Novel techniques for efficient quantum state tomography and quantum process tomography and their experimental implementation

Abstract

The study carried out in this thesis focuses on designing and experimentally imple- menting various quantum tomography protocols to efficiently characterize and recon- struct unknown quantum states and processes using spin ensemble based nuclear mag- netic resonance (NMR) quantum processors and superconducting technology-based IBM quantum processors. The task of reconstructing quantum states is achieved with the help of quantum state tomography (QST) protocols while quantum processes are characterized using quantum process tomography (QPT) protocols. Both QST and QPT are essential to check the reliability and to evaluate the performance of a quan- tum processor. However, both QST and QPT are cursed with a fundamental difficulty, i.e., the computational complexity increases exponentially with the size of the system which makes them infeasible to perform experimentally, even for smaller dimensional systems. Besides this, having finite size of ensembles and inevitable systematic errors will lead to unphysical density matrices and process matrices. To tackle such issues, numerous QST and QPT protocols have been proposed. However, most of them are yet to be experimentally demonstrated. The prime objective of the study undertaken in this thesis is to design experimental strategies to efficiently implement tomography protocols on NMR and IBM quantum processors. Generalized quantum circuits are proposed to efficiently acquire experimental data to perform QST and QPT and further demonstrated for two- and three-qubit quantum states and quantum processes. To tackle the issue of the unphysicality of experimentally reconstructed quantum states and processes using standard tomography techniques, the tasks of QST and QPT are converted into a constrained convex optimization (CCO) problem and the CCO problem is solved to reconstruct valid quantum states and processes which in case of QPT allows us to compute the complete set of Kraus operators corresponding to a given quantum process. Further, the compressed sensing (CS) and artificial neural network (ANN) techniques have also been employed to perform tomography of quan- tum states and gates from a heavily reduced data set as compared to standard meth- ods. CS and ANN based tomography methods are promising techniques to deal with complexity issue to characterize higher-dimensional quantum gates. Moreover, the problem of selective and direct estimation of desired elements of process matrix char- vii0. Abstract acterizing quantum process has also been explored, where partial knowledge about underlying unknown quantum process can be acquired efficiently using selective and efficient quantum process tomography protocol (SEQPT). A generalized quantum al- gorithm and quantum circuit to perform SEQPT has been proposed and successful experimental demonstration has been shown on NMR and IBM quantum processors. In addition to that, we also proposed an efficient direct QST and QPT scheme based on weak measurement approach and demonstrated experimentally using a three-qubit NMR system. The thesis also investigates the problem of experimentally simulating dynamics of open quantum systems based on dilation techniques. To show the efficacy of above-mentioned quantum tomography and simulation protocols, experimental re- sults are compared with theoretically predicted results in case of several two-and three- qubit quantum systems. The content of this thesis has been divided into eight chapters as described below: