Pure State Tomography with Fourier Transformation

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.

A noise-robust quantum dynamics learning protocol based on Choi–Jamiolkowski isomorphism: theory and experiment

“…The scalability of our protocol is highly related to the expressivity and trainability of PQCs, which have been extensively discussed in current research of variational quantum algorithms and quantum neural networks [30,31,[41][42][43][44][45]. Despite the difficulties of scaling a general PQCs, some prior knowledge about U, like the sparsity, locality and symmetry of the generator Hamiltonian, can usually be accessible and used to enhance the PQCs' performance nearby U while preserving a low circuit depth [8,46]. It is worth mentioning that a recent work [47] introduces a data quantum Fisher information metric to measure the model performance, which may be adopted here as an indicator for adaptively designing the PQCs' architecture even in the more general case.…”

“…To mitigate this overhead, efforts have been dedicated to designing feasible methods, even with limitations at times: low rank, sparsity, and operation symmetry are introduced to reduce learning consumption [5,6]. Besides, the adaptive measurement protocol and entanglement bases are helpful but with stringent realization conditions [7,8]. Machine learning methods which are applied to quantum physics, have brought apparent advantages as approximate methods [9][10][11].…”