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Keyword: toric code ×Clear all

3 claims from 1 paper

1. Physics and Astronomy › Quantum many-body systems

   Unifying neural-network quantum states and correlator product states via tensor networks

   Clark · Journal of Physics A Mathematical and Theoretical · 2018

   The paper uses tensor networks to link neural-network quantum states to correlator product states, giving exact representations of several well-known states and suggesting extensions to variational Monte Carlo.

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   1. UncheckedUsing tensor-network diagrams, the paper shows that neural-network quantum states are a special kind of correlator product state with new properties.“By employing the formalism of tensor networks we show that NQS are a special form of CPS with novel properties.”
   2. UncheckedNeural-network quantum states can be seen as correlator product states made of system-wide GHZ-form correlators, linked to a canonical polyadic tensor decomposition.“Namely, that NQS are CPS built from extensively sized GHZ-form correlators, which are related to a canonical polyadic decomposition of a tensor, making them uniquely unbiased geometrically.”
   3. UncheckedBecause neural-network quantum states are a form of correlator product state, they can represent several well-known quantum states exactly, as the paper states.“Another immediate implication of the equivalence to CPS is that we are able to formulate exact NQS representations for a wide range of paradigmatic states, including superposition of weighed-graph states, the Laughlin state, toric code states, and the resonating valence bond state.”