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Analog Quantum Error Correction with Encoding a Qubit into an Oscillator.

Kosuke Fukui1, Akihisa Tomita1, Atsushi Okamoto1

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This study introduces a hybrid quantum error correction method for Gottesman-Kitaev-Preskill (GKP) qubits. By combining digital and analog information, it significantly enhances fault-tolerant quantum computation capabilities.

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Area of Science:

  • Quantum Information Science
  • Quantum Computation
  • Quantum Error Correction

Background:

  • Gottesman-Kitaev-Preskill (GKP) qubits are crucial for fault-tolerant quantum computation.
  • Current methods often discard valuable analog information from GKP qubits by treating them as discrete variables.
  • This limits the potential for improved error tolerance in quantum systems.

Purpose of the Study:

  • To propose a novel hybrid quantum error correction approach for continuous-variable quantum computation.
  • To leverage both digital and analog information from GKP qubits for enhanced error correction.
  • To demonstrate improved error correction capabilities compared to conventional methods.

Main Methods:

  • Developed a hybrid quantum error correction strategy integrating digital and analog GKP qubit information.
  • Employed a maximum-likelihood method to process combined quantum information.
  • Applied the approach to standard quantum error correction codes, including the three-qubit bit-flip code and Knill's C4/C6 code.

Main Results:

  • The hybrid approach successfully corrected double errors using the bit-flip code, surpassing the single-error correction of conventional methods.
  • Knill's C4/C6 code, when implemented with this hybrid strategy, achieved the hashing bound for the quantum capacity of Gaussian quantum channels.
  • Demonstrated the first successful integration of both digital and analog GKP qubit information for quantum error correction.

Conclusions:

  • The proposed hybrid quantum error correction method offers a significant advancement in fault-tolerant quantum computation.
  • This approach unlocks the full potential of GKP qubits by utilizing their analog information.
  • Achieving the hashing bound for Gaussian quantum channels marks a key milestone in quantum communication and computation.