Modeling quantum noise for efficient testing of fault-tolerant circuits

Understanding fault-tolerant properties of quantum circuits is important for designing large-scale quantum information processors. In particular, simulating properties of encoded circuits is a crucial tool for investigating the relationship between properties such as the noise model, encoding scheme, and threshold value. For general noisy circuits, these simulations quickly become intractable in the size of the encoded circuit. We introduce a general theoretical method for approximating a noise process by one that allows for efficient Monte Carlo simulation of properties of encoded circuits. The approximation is as close to the original process as possible without overestimating its ability to preserve quantum information, a key property for obtaining honest estimates of threshold values. We numerically illustrate the method with various physically relevant noise models.

Figure 1

${\Lambda }_{\mathcal{P}}^{(3,j)}$ (dashed blue line), ${\Lambda }_{\mathcal{D}}^{(3,j)}$ (solid red line), ${\Lambda }_t^{(3,j)}$ (dotted gold line) for $j=0,1,2$. Left column: Action on the $x$-$z$ plane of the Bloch sphere. Right column: Input-output distinguishability for states $\rho$ at angle $\alpha$ relative to $z$ axis.