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Neural-Network-Based Design of Approximate Gottesman-Kitaev-Preskill Code.

Yexiong Zeng1,2, Wei Qin1,3,4, Ye-Hong Chen1,2,5,6

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Neural networks optimize Gottesman-Kitaev-Preskill (GKP) encoding for quantum computing. Optimized GKP codes use fewer squeezed states, improving error correction and reducing complexity.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Error Correction

Background:

  • Gottesman-Kitaev-Preskill (GKP) encoding is crucial for continuous-variable fault-tolerant quantum computing.
  • Ideal GKP encoding is nonphysical; approximate versions are practical but complex.
  • Conventional approximate GKP states require multiple squeezed coherent states, complicating preparation.

Purpose of the Study:

  • To minimize the tradeoff between codeword complexity and error correction capability in approximate GKP states.
  • To develop a method for generating optimal approximate GKP states using neural networks.
  • To enhance the performance of GKP codes for quantum error correction.

Main Methods:

  • Utilized a neural network to generate optimal approximate GKP states.
  • Compared the performance of optimized GKP codes against conventional ones.
  • Analyzed the number of squeezed coherent states required and stabilizer operator complexity.

Main Results:

  • Optimized GKP codes outperform conventional codes.
  • Achieved effective error correction with significantly fewer squeezed coherent states.
  • Demonstrated a reduction to one-third the number of squeezed coherent states at 9.55 dB squeezing.

Conclusions:

  • Neural network optimization drastically reduces the complexity of GKP codewords.
  • Optimized GKP codes offer improved error correctability compared to conventional methods.
  • This approach paves the way for more practical fault-tolerant quantum computing.