Direct fidelity estimation of quantum states using machine learning

Avi Vadali, Rutuja Kshirsagar, Prasanth Shyamsundar +1 more

Ting Lin, Zhihua Chen, Kai Wu +3 more

Xiaoqian Zhang, Maolin Luo, Zhaodi Wen +4 more

In almost all quantum applications, one of the key steps is to verify that the fidelity of the prepared quantum state meets expectations. In this Letter, we propose a new approach solving this problem using machine-learning techniques. Compared to other fidelity estimation methods, our method is applicable to arbitrary quantum states, the number of required measurement settings is small, and this number does not increase with the size of the system. For example, for a general five-qubit quantum state, only four measurement settings are required to predict its fidelity with ±1% precision in a nonadversarial scenario. This machine-learning-based approach for estimating quantum state fidelity has the potential to be widely used in the field of quantum information.

Onur Danaci, Sanjaya Lohani, Brian T. Kirby +1 more

Abstract Two-qubit systems typically employ 36 projective measurements for high-fidelity tomographic estimation. The overcomplete nature of the 36 measurements suggests possible robustness of the estimation procedure to missing measurements. In this paper, we explore the resilience of machine-learning-based quantum state estimation techniques to missing measurements by creating a pipeline of stacked machine learning models for imputation, denoising, and state estimation. When applied to simulated noiseless and noisy projective measurement data for both pure and mixed states, we demonstrate quantum state estimation from partial measurement results that outperforms previously developed machine-learning-based methods in reconstruction fidelity and several conventional methods in terms of resource scaling. Notably, our developed model does not require training a separate model for each missing measurement, making it potentially applicable to quantum state estimation of large quantum systems where preprocessing is computationally infeasible due to the exponential scaling of quantum system dimension.

Farzad Shahi, A. T. Rezakhani

Onur Danaci, Sanjaya Lohani, Brian T. Kirby +2 more

Reconstruction of two-qubit systems typically performed using 36 coincidence measurements. We trained an ensemble of CNN & XGBoost ML models, employed imputation to demonstrate high-fidelity state estimation when multiple measurements are missing.