Claim record · edition 0.1.0
Tensor-network time evolution is limited by entanglement growth, which forces the bond dimension upward as the simulated time increases.
Generic dynamics generate entanglement across cuts, and holding a fixed accuracy then requires a bond dimension that grows with it. This is the entanglement barrier.
Limits of this claim
The barrier is a property of the physics being simulated, not of a given implementation, so it is not removed by better engineering. Specific non-generic dynamics can evade it.
Supporting sources
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 →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 →