Calibration-free quantum error mitigation with classical shadows

Estimating expectation values is a key routine for near-term quantum simulation algorithms. However, the accumulation of noise in current devices severely affects the potential of such algorithms. The method of classical shadows, a randomized protocol for efficiently estimating a large collection of observables, was recently shown to possess inherent noise robustness. This robustness is achieved by performing a series of calibrating experiments, before executing the desired computational algorithm. This calibration step adds overhead to the overall runtime, and its correctness relies on simplifying assumptions about the device noise. In our work, we show that one may bypass these calibrating experiments if the desired (noiseless) quantum state obeys certain symmetries. This technique is enabled whenever the symmetries coincide with the irreducible representations of the classical shadows protocol. Our approach therefore allows for the mitigation of more realistic errors, without requiring a separate calibration step. A prime candidate for this technique is the simulation of electronic systems, wherein the particle-number symmetry can be exploited when performing classical shadows with fermionic measurements. We demonstrate the effectiveness of this idea with numerical simulations of noisy quantum circuits.