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Unifying methods for optimal control in non-Markovian quantum systems via process tensors
Carlos Ortega-Taberner1,2, Eoin O'Neill1,2, Eoin Butler1,2
1School of Physics, Trinity College Dublin, Dublin 2, Ireland.
The Journal of Chemical Physics
|September 30, 2024
Summary
We introduce a unifying framework using matrix-product-operators to simulate complex quantum systems. This approach enables efficient optimal control for non-Markovian quantum systems, overcoming environmental dimensionality challenges.
Area of Science:
- Quantum Physics
- Quantum Control
- Computational Chemistry
Background:
- Simulating open quantum systems beyond the Markovian approximation is challenging due to large environmental dimensionality.
- Existing methods reduce environmental complexity but lack a unified framework for optimal control applications.
Purpose of the Study:
- To develop a unifying framework for simulating non-Markovian quantum systems.
- To enable and compare different simulation methods within optimal control.
- To assess the efficiency of these methods for quantum control.
Main Methods:
- Representing various non-Markovian simulation methods using a process tensor.
- Formulating the process tensor as a matrix-product-operator.
- Utilizing backpropagation for gradient computation within this framework.
Main Results:
- Demonstrated that several non-Markovian simulation techniques can be unified via a matrix-product-operator process tensor.
- Established a general scheme for computing gradients essential for optimal control.
- Provided a method to compare the efficiency of different simulation techniques based on bond dimensions.
Conclusions:
- The matrix-product-operator framework unifies diverse methods for simulating non-Markovian quantum systems.
- This framework facilitates the application of optimal control to complex quantum systems.
- Efficiency comparison of simulation methods is enabled through the analysis of process tensor bond dimensions.
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