Quantum error mitigation using energy sampling and extrapolation enhanced Clifford data regression

TL;DR

This paper advances quantum error mitigation by extending Clifford Data Regression with energy sampling and non-Clifford extrapolation, significantly improving accuracy in noisy quantum chemistry simulations on NISQ devices.

Contribution

It introduces two novel enhancements to CDR—Energy Sampling and Non-Clifford Extrapolation—that improve error mitigation performance in quantum chemistry simulations.

Findings

Both methods outperform original CDR in simulations.

Energy Sampling biases training towards low-energy states.

NCE captures the evolution of noise effects with circuit complexity.

Abstract

Error mitigation is essential for the practical implementation of quantum algorithms on noisy intermediate-scale quantum (NISQ) devices. This work explores and extends Clifford Data Regression (CDR) to mitigate noise in quantum chemistry simulations using the Variational Quantum Eigensolver (VQE). Using the H$_4$ molecule with the tiled Unitary Product State (tUPS) ansatz, we perform noisy simulations with the ibm torino noise model to investigate in detail the effect of various hyperparameters in CDR on the error mitigation quality. Building on these insights, two improvements to the CDR framework are proposed. The first, Energy Sampling (ES), improves performance by selecting only the lowest-energy training circuits for regression, thereby further biasing the sample energies toward the target state. The second, Non-Clifford Extrapolation (NCE), enhances the regression model by including the number of non-Clifford parameters as an additional input, enabling the model to learn how the noisy-ideal mapping evolves as the circuit approaches the optimal one. Our numerical results demonstrate that both strategies outperform the original CDR.