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The small stellated dodecahedron code and friends.

J Conrad1, C Chamberland2, N P Breuckmann3

  • 1JARA Institute for Quantum Information, RWTH Aachen University, Aachen 52056, Germany.

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|May 30, 2018
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Summary
This summary is machine-generated.

The small stellated dodecahedron quantum code offers dense information storage with 3D connectivity. It outperforms the surface code in qubit encoding efficiency for quantum computing applications.

Keywords:
fault tolerancehomological quantum codesquantum error correction

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Topological Quantum Codes

Background:

  • Topological quantum codes are crucial for fault-tolerant quantum computing.
  • The surface code is a leading candidate but has limitations in qubit density and connectivity.
  • Homological quantum codes offer alternative structures for quantum data encoding.

Purpose of the Study:

  • To explore the small stellated dodecahedron code, a distance-3 homological CSS code.
  • To assess its suitability for dense quantum information storage and 3D connectivity.
  • To compare its performance against the established distance-3 surface code.

Main Methods:

  • Developed fault-tolerant parity check circuits for the small stellated dodecahedron code.
  • Implemented a decoder for the small stellated dodecahedron code.
  • Numerically assessed the circuit-based pseudo-threshold for performance comparison.

Main Results:

  • The small stellated dodecahedron code encodes 8 logical qubits into 30 physical qubits, significantly denser than the surface code's 1 logical qubit into 9 physical qubits.
  • Its qubit placement on a small stellated dodecahedron facilitates 3D connectivity.
  • Fault-tolerant circuits and a decoder were successfully developed and assessed.

Conclusions:

  • The small stellated dodecahedron code is a promising candidate for dense quantum information storage.
  • Its 3D connectivity makes it suitable for advanced quantum hardware architectures.
  • Further research into its performance and scalability is warranted for practical quantum computing.