TODO List Before paper

[MKrbm]

This issue tracks the implementation of pending enhancements in our rms project.

• [x] Implement mes method for enhanced simulation accuracy.
  • Doing in #23
• [x] Calculate optimized unitary for the Heisenberg model in various parameter regions.
• [x] Address and resolve the zero_worm bug, ensuring consistency with previous correct results.
  • This will be delt by issue
• [x] Implement test to check the simulation is correct
  • Use HPhi to validate solver_torch is correct
  • Then, use solver_torch to check worm is correct.
  • Tracked with issue

[MKrbm]

Additionaly

• [x] Device riemannian optimization for special linear group
• [x] Read into the BLBQ1D paper about what unitary matrix can remove negative sign
• [ ] Come up with better algorithm to optimizate unitary matrix. Currently it falls into local minimum too frequently

About Thesis

Introduction part (QMC)

• [x] Explain deeper about worm algorithm for HXXX model
• [x] How to observ two point correlation
• [x] About negative sign problem
• [x] How to remove negative sign?
• [x] About virtual hamiltonian

Figure

• [x] Select some parameters and run simulation on these parameters agains system size / temperature (fixing temperature / system size) #22
• [ ] Prepare table to compare worm result and analytical result
  • AKLT
  • MG
  • SS

[MKrbm]

It turned out optimized solution for BLBQ1D was not the same as analytical one, and what is worse, ground states are four-fold degenerated and will not provide average sign 1 in zero temperature.

[MKrbm]

Schedule

Todo Lists for thesis (Numerical Things)

Check the project

Presentation theis

• [x] 7. Prepare presentatino
• [x] 8. Practice with todo

Presentation FoPM

• [x] 8. Why simulation of quantum circuit is necessary ( two slides )
• [x] 9. [Explain my research quickly, what is basis rotation.]
• [x] 10. Review monte carlo method on quantum circuit.
• [x] 11. Idea to apply it.
• [x] 12. Plan of my PhD research.
• [x] 10. Pracice with todo / shiratani (if possible)