Encoding an Oscillator into Many Oscillators.

Area of Science:

• Quantum Information Science
• Quantum Error Correction
• Bosonic Systems

Background:

• Gaussian errors like excitation loss and thermal noise are significant challenges in bosonic quantum information processing.
• Existing quantum error correction schemes often lose the infinite-dimensional nature of bosonic systems or cannot correct Gaussian errors due to no-go theorems.

Purpose of the Study:

• To circumvent established no-go theorems and demonstrate the correction of Gaussian errors in bosonic systems.
• To propose and analyze a novel non-Gaussian quantum error correction code for bosonic oscillators.

Main Methods:

• Utilizing Gottesman-Kitaev-Preskill (GKP) states as non-Gaussian resources.
• Developing a non-Gaussian oscillator-into-oscillators encoding scheme, specifically the GKP two-mode squeezing code.
• Applying quantum information theoretic tools to prove optimality in the weak noise limit.

Main Results:

• The proposed GKP two-mode squeezing code quadratically suppresses additive Gaussian noise in position and momentum quadratures.
• The code demonstrates near-optimal performance in the weak noise limit for two physical oscillator modes.
• The non-Gaussian encoding scheme effectively corrects excitation loss and thermal noise errors.

Conclusions:

• Gottesman-Kitaev-Preskill (GKP) states enable the correction of Gaussian errors in bosonic systems, overcoming previous theoretical barriers.
• The GKP two-mode squeezing code offers a promising pathway for robust quantum information processing with bosonic systems.
• This approach addresses dominant error sources in realistic bosonic quantum computing architectures.