Statistical Signal Processing for Quantum Error Mitigation

2025-05-31

AI Summary

Addressing the unreliability of quantum measurements under depolarizing noise—dominant in the NISQ era—this paper proposes a statistically driven quantum error mitigation (QEM) method to accurately estimate the most probable noise-free output from noisy measurement samples. The method introduces an innovative two-stage “filtering + EM” framework: first, a heuristic filtering stage explicitly isolates and suppresses non-informative depolarizing noise; second, expectation-maximization (EM) is applied to the denoised data to enhance both interpretability and scalability of maximum-likelihood estimation. Small-scale experiments using Qiskit demonstrate that the approach significantly outperforms existing statistical QEM techniques. Further validation on synthetic datasets confirms its scalability to systems with ~100 qubits. By unifying theoretical rigor with engineering practicality, this work establishes a novel paradigm for error mitigation in intermediate-scale noisy quantum computation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• Estimating noiseless outputs from noisy quantum measurements
• Filtering depolarizing noise and applying EM for ML estimation
• Scaling statistical QEM methods for larger qubit systems

Innovation

• Statistical signal processing for quantum error mitigation
• Filtering stage to discard uninformative depolarizing noise
• Expectation-maximization algorithm for maximum likelihood estimation