Single-shot Hamiltonian parameter estimation by real-time sequential Monte-Carlo method*

Bayesian filter, also known as Kalman filter for linear system or particle filter for nonlinear system, allow optimal control in quantum and classical interface circuitry. While applying Bayesian filter to classical electronic applications have shown accurate estimation and controllability, little is experimentally known about efficiency of Bayesian filter in noisy quantum system where observation model is nonlinear, stochastic and discrete. Previous works using conventional Bayesian inference (Maximum a Posteriori) could suppress the noise of qubit by measurement-based feedback control. However, the conventional estimator needs sufficient statistics for accuracy, which requires a large mount of data obtained from projective measurements. We report the fast Hamiltonian estimation and feedback in a single projective measurement by the real-time particle filtering, also known as sequential Monte-Carlo method. Using a singlet-triplet semiconductor qubit under nuclear spin noise and charge noise, we show qubit frequency estimation per single-shot measurement improving the coherence time by more than two orders of magnitude. Moreover, we investigate the noise properties and discuss potential for improvement, limitation and universal state-space representation for various quantum computing platforms suffering from the fluctuating environment.