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

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.