Lightcone shading for classically accelerated quantum error mitigation

Quantum error mitigation (QEM) can recover accurate expectation values from a noisy quantum computer by trading off bias for variance, such that an averaged result is more accurate but takes longer to converge. Probabilistic error cancellation (PEC) stands out among QEM methods as an especially robust means of controllably eliminating bias. However, PEC often exhibits a much larger variance than other methods, inhibiting application to large problems for a given error rate. 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. Although a tight shaded lightcone is exponentially hard to compute, we present an algorithm providing a practical benefit for some problems even with modest classical resources, leveraging the ease of evolving an error instead of the state or the observable. The algorithm reduces the runtime that would be needed to apply PEC for a target accuracy in an example 127-qubit Trotter circuit by approximately two orders of magnitude compared to standard lightcone-PEC, expanding the domain of problems that can be computed via direct application of PEC on noisy hardware.