Adaptive quantum tomography in an indistinct measurement system with superconducting circuits

Abstract

We discuss adaptive tomography in superconducting circuits based on ambiguous measurements. Adaptive tomography, a type of quantum system state tomography, has been widely researched to enable faster tomography. In one study, adaptive tomography utilizing a method that aligns a measurement axis with the state of a qubit within an optical system based on projective measurements showed significantly higher efficiency compared to conventional state tomography methods. However, such a dramatic improvement have theoretical limitations when applied in systems relying on indistinct measurements. We proposed a new adaptive tomography approach in systems based on indistinct measurements by designing measurement axes in a new direction. We verified the approach by using a transmon system, which is one of superconducting qubit systems. The efficiency of this method was quantified by determining how many ensembles are required to achieve a specific error bound for tomography results. The predicted efficiency based on system variables was $33.74%$, while experimentation yielded an actual efficiency of $15.06%$.