Reconstrução pticográfica de estados de múltiplos qubits em um computador quântico - Warley Marcos Santos Alves (2023)
The development of second-generation quantum technologies (quantum sensors, quantum computers and quantum internet) has been carried out by large companies and has received state investments in the order of billions of dollars in several countries. Among these technologies, the quantum computer gained greater prominence in the media due to its promise to solve problems much faster and more efficiently than classical computers, which could produce numerous scientific advances with impacts on society and industry. In recent years, companies such as IBM, Google, Microsoft, among others, have made great progress in building the first prototypes of quantum hardware and software. However, these prototypes are devices that operate with few qubits and are heavily affected by noise, which still prevents them from performing truly useful computation. In particular, IBM has provided remote access to some of its machines available to the general public, as well as special access to selected researchers in its research program. Using this resource, in this work we study a method for reconstructing pure states of a multi-qubit system in a quantum computer. In the context of quantum computing, this is a very useful tool, for example, to determine input or output states of a given algorithm, or to characterize the logical operations that constitute the algorithm. The method we study is known as quantum ptychography, where a pure state is subjected to a set of projections with some degree of intersection between them, followed by a projective measurement on a single orthonormal basis. The results generated in the process serve as input to an iterative algorithm that estimates the state. Our study was divided between simulations and experiments. The simulations were carried out in ideal scenarios without noise and more realistic scenarios with noise, where the method was successfully demonstrated for a variety of states of up to 6 qubits. In experiments, we obtained good results for reconstructing states of up to 4 qubits; the results for a larger number were strongly affected by noise in the devices. The advantages and limitations of the ptychographic method are discussed in comparison with other state reconstruction methods. In addition to demonstrating quantum ptychography on a quantum computer, we also achieved some advances in the method. The first was a modification to the iterative reconstruction algorithm, which improves its convergence and, consequently, the state estimation. The second was the use of measurement bases that are less affected by noise in a quantum computer. This second advance is still part of a preliminary study but points to promising avenues for future investigations.