dorsal/arxiv
View SchemaTwo Qubit Quantum Computing in a Projected Subspace
| Authors | Bi Qiao, H. E. Ruda, M. S. Zhan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0110027 |
| URL | https://arxiv.org/abs/quant-ph/0110027 |
| DOI | 10.1103/PhysRevA.65.042325 |
Abstract
A formulation for performing quantum computing in a projected subspace is presented, based on the subdynamical kinetic equation (SKE) for an open quantum system. The eigenvectors of the kinetic equation are shown to remain invariant before and after interaction with the environment. However, the eigenvalues in the projected subspace exhibit a type of phase shift to the evolutionary states. This phase shift does not destroy the decoherence-free (DF) property of the subspace because the associated fidelity is 1. This permits a universal formalism to be presented - the eigenprojectors of the free part of the Hamiltonian for the system and bath may be used to construct a DF projected subspace based on the SKE. To eliminate possible phase or unitary errors induced by the change in the eigenvalues, a cancellation technique is proposed, using the adjustment of the coupling time, and applied to a two qubit computing system. A general criteria for constructing a DF projected subspace from the SKE is discussed. Finally, a proposal for using triangulation to realize a decoherence-free subsystem based on SKE is presented. The concrete formulation for a two-qubit model is given exactly. Our approach is novel and general, and appears applicable to any type of decoherence. Key Words: Quantum Computing, Decoherence, Subspace, Open System PACS number: 03.67.Lx,33.25.+k,.76.60.-k
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"abstract": "A formulation for performing quantum computing in a projected subspace is\npresented, based on the subdynamical kinetic equation (SKE) for an open quantum\nsystem. The eigenvectors of the kinetic equation are shown to remain invariant\nbefore and after interaction with the environment. However, the eigenvalues in\nthe projected subspace exhibit a type of phase shift to the evolutionary\nstates. This phase shift does not destroy the decoherence-free (DF) property of\nthe subspace because the associated fidelity is 1. This permits a universal\nformalism to be presented - the eigenprojectors of the free part of the\nHamiltonian for the system and bath may be used to construct a DF projected\nsubspace based on the SKE. To eliminate possible phase or unitary errors\ninduced by the change in the eigenvalues, a cancellation technique is proposed,\nusing the adjustment of the coupling time, and applied to a two qubit computing\nsystem. A general criteria for constructing a DF projected subspace from the\nSKE is discussed. Finally, a proposal for using triangulation to realize a\ndecoherence-free subsystem based on SKE is presented. The concrete formulation\nfor a two-qubit model is given exactly. Our approach is novel and general, and\nappears applicable to any type of decoherence. Key Words: Quantum Computing,\nDecoherence, Subspace, Open System PACS number: 03.67.Lx,33.25.+k,.76.60.-k",
"arxiv_id": "quant-ph/0110027",
"authors": [
"Bi Qiao",
"H. E. Ruda",
"M. S. Zhan"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.042325",
"title": "Two Qubit Quantum Computing in a Projected Subspace",
"url": "https://arxiv.org/abs/quant-ph/0110027"
},
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