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Numbers in parentheses are total physical qubits per logical qubit at that code distance.
The measurement of the stabilisers to perform a merge must occur d times, where d is the effective code distance of each planar code.
The class of such codes includes all the families of uniformly packed codes of sufficiently large length satisfying the condition d-ρ ≥ 2, where d is the code distance and ρ is the covering radius.
The T = 1.4 ms logical Bell pair creation time above arises from a surface code distance d = 33 and gate operation time t = 3.5 μs, for an NV− optical implementation30, and assumes that inter-container operations can be executed at the same rate as operations local to each memory unit.
Theoretically, the achievable gain is related to theminimum code distance of its corresponding finite state machine [29].
Consider that the state transition here is inhomogeneous, which means that the state transition probabilities change over time, and we can hardly employ a transition matrix to describe it, which also brings in great difficulty in analyzing the minimum code distance.
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The denser memory subsystems, differing physical gate times, and varying code distances for other options in Table 1 will result in different demands on the inter-container interfaces.
(d) Per-error correction cycle logical error rate PL as a function of physical error rate p for different code distances.
(Gridlines do not represent entanglement bonds). (b) Logical error rate as a function of physical error rate for different code distances.
The sixth column uses single-letter amino acid symbols to show the genetic code distances between all observed character states at each positively selected site.
Interestingly, both promoter and ORF HM code distances of duplicates in the group of trans-targeted genes are, on average, significantly higher than those in the group of controlling genes (Wilcoxon rank sum test: promoter, P = 0.003 and ORF, P = 0.0001).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com