Pure State Tomography with Fourier Transformation. Issue 8 (14th June 2022) - Wang, Yu; Li, Keren
Abstract: Extracting information from quantum devices has long been a crucial problem in the field of quantum mechanics. By performing elaborate measurements, quantum state tomography, an important and fundamental tool in quantum science and technology, can be used to determine unknown quantum states completely. In this study, methods to determine multi‐qubit pure quantum states uniquely and directly are explored. Two adaptive protocols are proposed, with their respective quantum circuits. Herein, two or three observables are sufficient, while the number of measurement outcomes are either the same as or fewer than those in existing methods. Additionally, experiments on the IBM 5‐qubit quantum computer, as well as numerical investigations, demonstrate the feasibility of the proposed protocols. Abstract : Two adaptive protocols with two or three observables are designed to uniquely and directly determine any unknown pure quantum states. The implementation circuits for the N ‐qubit case are depicted. The theories, numerical analysis, and the proof‐of‐principle experimental demonstrations are given.