Differentiable Maximum Likelihood Noise Estimation for Quantum Error Correction

TL;DR

This paper introduces a differentiable maximum likelihood framework for quantum noise estimation, enabling precise, efficient, and gradient-based optimization of noise parameters to improve quantum error correction performance.

Contribution

The paper presents a novel differentiable likelihood computation method that allows direct optimization of circuit-level noise parameters using gradient descent, applicable to surface and repetition codes.

Findings

Achieves near-exact error probability recovery in simulations.

Reduces logical error rates by up to 30.6% on experimental data.

Provides provably optimal, decoder-independent error priors.

Abstract

Accurate noise estimation is essential for fault-tolerant quantum computing, as decoding performance depends critically on the fidelity of the circuit-level noise parameters. In this work, we introduce a differentiable Maximum Likelihood Estimation (dMLE) framework that enables exact, efficient, and fully differentiable computation of syndrome log-likelihoods, allowing circuit-level noise parameters to be optimized directly via gradient descent. Leveraging the exact Planar solver for repetition codes and a novel, simplified Tensor Network (TN) architecture combined with optimized contraction path finding for surface codes, our method achieves tractable and fully differentiable likelihood evaluation even for distance 5 surface codes with up to 25 rounds. Our method recovers the underlying error probabilities with near-exact precision in simulations and reduces logical error rates by up to 30.6(3)% for repetition codes and 8.1(2)% for surface codes on experimental data from Google's processor compared to previous state-of-the-art methods: correlation analysis and Reinforcement Learning (RL) methods. Our approach yields provably optimal, decoder-independent error priors by directly maximizing the syndrome likelihood, offering a powerful noise estimation and control tool for unlocking the full potential of current and future error-corrected quantum processors.