English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We discuss the relations between restricted Boltzmann machine (RBM) statesand the matrix product states (MPS) for the ground states of 1D translationalinvariant stabilizer codes. A generic translational invariant and finitelyconnected RBM state can be expressed as an MPS, and the matrices of theresulting MPS are of rank 1. We dub such an MPS as an RBM-MPS. This provides anecessary condition for exactly realizing a quantum state as an RBM state, ifthe quantum state can be written as an MPS. For generic 1D stabilizer codeshaving a non-degenerate ground state with periodic boundary condition, weobtain an expression for the lower bound of their MPS bond dimension, and anupper bound for the rank of their MPS matrices. In terms of RBM, we provide analgorithm to derive the RBM for the cocycle Hamiltonians whose MPS matrices areproved to be of rank 1. Moreover, the RBM-MPS produced by our algorithm has theminimal bond dimension. A family of examples is provided to explain thealgorithm. We finally conjecture that these features hold true for all the 1Dstabilizer codes having a non-degenerate ground state with periodic boundarycondition, as long as their MPS matrices are of rank 1.

Restricted Boltzmann Machines and Matrix Product States of 1D Translational Invariant Stabilizer Codes