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All Pure Fermionic Non-Gaussian States Are Magic States for Matchgate Computations.

M Hebenstreit1, R Jozsa2, B Kraus1

  • 1Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21A, 6020 Innsbruck, Austria.

Physical Review Letters
|September 7, 2019
PubMed
Summary
This summary is machine-generated.

Magic states are resources that enable universal quantum computation. This study shows non-Gaussian fermionic states are magic states for matchgate computations, crucial for quantum computing hardware.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Condensed Matter Physics

Background:

  • Magic states are essential resources for achieving universal quantum computation within the Clifford circuit model.
  • Matchgate (MG) circuits, while powerful for simulating non-interacting fermions, have inherent locality constraints that complicate the notion of magic states.
  • Understanding magic states in MG circuits is key to bridging theoretical quantum computation with physical implementations.

Purpose of the Study:

  • To investigate the role and definition of magic states within the framework of matchgate (MG) circuits.
  • To determine which fermionic states qualify as magic states for MG computations.
  • To explore the implications of these findings for quantum computing implementations based on fermionic systems.

Main Methods:

  • Analysis of gate-gadget constructions in the context of MG circuits.
  • Characterization of pure fermionic states, distinguishing between Gaussian and non-Gaussian states.
  • Demonstration that non-Gaussian pure fermionic states are magic states for MG computations.

Main Results:

  • Every pure fermionic state that is non-Gaussian is identified as a magic state for MG computations.
  • This characterization holds despite the locality constraints inherent in MG circuits.
  • The findings establish a direct link between non-Gaussian fermionic states and computational magic.

Conclusions:

  • Non-Gaussian pure fermionic states serve as magic states for matchgate computations.
  • This research provides a theoretical foundation for using fermionic systems in quantum computing.
  • The results are significant for implementing quantum computers that leverage the dynamics of non-interacting fermions.