A rotated surface-code experiment measures a logical error per cycle of at distance

PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Open quantum systems, decoherence and error correction · Open quantum systems, decoherence and error correction

Quantum Information and Technology, Ch The stabilizer formalism

Problem

A rotated surface-code experiment measures a logical error per cycle of ϵ=0.5%\epsilon = 0.5\% at distance d=5d=5, and an error-suppression factor Λ=ϵd/ϵd+2=1.5\Lambda = \epsilon_d/\epsilon_{d+2} = 1.5 that is assumed to hold for every further step d→d+2d \to d+2. ((a)) Estimate the smallest odd distance dd needed to reach a logical error of 10−610^{-6} per cycle or lower. ((b)) Using 2d2−12d^2 - 1 physical qubits per logical qubit, estimate the number of physical qubits that one logical qubit at that distance would need.

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