Realistic Gottesman-Kitaev-Preskill Stabilizer States Enable Universal Quantum Computation

Area of Science:

• Quantum Information Science
• Quantum Computation
• Continuous-Variable Quantum Computing

Background:

• Physical Gottesman-Kitaev-Preskill (GKP) states are essential for quantum error correction but are inherently noisy.
• Ideal GKP states require infinite energy, making practical implementation challenging.
• Noise in GKP states is typically viewed as a limitation to be corrected.

Purpose of the Study:

• To demonstrate that imperfect GKP stabilizer states can be leveraged for quantum computation.
• To show how non-Clifford gates can be implemented using linear optical elements and imperfect GKP states.
• To establish a practical framework for achieving computational universality in continuous-variable quantum computation.

Main Methods:

• Utilizing Gaussian operations on normalizable GKP states.
• Employing homodyne measurements.
• Implementing clean projection onto Pauli eigenstates within the GKP code space.
• Achieving probabilistic projection of unmeasured modes onto non-Pauli eigenstates.

Main Results:

• Demonstrated high-fidelity implementation of Clifford gates using imperfect GKP states.
• Showcased probabilistic implementation of non-Pauli eigenstates, crucial for universal computation.
• Established that imperfect GKP states, combined with Gaussian operations and homodyne measurements, enable key computational primitives.
• Provided a practical pathway towards computational universality in continuous-variable quantum computation.

Conclusions:

• Imperfect GKP stabilizer states are not merely a deficiency but a resource for quantum computation.
• Gaussian operations and homodyne measurements on normalizable GKP states facilitate universal quantum computation.
• This work presents a realistic framework for measurement-based quantum computation in continuous-variable systems.