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All-Gaussian Universality and Fault Tolerance with the Gottesman-Kitaev-Preskill Code.

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Gottesman-Kitaev-Preskill (GKP) error correction on Gaussian states generates magic states, enabling universal quantum computing with only Gaussian operations. This approach offers a path to fault-tolerant quantum computation using bosonic systems.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Error Correction

Background:

  • The Gottesman-Kitaev-Preskill (GKP) encoding is a promising method for representing qubits in bosonic systems.
  • Gaussian operations are essential for quantum error correction and computation, but achieving universality often requires non-Gaussian resources.

Purpose of the Study:

  • To investigate if GKP error correction, combined with Gaussian operations, can achieve universal quantum computation.
  • To determine if distillable magic states can be generated from Gaussian states using GKP error correction.

Main Methods:

  • Applying GKP error correction to Gaussian input states, specifically the vacuum state.
  • Analyzing the properties of the resulting states to identify the generation of magic states.
  • Assessing the conditions for fault tolerance, including squeezing levels and external noise.

Main Results:

  • GKP error correction applied to Gaussian states, such as vacuum, successfully produces distillable magic states.
  • This process achieves quantum computational universality without the need for additional non-Gaussian elements.
  • Fault tolerance is attainable with adequate squeezing and sufficiently low environmental noise.

Conclusions:

  • Gaussian operations alone, when combined with GKP error correction and a supply of encoded Pauli eigenstates, are sufficient for fault-tolerant universal quantum computing.
  • The generation of magic states from Gaussian states via GKP error correction simplifies the requirements for building universal quantum computers with bosonic systems.