Concept record · edition 0.1.0
SVD truncation and discarded weight
Reducing a bond to the D largest singular values, discarding the remaining tail of the Schmidt spectrum.
Why it matters
Discarded weight is the error measure that makes a tensor-network computation auditable rather than merely convergent-looking.
What this does not establish
Small discarded weight at each step does not bound the global error in general, particularly when truncations accumulate across many time steps.
Claims using this concept
- tn-004 · Established resultTensor-network accuracy is controlled by singular-value truncation, and the discarded weight is the quantity that makes a result interpretable.
- tn-010 · Established resultTensor-network time evolution is limited by entanglement growth, which forces the bond dimension upward as the simulated time increases.
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 →