Synchronization of a non-markovian quantum system
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 an...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Final Year Project (FYP) |
| Language: | English |
| Published: |
Nanyang Technological University
2024
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/175659 |
| _version_ | 1826121548763758592 |
|---|---|
| author | Lim, Zi Yao |
| author2 | Gu Mile |
| author_facet | Gu Mile Lim, Zi Yao |
| author_sort | Lim, Zi Yao |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T05:34:21Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/175659 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:34:21Z |
| publishDate | 2024 |
| publisher | Nanyang Technological University |
| record_format | dspace |
| spelling | ntu-10356/1756592024-05-06T15:37:12Z Synchronization of a non-markovian quantum system Lim, Zi Yao Gu Mile School of Physical and Mathematical Sciences gumile@ntu.edu.sg Physics Quantum information Synchronization Non-Markovianity 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. Bachelor's degree 2024-05-02T06:51:34Z 2024-05-02T06:51:34Z 2024 Final Year Project (FYP) Lim, Z. Y. (2024). Synchronization of a non-markovian quantum system. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/175659 https://hdl.handle.net/10356/175659 en application/pdf Nanyang Technological University |
| spellingShingle | Physics Quantum information Synchronization Non-Markovianity Lim, Zi Yao Synchronization of a non-markovian quantum system |
| title | Synchronization of a non-markovian quantum system |
| title_full | Synchronization of a non-markovian quantum system |
| title_fullStr | Synchronization of a non-markovian quantum system |
| title_full_unstemmed | Synchronization of a non-markovian quantum system |
| title_short | Synchronization of a non-markovian quantum system |
| title_sort | synchronization of a non markovian quantum system |
| topic | Physics Quantum information Synchronization Non-Markovianity |
| url | https://hdl.handle.net/10356/175659 |
| work_keys_str_mv | AT limziyao synchronizationofanonmarkovianquantumsystem |