Claim record · edition 0.1.0
Tensor-network accuracy is controlled by singular-value truncation, and the discarded weight is the quantity that makes a result interpretable.
Each bond is reduced to its D largest singular values; the discarded tail is a measurable error. A result reported without its bond dimension and discarded weight cannot be assessed.
Limits of this claim
Small per-step discarded weight does not bound global error in general. Truncations accumulate, and a sweep can converge cleanly onto a state that the truncation put out of reach.
Supporting sources
review article · identifier verified
The density-matrix renormalization group in the age of matrix product states
Ulrich Schollwöck · 2010
arXiv:1008.3477
Standard reference for MPS canonical forms, SVD truncation, and the reformulation of DMRG in tensor-network language.
Source record →primary paper · identifier verified
Efficient classical simulation of slightly entangled quantum computations
Guifré Vidal · 2003
arXiv:quant-ph/0301063
Ties classical simulation cost to the entanglement carried across a cut, which is the quantity a bond dimension budgets.
Source record →