Efficient online quantum state estimation using a matrix-exponentiated gradient method
arXiv:1807.01852 · doi:10.1088/1367-2630/ab0438
Abstract
In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that determines how much weight is given to the new measurement results obtained in each step. We show convergence of the running state estimate in probability to the true state for both noiseless and noisy measurements. We find that in the latter case the learning rate has to be chosen adaptively and decreasing to guarantee convergence beyond the noise threshold. As a practical alternative we then propose to use running averages of the measurement statistics and a constant learning rate to overcome the noise problem. The proposed algorithm is numerically compared with batch maximum-likelihood and least-squares estimators. The results show a superior performance of the new algorithm in terms of accuracy and runtime complexity.
References in corpus (13)
- Quantum state tomography via compressed sensing
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Unknown Quantum States and Operations, a Bayesian View
- Quantum state estimation
- Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
- Maximum Likelihood, Minimum Effort
- Diluted maximum-likelihood algorithm for quantum tomography
- Sample-optimal tomography of quantum states
- Quantum State Tomography via Linear Regression Estimation
- Fast linear algebra is stable
- Superfast maximum likelihood reconstruction for quantum tomography
- Practical Bayesian Tomography
- The Learnability of Quantum States
Cited by in corpus (6)
- Satellite-to-Earth Quantum Key Distribution via Orbital Angular Momentum
- Beyond Quantum Noise Spectroscopy: modelling and mitigating noise with quantum feature engineering
- Modeling and Control of a Reconfigurable Photonic Circuit using Deep Learning
- Learning quantum many-body systems from a few copies
- Limitations of optimization algorithms on noisy quantum devices
- Efficient Quantum State Tracking in Noisy Environments