MoSAIC: Scalable Probabilistic Error Cancellation via Variational Blockwise Noise Aggregation

Abstract

Quantum error mitigation is essential for extracting trustworthy results from noisy intermediate-scale quantum (NISQ) processors. Yet, current approaches face a core scalability bottleneck: unbiased methods such as probabilistic error cancellation (PEC) incur exponential sampling overhead, while approximate techniques like zero-noise extrapolation trade accuracy for efficiency. We introduce and experimentally demonstrate MoSAIC (Modular Spatio-temporal Aggregation for Inverted Channels), a scalable quantum error mitigation framework that preserves the unbiasedness of PEC while dramatically reducing sampling costs. MoSAIC partitions a circuit into noise-aligned blocks, learns an effective block noise model using classical variational optimization, and applies quasi-probabilistic inversion once per block instead of after every layer. This blockwise aggregation reduces both sampling overhead and circuit-depth overhead, enabling mitigation far beyond the operating regime of standard PEC. We also experimentally validate MoSAIC on IBM's 156-qubit Heron processors, performing the largest PEC-based mitigation demonstration on hardware to date. As a physically meaningful benchmark, we prepare the critical one-dimensional transverse-field Ising (TFIM) ground state for system sizes up to 50 qubits. We show that MoSAIC can achieve at least 1 to 2 orders of magnitude better accuracy than standard PEC under identical sampling budgets. This enables MoSAIC to recover accurate observables for larger system sizes, even when standard PEC fails due to its prohibitive sampling overhead. We also present CUDA-Q accelerated simulations to validate performance trends under a range of different noise models. These results demonstrate that MoSAIC is not only theoretically scalable but also practically deployable for high-accuracy, large-scale quantum experiments on today's quantum hardware.

Figures (5)

• Figure 1: Sampling-overhead scaling of PEC vs MoSAIC. Sampling overhead factor $\gamma$ for standard PEC and MoSAIC as a function of (a) system size $N$, (b) circuit depth $L$, and (c) Pauli noise strength $p$, with the remaining parameters held fixed in each panel. Insets show the overhead ratio $\gamma_{\mathrm{PEC}}/\gamma_{\mathrm{MoSAIC}}$ on a logarithmic scale. Across all settings, blockwise inversion yields substantially slower growth of $\gamma$ than layerwise PEC, indicating a reduced effective exponent and a rapidly increasing relative advantage with $N$, $L$, and $p$.
• Figure 2: VQE benchmark results on the transverse-field Ising model.
• Figure 3: Numerical evaluation of MoSAIC on noisy quantum circuit simulations.
• Figure 4: Overview of the MoSAIC error mitigation framework. The workflow proceeds in four main stages: (a) Partitioning: A transpiled quantum circuit is divided into noise-scoped subcircuits (blocks). (b) Characterization: Each block is characterized to learn its effective noise and compute a corresponding quasi-probabilistic recovery distribution. (c) Sampling & Execution: New composite circuits are formed by sampling from the inverted quasi-probability distributions and are evaluated on the QPU via Monte Carlo sampling. (d) Post-processing: The results are classically combined to yield the final error-mitigated expectation value. Boxed components in the diagram highlight the novel contributions of this work, while the remaining steps adapt the standard PEC procedure with slight modifications.
• Figure 5: Noise-scope partitioning and corresponding subcircuit characterization.