Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control

Details Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control

2004-05-20

arxiv.org/abs/quant-ph/0405115v1

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevA.71.052312

When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations can be done with entangling many-qudit Hamiltonians and local unitary control. By entangling we mean that every qudit is coupled to every other qudit, at least indirectly. We demonstrate that the only class of finite-dimensional entangling Hamiltonians that aren't universal for simulation is the class of entangling Hamiltonians on qubits whose Pauli operator expansion contains only terms coupling an odd number of systems, as identified by Bremner et. al. [Phys. Rev. A, 69, 012313 (2004)]. We show that in all other cases entangling many-qudit Hamiltonians are universal for simulation.

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