Adaptive Quantum Tomography in Weak Measurement with Superconducting Circuits

Abstract

Adaptive tomography has been widely investigated to obtain faster state tomography process for quantum computation. Infidelity [1 - F (rho, sigma)] on nearly pure states in quantum information process scales generally as O(1/N), which requires a large number of statistical ensembles in comparison to the hifidelity scaling on mixed states of O(1/root N). Recently, optimization of a measurement basis in a photonic qubit system, whose state tomography uses projective measurements, reported improved infidelity scaled as O (1/root N). However, this dramatic improvement cannot be applied to a weak-value based measurement system, which can be attributed to the fact that one cannot distinguish two quantum states with perfect measurement reliability. We introduce new optimal measurement basis to achieve a fast adaptive quantum state tomography and minimum magnitude of infidelity in this weak measurement system. This novel protocol allows us to accomplish approximately 80% error reduction without changing the scaling of O(1/root N) in numerical simulations and realize approximately 90% error reduction in superconducting circuit QED experiments.