Quantum state tomography with gradient descent

Sammanfattning

Quantum technologies, particularly quantum computing, are advancing by leapsand bounds in recent years. Quantum computing can be implemented using two approaches: one with discrete variables utilizing qubits and the other with continuousvariables inspired by the components of the electromagnetic field. A crucial aspectof quantum computing is knowing the system’s quantum state. With the quantumstate, it is possible to understand and control the system, and know if an algorithmwas executed correctly. However, since it is a quantum system, we cannot knowthe quantum state directly, but we need to infer it from different measurements.Eventually, with the collected data from the measurements, the state of the systemcan be reconstructed. This reconstruction process is known as quantum state tomography, which is not trivial.Different approaches have been implemented to solve the reconstruction task. Themost standard approach is the maximum-likelihood method. However, it has beenshown that there may be other methods that outperform this standard method indifferent aspects, e.g., a recently proposed machine-learning method with a conditional generative adversarial neural network (CGAN). In this thesis, we proposethree methods based on gradient descent to perform quantum state tomography.We benchmark these methods against the standard method of maximum likelihood;for continuous variables, we also benchmark them against the CGAN-based method.Our results indicate that in certain parameter regimes, some gradient descent-basedmethods are more efficient and/or reconstruct the state better than the maximumlikelihood method and the CGAN method. The advantages we find are in terms ofbetter overall reconstruction times, using fewer measurement operators, and reconstructing effectively even in the presence of noise in the system.