reducing the Trotter errors in a scalable way

[AbdullahKazi500]

Issue Description

Implementing an adaptive Trotter decomposition that dynamically adjusts the number of Trotter steps based on the complexity of the quantum circuit. This would allow for more accurate error mitigation in a scalable manner.

Developing a feature for Mitiq to intelligently select qubits for error mitigation based on their susceptibility to Trotter errors. This could involve analyzing historical data or using heuristics to identify qubits that are more prone to errors and prioritizing their mitigation. Introducing a mechanism functionality for dynamically adjusting the error threshold used in error mitigation. This could involve monitoring the performance of previous error mitigation attempts and adapting the threshold to achieve optimal reduction without sacrificing computational efficiency.

Proposed Solution

We can Create a simulation configuration where the Trotter error arising from non-commuting Hamiltonians in a multi-qubit system offset, to some extent, the Trotter error between the unitary component and the noise component of the simulated dynamics. Alternatively, we can also explore methodologies that eliminate time discretization as an intermediary step and focus on continuous-in-time mappings to transition from one dissipative dynamics to another.

Additional References

https://www.nature.com/articles/s41534-019-0192-5 @FarLab @natestemen @nathanshammah

[github-actions[bot]]

Hello @AbdullahKazi500, thank you for your interest in Mitiq! If this is a bug report, please provide screenshots and/or minimum viable code to reproduce your issue, so we can do our best to help get it fixed. If you have any questions in the meantime, you can also ask us on the Unitary Fund Discord.