There are two recent papers which use Pauli error propagation to reduce the sampling overhead for PEC.
In both cases, the trick is to propagate error locations throughout the circuit (whenever it is possible), and calculate the coefficients of aggregated error locations. The result is that the Monte Carlo sampling routine of PEC is performed on a quasi-probability distribution with less coefficients, reducing the sampling cost.
I have written one of those two papers arXiv:2411.06422, which focused on an extremely favourable case: phase-flip biased noise on circuits of bias-preserving gates. In this setting, one can aggregate all the Pauli-Z errors, leading to an exponential suppression of the sampling cost. I have an open source implementation of the protocol that I would be very happy to adapt to mitiq. (Thank you @FarLab for the suggestion!)
A more recent paper arXiv:2412.01311v3 a more general setting, but in a similar spirit, by propagating all Pauli errors to reduce the sample overhead. Both works take inspiration from arXiv:2101.09290
While writing this issue, I have found several more recent papers discussing this approach:
Proposal
Step 1. Revisit Block/Stratified/Aggregated sampling for quasi-probability decompositions, in an unified framework.
Step 2. Produce a catalog of the sampling cost gains, and under which conditions.
Step 3. Establish how to integrate this classical pre-processing approach to PEC.
Step 4. Evaluate how this approach could be applied to ZNE or NEPEC.
Step 1 & 2 mostly involve some literature research and I am very confident that I can do it on my own.
Step 3 require some feedback on integration. Step 4 is an open problem (although I would qualify it as a low-hanging fruit).
There are two recent papers which use Pauli error propagation to reduce the sampling overhead for PEC.
In both cases, the trick is to propagate error locations throughout the circuit (whenever it is possible), and calculate the coefficients of aggregated error locations. The result is that the Monte Carlo sampling routine of PEC is performed on a quasi-probability distribution with less coefficients, reducing the sampling cost.
I have written one of those two papers arXiv:2411.06422, which focused on an extremely favourable case: phase-flip biased noise on circuits of bias-preserving gates. In this setting, one can aggregate all the Pauli-Z errors, leading to an exponential suppression of the sampling cost. I have an open source implementation of the protocol that I would be very happy to adapt to mitiq. (Thank you @FarLab for the suggestion!)
A more recent paper arXiv:2412.01311v3 a more general setting, but in a similar spirit, by propagating all Pauli errors to reduce the sample overhead. Both works take inspiration from arXiv:2101.09290
While writing this issue, I have found several more recent papers discussing this approach:
Proposal
Step 1. Revisit Block/Stratified/Aggregated sampling for quasi-probability decompositions, in an unified framework.
Step 2. Produce a catalog of the sampling cost gains, and under which conditions.
Step 3. Establish how to integrate this classical pre-processing approach to PEC.
Step 4. Evaluate how this approach could be applied to ZNE or NEPEC.
Step 1 & 2 mostly involve some literature research and I am very confident that I can do it on my own.
Step 3 require some feedback on integration. Step 4 is an open problem (although I would qualify it as a low-hanging fruit).