Classical Noise Inversion: A Practical and Optimal framework for Robust Quantum Applications

TL;DR

This paper introduces Classical Noise Inversion (CNI), a novel framework that effectively mitigates quantum noise through classical post-processing, reducing costs and handling realistic, gate-dependent noise for scalable quantum applications.

Contribution

The paper presents CNI, a new noise mitigation method that bypasses quantum sampling costs and manages gate-dependent noise, enhancing practical quantum computing.

Findings

CNI reduces statistical variance in quantum property estimation.

CNI provides unbiased estimates under realistic noise conditions.

Noise compression achieves optimal error mitigation overhead.

Abstract

Quantum error mitigation is a critical technology for extracting reliable computations from noisy quantum processors, proving itself essential not only in the near term but also as a valuable supplement to fully fault-tolerant systems in the future. However, its practical implementation is hampered by two major challenges: the expansive cost of sampling from quantum circuits and the reliance on unrealistic assumptions, such as gate-independent noise. Here, we introduce Classical Noise Inversion (CNI), a framework that fundamentally bypasses these crucial limitations and is well-suited for various quantum applications. CNI effectively inverts the accumulated noise entirely during classical post-processing, thereby eliminating the need for costly quantum circuit sampling and remaining effective under the realistic condition of gate-dependent noise. Apart from CNI, we introduce noise compression, which groups noise components with equivalent effects on measurement outcomes, achieving the optimal overhead for error mitigation. We integrate CNI with the framework of shadow estimation to create a robust protocol for learning quantum properties under general noise. Our analysis and numerical simulations demonstrate that this approach substantially reduces statistical variance while providing unbiased estimates in practical situations where previous methods fail. By transforming a key quantum overhead into a manageable classical cost, CNI opens a promising pathway towards scalable and practical quantum applications.