Fig. 4
From: One-dimensional quantum computing with a ‘segmented chain’ is feasible with today’s gate fidelities
a The rate of errors on a surface-code logical qubit per round of stabiliser measurements pL as a function of the physical-qubit CNOT-gate error rate ε2 and the code distance d. When the physical error rate is lower than the threshold marked by the vertical gray line, the logical error rate decreases with the code distance. Circles are data calculated numerically using the Monte Carlo method. Dashed lines are obtained by fitting circles (in the sub-threshold regime) using Eq. (1). Dotted lines are calculated using Eq. (2). Error bars show one standard deviation, and error bars smaller than the size of circles have been removed from the figure. b The logical CNOT gate error rate of the four-qubit gauge code PCNOT as a function of the logical CNOT gate error rate of the surface code pCNOT. Gauge-code logical qubits are encoded in surface-code logical qubits, and the gauge code is concatenated. The level of the gauge-code concatenation is marked in the figure. The surface-code CNOT gate error rate is pCNOT = 14dpL. Error bars show one standard deviation, and error bars with invisible gaps have been removed from the figure
