Faster CMB lensing with control variates

We present a new method for fast computation of the realization-dependent bias, a major computational bottleneck in measurements of the cosmic microwave background (CMB) lensing power spectrum. The method accelerates the bias calculation by differencing two correlated estimates: one based on fully realistic masked simulations and the other on isotropic simulations, for which the bias is analytically tractable. We show that our algorithm reduces the total computational cost of a lensing power spectrum measurement by approximately a factor of five for Atacama Cosmology Telescope- or Simons Observatory-like noise levels, or by a factor of three if current anisotropic filtering methods are left unchanged. Owing to its simplicity, the method can be readily implemented in existing CMB lensing analysis pipelines.