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Entanglement purification for quantum computation.

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Fault-tolerant quantum computation thresholds depend only on single-system operation quality when using d-dimensional systems (8 ≤ d ≤ 32). High-fidelity logical qubits are achievable even with imperfect two-system operations.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Error Correction Codes

Background:

  • Achieving fault-tolerant quantum computation is crucial for reliable quantum information processing.
  • Current quantum error correction schemes often require high-fidelity gates and complex encoding.
  • Utilizing multi-dimensional systems offers new possibilities for qubit encoding and manipulation.

Purpose of the Study:

  • To determine the fundamental limits on fault-tolerant quantum computation thresholds.
  • To explore the role of multi-dimensional systems in quantum error correction.
  • To identify conditions under which high-quality logical qubits can be realized with imperfect physical operations.

Main Methods:

  • Theoretical analysis of fault-tolerant thresholds using d-dimensional qudits (8 ≤ d ≤ 32).
  • Development of a scheme leveraging auxiliary dimensions for entanglement creation and purification.
  • Investigation of the impact of probabilistic two-qubit gate errors on logical qubit fidelity.

Main Results:

  • Fault-tolerant thresholds are solely determined by the quality of single-system operations.
  • Physical two-qubit gate error rates up to 2/3 are tolerable for deterministic logical gates.
  • Achievable logical error rates are comparable to single-system operation error rates.

Conclusions:

  • Multi-dimensional systems significantly enhance the feasibility of fault-tolerant quantum computation.
  • The proposed scheme offers a pathway to robust quantum computation with less stringent physical gate requirements.
  • Potential physical implementations are explored, paving the way for practical applications.