Synchronization of a non-markovian quantum system - Lim, Zi Yao (Nanyang Technological University, 2024)
Models are employed to understand the behaviour of complex systems. For example, a dilated representation of a system can be a model. It is known that any arbitrary open quantum evolution process can be seen as a bipartite system-memory channel in some dilation. Then, given a bipartite channel and we are only able to access one half of the system, how would we be able to learn more about the inaccessible part, or in other words find the hidden state of the model? One way is to manipulate the half of the system that we can access, applying quantum actions such as measurements, to influence its entangled half which we cannot access. We refer to this act of applying actions onto the accessible part in order to determine the inaccessible part as quantum synchronization. This final year project aims to explore how are the correlations induced by the system’s evolution between the accessible and inaccessible subsystems related to the system’s synchroniza tion rate. The hypotheses are that I) bipartite gates that are unitarily equivalent to each other share the same synchronization rate; II) the synchronization rate is positively re lated to the amount of system-memory correlations induced by an evolution; and III) that there are optimization strategies which can drastically enhance synchronization rates, for example using the correct sequences of measurement bases. To address these hypothe ses, we employed numerical simulations via the Python package QuTiP. We measured the average synchronization rates of all two-qubit quantum gates according to a random strategy, and a gradient-based optimised strategy. The synchronization rates of each gate were characterised by an exponential fit, and compared to measures of the correlations induced by the gate. We found that the synchronization rate is highly correlated with the total mutual information of the Choi state of the gate, and that optimisation dras tically increases the synchronization rate, confirming all three of our hypotheses. This provides substantial motivation for the use of optimized procedures to learn the hidden states of quantum models. Faster synchronization will lead to improved ability to predict the behaviour of an environment and consequently enhanced decision making for arbitrary quantum control problems.