Hierarchical Progressive Pauli Noise Modeling with Residual Compensation for Multi-Qubit Quantum Circuits

TL;DR

This paper introduces a scalable hierarchical optimization framework for quantum noise modeling in multi-qubit systems, significantly reducing complexity and improving error mitigation in quantum algorithms.

Contribution

It proposes a novel hierarchical progressive optimization method with combinatorial projection masks to efficiently extract high-order crosstalk, enabling scalable quantum noise modeling.

Findings

Achieves 96.3% parameter compression on a 5-qubit system.

Breaks crosstalk bottleneck, improving fidelity from 0.7431 to 0.9381.

Reduces optimization complexity from exponential to linear in qubit number.

Abstract

Quantum Noise Characterization (QNC) is indispensable for benchmarking and mitigating errors in Noisy Intermediate-Scale Quantum (NISQ) devices. However, traditional Quantum Process Tomography (QPT) suffers from an exponential parameter explosion $O(4^N)$, severely hindering its scalability. In this paper, we propose a Hierarchical Progressive Optimization (HPO) framework to efficiently extract high-order spatial crosstalk in multi-qubit systems. By introducing a mathematically rigorous combinatorial projection mask, the HPO framework strategically freezes foundational low-weight topologies and exclusively isolates high-weight Pauli correlations. This progressive masking mechanism effectively reduces the optimization complexity from $O(4^N)$ to a scalable $O(N \cdot 4^w)$, successfully mitigating the barren plateau phenomenon. Simulations show that our method achieves a remarkable parameter compression rate of 96.3% on a 5-qubit system while maintaining machine precision convergence. Furthermore, to validate its practical utility, we apply the extracted spatial crosstalk model to perform Quantum Error Mitigation (QEM) on a deep-circuit 10-qubit Harrow-Hassidim-Lloyd (HHL) algorithm. Compared to the traditional global depolarizing baseline, the HPO-guided mitigation scheme breaks the unmitigated crosstalk bottleneck, achieving an unprecedented state fidelity recovery from 0.7431 to 0.9381 ($\Delta F \approx 19.5\%$). Our work provides a scalable, highly accurate, and indispensable blueprint for modeling and mitigating complex multi-body errors in large-scale quantum algorithms.