TEBD truncation error

[A-tA-v]

Hi All,

I am currently working with 1D TEBD time evolution and trying to figure out how to monitor the truncation error during the simulation. My goal is to terminate the evolution once the cumulative truncation error exceeds a predefined threshold.

Some libraries, such as TeNPy, provide built-in facilities for tracking this. However, I have not found a similar mechanism in Quimb.

Has anyone encountered this issue before? I'd appreciate any suggestions, workarounds, or existing code snippets for tracking truncation errors in Quimb.

Thanks in advance!

[jcmgray]

Hi @A-tA-v, yes the TEBD could do with a bit of a revamp. The simplest answer is just to call:

nrm = tebd.pt.norm()

this squared (or not depending on your fidelity definition), gives you the fidelity estimate. 1 minus that gives you the total truncated weight, or error estimate. This of course relies on not renormalizing the singular values during evolution.

If you know the canonical center of the MPS, you can just compute the norm of that site tensor instead, which is much cheaper. TEBD I think always ends in right orthogonal form, so one could call:

nrm = tebd.pt[-1].norm()

It would be nice to add this to be automatically tracked in the TEBD class, similar to the more recent CircuitMPS class.

[A-tA-v]

Thank you so much, Johnnie.