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• W2071522897 abstract "We study the structure of logical operators in local $D$-dimensional quantum codes, considering both subsystem codes with geometrically local gauge generators and codes defined by geometrically local commuting projectors. We show that if the code distance is $d$, then any logical operator can be supported on a set of specified geometry containing $stackrel{ifmmode tilde{}else ~{}fi{}}{d}$ qubits, where $stackrel{ifmmode tilde{}else ~{}fi{}}{d}{d}^{1/(Densuremath{-}1)}=O(n)$ and $n$ is the code length. Our results place limitations on partially self-correcting quantum memories, in which at least some logical operators are protected by energy barriers that grow with system size. We also show that for any two-dimensional local commuting projector code there is a nontrivial logical ``string'' operator supported on a narrow strip, where the operator is only slightly entangling across any cut through the strip." @default.
• W2071522897 created "2016-06-24" @default.
• W2071522897 creator A5036464616 @default.
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• W2071522897 date "2012-09-07" @default.
• W2071522897 modified "2023-10-17" @default.
• W2071522897 title "Logical-operator tradeoff for local quantum codes" @default.
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• W2071522897 doi "https://doi.org/10.1103/physreva.86.032308" @default.
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