Physics – Quantum Physics
Scientific paper
2001-09-17
special issue on quantum computation of J. Math. Phys. 43, 4506 (2002)
Physics
Quantum Physics
17 pages, no figures. v3: This version to appear in J. Math. Phys., special issue on quantum computation
Scientific paper
10.1063/1.1499208
Qubits are neither fermions nor bosons. A Fock space description of qubits leads to a mapping from qubits to parafermions: particles with a hybrid boson-fermion quantum statistics. We study this mapping in detail, and use it to provide a classification of the algebras of operators acting on qubits. These algebras in turn classify the universality of different classes of physically relevant qubit-qubit interaction Hamiltonians. The mapping is further used to elucidate the connections between qubits, bosons, and fermions. These connections allow us to share universality results between the different particle types. Finally, we use the mapping to study the quantum computational power of certain anisotropic exchange Hamiltonians. In particular, we prove that the XY model with nearest-neighbor interactions only is not computationally universal. We also generalize previous results about universal quantum computation with encoded qubits to codes with higher rates.
Lidar Daniel A.
Wu Ling-An
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