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Fermion-Parity-Based Computation and Its Majorana-Zero-Mode Implementation.

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We introduce fermion-parity-based computation (FPBC), a measurement-based scheme that virtually increases Majorana zero modes (MZMs) for topological quantum computation. This approach simplifies MZM hardware requirements and introduces the "logical braid group".

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Area of Science:

  • Quantum Computing
  • Condensed Matter Physics

Background:

  • Majorana zero modes (MZMs) offer a path toward topologically protected quantum computation.
  • Significant challenges exist in creating multiple MZMs and performing necessary quantum transformations.

Purpose of the Study:

  • Introduce fermion-parity-based computation (FPBC) as a novel measurement-based quantum computing scheme.
  • Address hardware constraints by proposing a design for directly measurable MZM parities.
  • Identify the fermionic analog of the Clifford group, termed the "logical braid group".

Main Methods:

  • Developed a measurement-based quantum computation scheme inspired by Pauli-based computation.
  • Utilized efficient classical processing to virtually increase the number of available MZMs.
  • Designed MZM hardware enabling direct measurement of all MZM parities.

Main Results:

  • FPBC enables quantum computation with virtual MZM multiplication and without transformations for magic state inputs.
  • The proposed design overcomes hardware limitations by ensuring direct parity measurability.
  • The "logical braid group" was identified as the fermionic analog of the Clifford group.

Conclusions:

  • FPBC presents a viable and simplified approach to topological quantum computation using MZMs.
  • The developed MZM hardware design is well-suited for FPBC implementation.
  • The identification of the logical braid group advances the theoretical understanding of fermionic quantum computation.