RSS icon
Twitter icon
Facebook icon
Vimeo icon
YouTube icon

The limits of Matrix Product State Models

February 10, 2016 - 11:00am
Speaker: 
Miguel Navascues
Institution: 
IQOQI-Vienna

For the past twenty years, Tensor Network States (TNS) have been widely used to model the low energy sector of local Hamiltonians. Their success in doing so has led to the wide-held mantra that TNS of low bond dimension are the `only physical states' of natural condensed matter systems. However, given our experimental limitations to interact with such systems, it is not clear how this conjecture translates into any observable effect. In this Letter we give a first step in this direction by identifying particular operational features pertaining to all Matrix Product States (MPS), the class of TNS used to model non-critical one-dimensional spin chains. By exploiting two surprising structural constraints of MPS, we show how to systematically derive `bond dimension witnesses', or k-local operators whose expectation value allows us to lower bound the bond dimension of the underlying quantum state. We extend some of these results to the ansatz of Projected Entangled Pairs States (PEPS). As a bonus, we use our insight on the structure of MPS to derive some limitations on the use of MPS and PEPS for ground state energy computations

3100A Computer and Space Sciences
College Park, MD 20742

Subscribe to A Quantum Bit 

Quantum physics began with revolutionary discoveries in the early twentieth century and continues to be central in today’s physics research. Learn about quantum physics, bit by bit. From definitions to the latest research, this is your portal. Subscribe to receive regular emails from the quantum world. Previous Issues...

Sign Up Now

Sign up to receive A Quantum Bit in your email!

 Have an idea for A Quantum Bit? Submit your suggestions to jqi-comm@umd.edu