Surface codes, quantum circuits, and entanglement phases
Surface codes—leading candidates for quantum error correction (QEC)—and entanglement phases—a key notion for many-body quantum dynamics—have heretofore been unrelated. Here we establish a link between the two. We map two-dimensional (2D) surface codes under a class of incoherent or coherent errors (...
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| Format: | Article |
| Language: | English |
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American Physical Society
2024-02-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.013137 |
| _version_ | 1827285061542608896 |
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| author | Jan Behrends Florian Venn Benjamin Béri |
| author_facet | Jan Behrends Florian Venn Benjamin Béri |
| author_sort | Jan Behrends |
| collection | DOAJ |
| description | Surface codes—leading candidates for quantum error correction (QEC)—and entanglement phases—a key notion for many-body quantum dynamics—have heretofore been unrelated. Here we establish a link between the two. We map two-dimensional (2D) surface codes under a class of incoherent or coherent errors (bit flips or uniaxial rotations) to (1+1)D free-fermion quantum circuits via Ising models. We show that the error-correcting phase implies a topologically nontrivial area law for the circuit's 1D long-time state |Ψ_{∞}〉. Above the error threshold, we find a topologically trivial area law for incoherent errors and logarithmic entanglement in the coherent case. In establishing our results, we formulate 1D parent Hamiltonians for |Ψ_{∞}〉 via linking Ising models and 2D scattering networks, the latter displaying respective insulating and metallic phases and setting the 1D fermion gap and topology via their localization length and topological invariant. We expect our results to generalize to a duality between the error-correcting phase of (d+1)D topological codes and d-dimensional area laws; this can facilitate assessing code performance under various errors. The approach of combining Ising models, scattering networks, and parent Hamiltonians can be generalized to other fermionic circuits and may be of independent interest. |
| first_indexed | 2024-04-24T10:07:41Z |
| format | Article |
| id | doaj.art-b42b35bdd209472bbaf5b7009a6b4c9f |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:07:41Z |
| publishDate | 2024-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-b42b35bdd209472bbaf5b7009a6b4c9f2024-04-12T17:38:55ZengAmerican Physical SocietyPhysical Review Research2643-15642024-02-016101313710.1103/PhysRevResearch.6.013137Surface codes, quantum circuits, and entanglement phasesJan BehrendsFlorian VennBenjamin BériSurface codes—leading candidates for quantum error correction (QEC)—and entanglement phases—a key notion for many-body quantum dynamics—have heretofore been unrelated. Here we establish a link between the two. We map two-dimensional (2D) surface codes under a class of incoherent or coherent errors (bit flips or uniaxial rotations) to (1+1)D free-fermion quantum circuits via Ising models. We show that the error-correcting phase implies a topologically nontrivial area law for the circuit's 1D long-time state |Ψ_{∞}〉. Above the error threshold, we find a topologically trivial area law for incoherent errors and logarithmic entanglement in the coherent case. In establishing our results, we formulate 1D parent Hamiltonians for |Ψ_{∞}〉 via linking Ising models and 2D scattering networks, the latter displaying respective insulating and metallic phases and setting the 1D fermion gap and topology via their localization length and topological invariant. We expect our results to generalize to a duality between the error-correcting phase of (d+1)D topological codes and d-dimensional area laws; this can facilitate assessing code performance under various errors. The approach of combining Ising models, scattering networks, and parent Hamiltonians can be generalized to other fermionic circuits and may be of independent interest.http://doi.org/10.1103/PhysRevResearch.6.013137 |
| spellingShingle | Jan Behrends Florian Venn Benjamin Béri Surface codes, quantum circuits, and entanglement phases Physical Review Research |
| title | Surface codes, quantum circuits, and entanglement phases |
| title_full | Surface codes, quantum circuits, and entanglement phases |
| title_fullStr | Surface codes, quantum circuits, and entanglement phases |
| title_full_unstemmed | Surface codes, quantum circuits, and entanglement phases |
| title_short | Surface codes, quantum circuits, and entanglement phases |
| title_sort | surface codes quantum circuits and entanglement phases |
| url | http://doi.org/10.1103/PhysRevResearch.6.013137 |
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