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

Yuan-Hang Zhang1,2, Zhian Jia3,4,5,6, Yu-Chun Wu4,5

  • 1Department of Physics, University of California, San Diego, CA 92093, USA.

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Summary
This summary is machine-generated.

Restricted Boltzmann machines (RBMs) can now exactly represent stabilizer code states, crucial for quantum error correction. This breakthrough enables efficient classical simulation of these complex quantum systems.

Keywords:
neural network quantum statequantum stabilizer coderestricted Boltzmann machine

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Machine Learning

Background:

  • Restricted Boltzmann machines (RBMs) are increasingly used as variational quantum states.
  • The full representational power of RBMs, especially for highly entangled states, is not yet fully understood.
  • Stabilizer code states are fundamental to quantum error correction due to their unique properties.

Purpose of the Study:

  • To analytically prove that Restricted Boltzmann machines (RBMs) can exactly and efficiently represent stabilizer code states.
  • To develop an efficient algorithm for constructing RBMs that represent specific stabilizer code states.
  • To provide new insights into the expressive power of RBMs in the context of quantum information.

Main Methods:

  • Analytical proof demonstrating the capability of RBMs to represent stabilizer code states.
  • Development of an efficient algorithm to determine RBM architecture and parameters from stabilizer generators.
  • Focus on the exact representation of highly entangled quantum states.

Main Results:

  • An analytical proof confirms that RBMs can exactly and efficiently represent stabilizer code states.
  • An efficient algorithm is presented for constructing RBMs corresponding to given stabilizer codes.
  • Demonstration of RBMs' capability to encode complex, highly entangled quantum states.

Conclusions:

  • RBMs possess significant representational power, capable of encoding stabilizer code states.
  • The findings offer a novel approach for the classical simulation of quantum error-correcting codes.
  • This work deepens the understanding of RBMs' utility in quantum information processing.