Sep 22, 2001• 1 citation
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Abstract

We give a necessary condition for the simulation of Hamiltonians, which is independent of the eigenvalues and based on the algebraic-geometric invariants introduced recently in [1] and [2]. The result shows that the problem of simulation of arbitrary bipartite Hamiltonians cannot be described by only using eigenvalues, which is quite different to the two-qubit case.

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We give a necessary condition for the simulation of Hamiltonians, which is independent of the eigenvalues and based on the algebraic-geometric invariants introduced recently in [1] and [2]. The result shows that the problem of simulation of arbitrary bipartite Hamiltonians cannot be described by only using eigenvalues, which is quite different to the two-qubit case.
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.