Quantum state tomography with gradient descent
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Nanotechnology (MPNAT), MSc
Publicerad
2024
Författare
Torres Hernandez, Manuel Sebastian
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Quantum technologies, particularly quantum computing, are advancing by leaps
and bounds in recent years. Quantum computing can be implemented using two approaches: one with discrete variables utilizing qubits and the other with continuous
variables inspired by the components of the electromagnetic field. A crucial aspect
of quantum computing is knowing the system’s quantum state. With the quantum
state, it is possible to understand and control the system, and know if an algorithm
was executed correctly. However, since it is a quantum system, we cannot know
the quantum state directly, but we need to infer it from different measurements.
Eventually, with the collected data from the measurements, the state of the system
can 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. The
most standard approach is the maximum-likelihood method. However, it has been
shown that there may be other methods that outperform this standard method in
different aspects, e.g., a recently proposed machine-learning method with a conditional generative adversarial neural network (CGAN). In this thesis, we propose
three 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-based
methods are more efficient and/or reconstruct the state better than the maximumlikelihood method and the CGAN method. The advantages we find are in terms of
better overall reconstruction times, using fewer measurement operators, and reconstructing effectively even in the presence of noise in the system.
Beskrivning
Ämne/nyckelord
quantum computing, quantum state tomography, maximum likelihood, machine learning, gradient descent, measurement operators, discrete variables, continuous variable