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Using a Self-Kerr Nonlinearity for Magic State Preparation in Grid Codes.

Jérémie Boudreault1, Ross Shillito2, Jean-Baptiste Bertrand1

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Summary
This summary is machine-generated.

We present a new method for preparing magic states crucial for fault-tolerant quantum computation using Gottesman-Kitaev-Preskill (GKP) codes. This approach utilizes a self-Kerr nonlinearity to implement a key logical gate, enhancing quantum computing capabilities.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing Architectures
  • Error Correction Codes

Background:

  • Magic state distillation and injection are vital for universal fault-tolerant quantum computation.
  • Gottesman-Kitaev-Preskill (GKP) grid codes offer a promising architecture but face challenges with non-Clifford gates.
  • Implementing non-Clifford gates is essential for achieving universal quantum computation.

Purpose of the Study:

  • To address the challenge of GKP magic state preparation.
  • To implement a logical gate sqrt[H]_{L} for square grid GKP codes using a non-Gaussian unitary.
  • To propose a practical implementation compatible with finite energy constraints.

Main Methods:

  • Studied a non-Gaussian unitary mediated by a self-Kerr nonlinearity.
  • Developed a method for GKP magic state preparation without auxiliary qubits.
  • Investigated the use of the small-Big-small error correction protocol and postselection for fidelity enhancement.

Main Results:

  • Successfully realized the logical gate sqrt[H]_{L} for square grid GKP codes.
  • Demonstrated a scheme compatible with finite energy constraints of the GKP code.
  • Showed that fidelity can be enhanced and the scheme is robust against single photon loss.

Conclusions:

  • The proposed method provides a viable route for GKP magic state preparation.
  • The self-Kerr nonlinearity offers a practical approach for implementing essential gates in GKP-based quantum computers.
  • The scheme's robustness and compatibility with error correction protocols pave the way for fault-tolerant quantum computation.