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Trapped Ion Quantum Computing Quantum Simulation

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

arXiv
Authors: Yuan-Hang Zhang, Zhian Jia, Yu-Chun Wu, Guang-Can Guo

Year

2018

Paper ID

7450

Status

Preprint

Abstract Read

~2 min

Abstract Words

109

Citations

N/A

Abstract

Restricted Boltzmann machines (RBMs) have demonstrated considerable success as variational quantum states; however, their representational power remains incompletely understood. In this work, we present an analytical proof that RBMs can exactly and efficiently represent stabilizer code states (a class of highly entangled quantum states that are central to quantum error correction). Given a set of stabilizer generators, we develop an efficient algorithm to determine both the RBM architecture and the exact values of its parameters. Our findings provide new insights into the expressive power of RBMs, highlighting their capability to encode highly entangled states, and may serve as a useful tool for the classical simulation of quantum error-correcting codes.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2018 reference point for readers tracking recent quantum research.
  • Restricted Boltzmann machines (RBMs) have demonstrated considerable success as variational quantum states; however, their representational power remains incompletely understood.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1809.08631 [2] arXiv https://arxiv.org/abs/1809.08631 [3] Publisher https://arxiv.org/abs/1809.08631

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