Journal
PHYSICAL REVIEW A
Volume 87, Issue 6, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.87.062320
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Funding
- Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology [CE110001027]
- Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior National Business Center [D11PC20166]
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Cyclic boundaries are used in many branches of physics and mathematics, typically to assist the approximation of a large space. We show that when determining the performance of planar, fault-tolerant, topological quantum error correction, using cyclic boundaries leads to a significant underestimate of the logical error rate. We present cyclic and noncyclic surface code simulations exhibiting this discrepancy and analytic formulas precisely reproducing the observed behavior in the limit of low physical error. These asymptotic formulas are then used to prove that the underestimate is exponentially large in the code distance d at any fixed physical error rate p below the threshold error rate p(th).
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