dorsal/arxiv
View SchemaEncoded Universality for Generalized Anisotropic Exchange Hamiltonians
| Authors | Jiri Vala, K. Birgitta Whaley |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0204016 |
| URL | https://arxiv.org/abs/quant-ph/0204016 |
| DOI | 10.1103/PhysRevA.66.022304 |
| Journal | Phys. Rev. A 66, 022304 (2002) |
Abstract
We derive an encoded universality representation for a generalized anisotropic exchange Hamiltonian that contains cross-product terms in addition to the usual two-particle exchange terms. The recently developed algebraic approach is used to show that the minimal universality-generating encodings of one logical qubit are based on three physical qubits. We show how to generate both single- and two-qubit operations on the logical qubits, using suitably timed conjugating operations derived from analysis of the commutator algebra. The timing of the operations is seen to be crucial in allowing simplification of the gate sequences for the generalized Hamiltonian to forms similar to that derived previously for the symmetric (XY) anisotropic exchange Hamiltonian. The total number of operations needed for a controlled-Z gate up to local transformations is five. A scalable architecture is proposed.
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"abstract": "We derive an encoded universality representation for a generalized\nanisotropic exchange Hamiltonian that contains cross-product terms in addition\nto the usual two-particle exchange terms. The recently developed algebraic\napproach is used to show that the minimal universality-generating encodings of\none logical qubit are based on three physical qubits. We show how to generate\nboth single- and two-qubit operations on the logical qubits, using suitably\ntimed conjugating operations derived from analysis of the commutator algebra.\nThe timing of the operations is seen to be crucial in allowing simplification\nof the gate sequences for the generalized Hamiltonian to forms similar to that\nderived previously for the symmetric (XY) anisotropic exchange Hamiltonian. The\ntotal number of operations needed for a controlled-Z gate up to local\ntransformations is five. A scalable architecture is proposed.",
"arxiv_id": "quant-ph/0204016",
"authors": [
"Jiri Vala",
"K. Birgitta Whaley"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.022304",
"journal_ref": "Phys. Rev. A 66, 022304 (2002)",
"title": "Encoded Universality for Generalized Anisotropic Exchange Hamiltonians",
"url": "https://arxiv.org/abs/quant-ph/0204016"
},
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