Statistical Signal Processing for Quantum Error Mitigation

TL;DR

This paper introduces a statistical signal processing method for quantum error mitigation that estimates noiseless outputs from noisy measurements, demonstrating scalability and effectiveness in NISQ quantum systems.

Contribution

It presents a novel two-step statistical approach combining filtering and EM algorithms for scalable quantum error mitigation in NISQ devices.

Findings

Effective on small-qubit IBM simulations

Scales to larger qubit systems with synthetic data

Outperforms some existing statistical QEM techniques

Abstract

In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation (QEM) is essential for producing reliable outputs from quantum circuits. We present a statistical signal processing approach to QEM that estimates the most likely noiseless outputs from noisy quantum measurements. Our model assumes that circuit depth is sufficient for depolarizing noise, producing corrupted observations that resemble a uniform distribution alongside classical bit-flip errors from readout. Our method consists of two steps: a filtering stage that discards uninformative depolarizing noise and an expectation-maximization (EM) algorithm that computes a maximum likelihood (ML) estimate over the remaining data. We demonstrate the effectiveness of this approach on small-qubit systems using IBM circuit simulations in Qiskit and compare its performance to contemporary statistical QEM techniques. We also show that our method scales to larger qubit counts using synthetically generated data consistent with our noise model. These results suggest that principled statistical methods can offer scalable and interpretable solutions for quantum error mitigation in realistic NISQ settings.