Fig. 6: Sensitivity of fidelity in various hardware parameters for nitrogen-vacancy (NV) repeater chains.

The NV hardware model consists of ~15 parameters and from those we focus on four parameters in this figure: (A) two-qubit gate fidelity, (B) detection probability, (C) induced storage qubit noise and (D) visibility. We start by improving all ~15 parameters, including the four designated ones, using an improvement factor of 3 (Methods, section ‘How we choose improved hardware parameters’). Then, for each of the four parameters only, we individually decrease their improvement factor to 2, or increase it to 10 or 50. The figure shows the resulting fidelity (horizontal and vertical grid lines; dashed line indicates maximal fidelity which can be attained classically). Note that at an improvement factor of 3 (orange line), all ~15 parameters are improved by three times, resulting in a fidelity of 0.39. In addition, we vary the improvement factor for combinations of two of the four parameters (diagonal lines). The 3 × improved parameter values can be found in Supplementary Table II. The other values (at 2/10/50×) are approximately: two-qubit gate fidelity F_EC (0.985/0.997/0.9994), detection probability \({p}_{\,\text{det}}^{\text{nofibre}\,}\) (6.8%/58%/90%), induced storage qubit noise N_1/e (2800/14,000/70,000), visibility V (95%/99%/99.8%). The fidelities shown are obtained by simulation of the SWAP-ASAP protocol (three repeaters) with a total spanned distance of 500 km. Each data point represents the average of 1000 runs (standard deviation on fidelity < 0.002).