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The restricted Boltzmann machine (RBM) has seen great success as avariational quantum state, but its representational power is far lessunderstood. We analytically give the first proof that RBMs can exactly andefficiently represent stabilizer code states, a family of highly entangledstates of great importance in the field of quantum error correction. Given thestabilizer generators, we present an efficient algorithm to compute thestructure of the RBM, as well as the exact values of RBM parameters. This opensup a new perspective on the representational power of RBMs, justifying thesuccess of RBMs in representing highly entangled states, and is potentiallyuseful in the classical simulation of quantum error-correcting codes.

An Efficient Algorithmic Way to Construct Boltzmann Machine Representations for Arbitrary Stabilizer Code