Adaptive Quantum State Tomography

Abstract

Quantum state tomography (QST), a required technology for the characterization of quantum communication or computing systems, remains an active research area to increase the throughput of any quantum information system. Traditional fixed Pauli-basis routines take many measurement shots to reach the fidelities demanded by quantum calibration, communication, and sensing protocols. To address this problem for a single-qubit system, we propose a novel adaptive QST method that achieves optimally bounded measurements. Using a discretized Bloch sphere, we update a Bayesian posterior after each measurement to select a new measurement axis, determined by expected information gain. Such a method takes advantage of the infinite dimensionality of Hilbert space by including numerous measurement bases - far more than the standard Pauli triad - and uniquely motivating a search-space reduction method to discard unlikely states and uninformative bases, making the high basis count manageable. Our adaptive QST offers tunable convergence controls such that users can adapt according to required speed and accuracy, noise environments, and workload constraints. Large-scale simulations show our method rapidly approaches the best possible fidelity that closely track the Massar-Popescu optimal mean-fidelity curve with standard deviation scaling of $\mathcal {O}(1/N)$ . A photonic experiment implementing QST over 13 candidate bases validates our multi-basis theory.