dorsal/arxiv
View SchemaComputation on a Noiseless Quantum Code and Symmetrization
| Authors | Paolo Zanardi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9901047 |
| URL | https://arxiv.org/abs/quant-ph/9901047 |
| DOI | 10.1103/PhysRevA.60.R729 |
| Journal | Phys. Rev. A 60 (1999) R729 |
Abstract
Let ${\cal H}$ be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra ${\cal L}.$ Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal C}\subset{\cal H}$ annihilated by ${\cal L}.$ We show that a universal set of gates over $\cal C$ is obtained by any generic pair of ${\cal L}$-invariant gates. Such gates - if not available from the outset - can be obtained by resorting to a symmetrization with respect to the group generated by ${\cal L}.$ Any computation can then be performed completely within the coding decoherence-free subspace.
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"abstract": "Let ${\\cal H}$ be the state-space of a quantum computer coupled with the\nenvironment by a set of error operators spanning a Lie algebra ${\\cal L}.$\nSuppose ${\\cal L}$ admits a noiseless quantum code i.e., a subspace ${\\cal\nC}\\subset{\\cal H}$ annihilated by ${\\cal L}.$ We show that a universal set of\ngates over $\\cal C$ is obtained by any generic pair of ${\\cal L}$-invariant\ngates. Such gates - if not available from the outset - can be obtained by\nresorting to a symmetrization with respect to the group generated by ${\\cal\nL}.$ Any computation can then be performed completely within the coding\ndecoherence-free subspace.",
"arxiv_id": "quant-ph/9901047",
"authors": [
"Paolo Zanardi"
],
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"quant-ph"
],
"doi": "10.1103/PhysRevA.60.R729",
"journal_ref": "Phys. Rev. A 60 (1999) R729",
"title": "Computation on a Noiseless Quantum Code and Symmetrization",
"url": "https://arxiv.org/abs/quant-ph/9901047"
},
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