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

Journal Article · Sun May 15 04:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.71.052312· OSTI ID:20717723

Bremner, Michael J ^[1]; Bacon, Dave ^[2]; Nielsen, Michael A ^[1]

---

1. School of Physical Sciences, The University of Queensland, Queensland 4072 (Australia)
2. Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States)

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 are not 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.

• OSTI ID: 20717723
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 71; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
CAPACITY
COMPUTERIZED SIMULATION
CONTROL
COUPLING
HAMILTONIANS
QUANTUM COMPUTERS
QUANTUM ENTANGLEMENT
QUBITS