Lightcone shading for classically accelerated quantum error mitigation

Quantum error mitigation methods trade off bias for variance in the output of a noisy quantum computer, such that the averaged result is more accurate but takes longer to converge. Probabilistic error cancellation (PEC) stands out as a method that controllably eliminates bias rather than heuristically reducing it, but at the cost of a much larger variance, inhibiting application at scale. Recent analyses have shown that the variance of PEC can be reduced by not mitigating errors lying outside the causal lightcone of the desired observable. Here, we improve the lightcone approach by classically computing tighter bounds on how much each error channel in the circuit can bias the final result. This set of bounds, which we refer to as a "shaded lightcone," enables a more targeted application of PEC, improving the tradespace of bias and variance, while illuminating how the structure of a circuit determines the difficulty of error-mitigated computation. While a tight shaded lightcone is exponentially hard to compute, we numerically demonstrate an algorithm providing a practical benefit for example problems even with modest classical resources, leveraging Pauli propagation and Lieb-Robinson inpsired speed-limit methods to mine the accessible information near the beginning and end of the circuit. Numerics show the algorithm greatly reduces the time that would be needed to apply PEC for a target accuracy in an example 127-qubit Trotter circuit compared to standard lightcone-PEC, expanding the domain of problems that can be computed via direct application of PEC.