Hybrid physical/logical zero-noise extrapolation with limited logical executions

arXiv:2604.15014v3 Announce Type: replace Abstract: Partially error-corrected logical executions are expected to become available before fully fault-tolerant quantum computation, but such executions usually take much longer runtime than physical, unencoded ones. We formulate zero-noise extrapolation in this regime as a statistical resource-allocation problem in which the physical/logical execution mode is itself an extrapolation design variable. In the proposed mixed strategy, one or a few logical circuits provide low-noise anchor points, while cheaper folded physical circuits provide a larger extrapolation lever arm. Within an effective error suppression model $p_L=\gamma p$, we derive Richardson variance prefactors for all-logical and mixed data sets, include folded-circuit runtime accounting, obtain the optimal shot allocation for a prescribed target variance, and state the bias--variance criterion determining when the mixed estimator improves finite-runtime accuracy. We illustrate the mixed-data strategy via simulating dynamics of transverse-field Ising model. For error suppression factor $\gamma\lesssim 0.1$ the mixed strategy can significantly(orders-of-magnitude) reduce the runtime needed to reach a fixed estimator variance, as well as provide better mean-square-error estimators in reasonable parameter regions.

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