Probabilistic error cancellation (PEC) is one way to deal with noise on today’s quantum hardware without using additional ancilla qubits. PEC works at the level of data analysis: it uses knowledge of the device's noise to undo the effect of that noise statistically. The goal is to recover what an ideal, noise-free circuit would have produced, even though every run of the experiment is executed on imperfect hardware.
The basic idea is to model each noisy gate as a known quantum channel, then express the inverse of that noise as a weighted combination of operations that can actually be implemented. This leads to a quasi-probability decomposition, where different circuits are run with certain weights, some of which can be negative or larger than one. When the measurement results are combined with these weights, the average converges to the unbiased expectation value. In theory, if the noise model is accurate, this completely removes bias from the result.
The price for this accuracy is statistical overhead. Because the weights amplify fluctuations, PEC requires many more circuit executions than a naive experiment, and the number grows quickly as noise increases or circuits get larger. That makes scalability the central challenge. Still, PEC provides a clean reference point: it shows what is possible when noise is perfectly characterized and inverted, and it serves as a foundation for more practical, structure-aware approaches that aim to keep the overhead manageable on real devices.