dorsal/arxiv
View SchemaTopological quantum memory
| Authors | Eric Dennis, Alexei Kitaev, Andrew Landahl, John Preskill |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0110143 |
| URL | https://arxiv.org/abs/quant-ph/0110143 |
| DOI | 10.1063/1.1499754 |
| Journal | J. Math. Phys. 43, 4452-4505 (2002). |
Abstract
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z_2 lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require measurement or fast classical processing; however for this procedure the quantum gates are local only if the qubits are arranged in four or more spatial dimensions. We discuss procedures for encoding, measurement, and performing fault-tolerant universal quantum computation with surface codes, and argue that these codes provide a promising framework for quantum computing architectures.
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"abstract": "We analyze surface codes, the topological quantum error-correcting codes\nintroduced by Kitaev. In these codes, qubits are arranged in a two-dimensional\narray on a surface of nontrivial topology, and encoded quantum operations are\nassociated with nontrivial homology cycles of the surface. We formulate\nprotocols for error recovery, and study the efficacy of these protocols. An\norder-disorder phase transition occurs in this system at a nonzero critical\nvalue of the error rate; if the error rate is below the critical value (the\naccuracy threshold), encoded information can be protected arbitrarily well in\nthe limit of a large code block. This phase transition can be accurately\nmodeled by a three-dimensional Z_2 lattice gauge theory with quenched disorder.\nWe estimate the accuracy threshold, assuming that all quantum gates are local,\nthat qubits can be measured rapidly, and that polynomial-size classical\ncomputations can be executed instantaneously. We also devise a robust recovery\nprocedure that does not require measurement or fast classical processing;\nhowever for this procedure the quantum gates are local only if the qubits are\narranged in four or more spatial dimensions. We discuss procedures for\nencoding, measurement, and performing fault-tolerant universal quantum\ncomputation with surface codes, and argue that these codes provide a promising\nframework for quantum computing architectures.",
"arxiv_id": "quant-ph/0110143",
"authors": [
"Eric Dennis",
"Alexei Kitaev",
"Andrew Landahl",
"John Preskill"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-lat",
"hep-th"
],
"doi": "10.1063/1.1499754",
"journal_ref": "J. Math. Phys. 43, 4452-4505 (2002).",
"title": "Topological quantum memory",
"url": "https://arxiv.org/abs/quant-ph/0110143"
},
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