Probabilistic Error Cancellation and Scalable Mitigation Protocols for Noisy Intermediate-Scale Quantum Circuits
As noisy intermediate-scale quantum (NISQ) processors scale toward hundreds of physical qubits, gate infidelity and decoherence continue to severely limit circuit depth and computational fidelity, impeding practical utility prior to the realization of universal fault-tolerant error correction. Quantum error mitigation (QEM) techniques offer a vital near-term recourse by suppressing expectation value estimation errors through post-processing and randomized circuit sampling without requiring massive physical qubit overhead. This paper presents an advanced probabilistic error cancellation (PEC) protocol optimized for multi-qubit superconducting processors. By characterizing precise Pauli noise channels via randomized benchmarking and constructing quasi-probability quasiparticle representations, our mitigation framework isolates and cancels hardware noise contributions down to sub-percent error margins. We benchmark the protocol on complex quantum chemistry simulation circuits and combinatorial optimization problems executed across 127-qubit hardware platforms. Our empirical results demonstrate that PEC successfully extends reliable circuit execution depths by an order of magnitude, reducing expectation value bias by 84% compared to unmitigated baselines. Furthermore, we analyze sampling overhead scaling relative to circuit width, introducing variance reduction heuristics that mitigate the exponential sampling cost traditionally associated with probabilistic cancellation methods. The research delivers a scalable software toolkit for near-term quantum algorithms, bridging the gap between current noisy hardware limitations and transformative computational supremacy in quantum chemistry and materials science.